Astronomy calculation for Sun, Moon, and planets.

# Astronomy Engine (Python)

This is the complete programming reference for the Python version of Astronomy Engine. Supports Python 3. Does NOT support Python 2. See the home page for more info.

## Quick Start

To include Astronomy Engine in your own Python program, you can use the astronomy-engine package:

pip install astronomy-engine


Alternatively, you can copy the file astronomy/astronomy.py into your project directory.

With either approach, add the following line toward the top of your program:

import astronomy


To get started quickly, here are some examples.

## Topic Index

### Position of Sun, Moon, and planets

Function Description
HelioVector Calculates body position vector with respect to the center of the Sun.
GeoVector Calculates body position vector with respect to the center of the Earth.
Equator Calculates right ascension and declination.
Ecliptic Converts J2000 equatorial coordinates to J2000 ecliptic coordinates.
EclipticLongitude Calculates ecliptic longitude of a body in the J2000 system.
Horizon Calculates horizontal coordinates (azimuth, altitude) for a given observer on the Earth.
PairLongitude Calculates the difference in apparent ecliptic longitude between two bodies, as seen from the Earth.
BaryState Calculates the barycentric position and velocity vectors of the Sun or a planet.

### Geographic helper functions

Function Description
ObserverVector Calculates a vector from the center of the Earth to an observer on the Earth's surface.
VectorObserver Calculates the geographic coordinates for a geocentric equatorial vector.

### Rise, set, and culmination times

Function Description
SearchRiseSet Finds time of rise or set for a body as seen by an observer on the Earth.
SearchAltitude Finds time when a body reaches a given altitude above or below the horizon. Useful for finding civil, nautical, or astronomical twilight.
SearchHourAngle Finds when body reaches a given hour angle for an observer on the Earth. Hour angle = 0 finds culmination, the highest point in the sky.

### Moon phases

Function Description
MoonPhase Determines the Moon's phase expressed as an ecliptic longitude.
SearchMoonPhase Finds the next instance of the Moon reaching a specific ecliptic longitude separation from the Sun.
SearchMoonQuarter Finds the first quarter moon phase after a given date and time.
NextMoonQuarter Finds the next quarter moon phase after a previous one that has been found.

### Eclipses and Transits

Function Description
SearchLunarEclipse Search for the first lunar eclipse after a given date.
NextLunarEclipse Continue searching for more lunar eclipses.
SearchGlobalSolarEclipse Search for the first solar eclipse after a given date that is visible anywhere on the Earth.
NextGlobalSolarEclipse Continue searching for solar eclipses visible anywhere on the Earth.
SearchLocalSolarEclipse Search for the first solar eclipse after a given date that is visible at a particular location on the Earth.
NextLocalSolarEclipse Continue searching for solar eclipses visible at a particular location on the Earth.
SearchTransit Search for the next transit of Mercury or Venus.
NextTransit Continue searching for transits of Mercury or Venus.

### Lunar perigee and apogee

Function Description
SearchLunarApsis Finds the next perigee or apogee of the Moon after a specified date.
NextLunarApsis Given an already-found apsis, finds the next perigee or apogee of the Moon.

### Planet perihelion and aphelion

Function Description
SearchPlanetApsis Finds the next perihelion or aphelion of a planet after a specified date.
NextPlanetApsis Given an already-found apsis, finds the next perihelion or aphelion of a planet.

### Visual magnitude and elongation

Function Description
Illumination Calculates visual magnitude and phase angle of bodies as seen from the Earth.
SearchPeakMagnitude Searches for the date and time Venus will next appear brightest as seen from the Earth.
AngleFromSun Returns full angle seen from Earth between body and Sun.
Elongation Calculates ecliptic longitude angle between a body and the Sun, as seen from the Earth.
SearchMaxElongation Searches for the next maximum elongation event for Mercury or Venus that occurs after the given date.

### Oppositions and conjunctions

Function Description
SearchRelativeLongitude Finds oppositions and conjunctions of planets.

### Equinoxes, solstices, and apparent solar motion

Function Description
SearchSunLongitude Finds the next time the Sun reaches a specified apparent ecliptic longitude in the true equator of date system.
Seasons Finds the equinoxes and solstices for a given calendar year.
SunPosition Calculates the Sun's apparent ecliptic coordinates as seen from the Earth.

### Coordinate transforms

The following five orientation systems are supported. Astronomy Engine can convert a vector from any of these orientations to any of the others. It also allows converting from a vector to spherical (angular) coordinates and back, within a given orientation. Note the 3-letter codes for each of the orientation systems; these are used in function and type names.

• EQJ = Equatorial J2000: Uses the Earth's equator on January 1, 2000, at noon UTC.
• EQD = Equator of-date: Uses the Earth's equator on a given date and time, adjusted for precession and nutation.
• ECL = Ecliptic: Uses the mean plane of the Earth's orbit around the Sun. The x-axis is referenced against the J2000 equinox.
• HOR = Horizontal: Uses the viewpoint of an observer at a specific location on the Earth at a given date and time.
• GAL = Galactic: Based on the IAU 1958 definition of galactic coordinates.
Function Description
RotateVector Applies a rotation matrix to a vector, yielding a vector in another orientation system.
InverseRotation Given a rotation matrix, finds the inverse rotation matrix that does the opposite transformation.
CombineRotation Given two rotation matrices, returns a rotation matrix that combines them into a net transformation.
IdentityMatrix Returns a 3x3 identity matrix, which can be used to form other rotation matrices.
Pivot Transforms a rotation matrix by pivoting it around a given axis by a given angle.
VectorFromSphere Converts spherical coordinates to Cartesian coordinates.
SphereFromVector Converts Cartesian coordinates to spherical coordinates.
EquatorFromVector Given an equatorial vector, calculates equatorial angular coordinates.
VectorFromHorizon Given apparent angular horizontal coordinates, calculates horizontal vector.
HorizonFromVector Given a vector in horizontal orientation, calculates horizontal angular coordinates.
Rotation_EQD_EQJ Calculates a rotation matrix from equatorial of-date (EQD) to equatorial J2000 (EQJ).
Rotation_EQD_ECL Calculates a rotation matrix from equatorial of-date (EQD) to ecliptic J2000 (ECL).
Rotation_EQD_HOR Calculates a rotation matrix from equatorial of-date (EQD) to horizontal (HOR).
Rotation_EQJ_EQD Calculates a rotation matrix from equatorial J2000 (EQJ) to equatorial of-date (EQD).
Rotation_EQJ_ECL Calculates a rotation matrix from equatorial J2000 (EQJ) to ecliptic J2000 (ECL).
Rotation_EQJ_HOR Calculates a rotation matrix from equatorial J2000 (EQJ) to horizontal (HOR).
Rotation_ECL_EQD Calculates a rotation matrix from ecliptic J2000 (ECL) to equatorial of-date (EQD).
Rotation_ECL_EQJ Calculates a rotation matrix from ecliptic J2000 (ECL) to equatorial J2000 (EQJ).
Rotation_ECL_HOR Calculates a rotation matrix from ecliptic J2000 (ECL) to horizontal (HOR).
Rotation_HOR_EQD Calculates a rotation matrix from horizontal (HOR) to equatorial of-date (EQD).
Rotation_HOR_EQJ Calculates a rotation matrix from horizontal (HOR) to J2000 equatorial (EQJ).
Rotation_HOR_ECL Calculates a rotation matrix from horizontal (HOR) to ecliptic J2000 (ECL).
Rotation_EQJ_GAL Calculates a rotation matrix from equatorial J2000 (EQJ) to galactic (GAL).
Rotation_GAL_EQJ Calculates a rotation matrix from galactic (GAL) to equatorial J2000 (EQJ).

### Gravitational simulation of small bodies

Astronomy Engine provides a GravitySimulator class that allows you to model the trajectories of one or more small bodies like asteroids, comets, or coasting spacecraft. If you know an initial position vector and velocity vector for a small body, the gravity simulator can incrementally simulate the pull of gravity on it from the Sun and planets, to calculate its movement through the Solar System.

## Constants

The following numeric constants are exported by the astronomy module. They may be of use for unit conversion. Note: For the other supported programming languages, Astronomy Engine defines helper constants DEG2RAD and RAD2DEG to convert between angular degrees and radians. However, because Python defines the angular conversion functions math.degrees() and math.radians(), they are not needed in the Python version.

### CALLISTO_RADIUS_KM = 2410.3

The mean radius of Jupiter's moon Callisto, expressed in kilometers.

### C_AUDAY = 173.1446326846693

The speed of light expressed in astronomical units per day.

### EUROPA_RADIUS_KM = 1560.8

The mean radius of Jupiter's moon Europa, expressed in kilometers.

### GANYMEDE_RADIUS_KM = 2631.2

The mean radius of Jupiter's moon Ganymede, expressed in kilometers.

### IO_RADIUS_KM = 1821.6

The mean radius of Jupiter's moon Io, expressed in kilometers.

### JUPITER_EQUATORIAL_RADIUS_KM = 71492.0

The equatorial radius of Jupiter, expressed in kilometers.

### JUPITER_MEAN_RADIUS_KM = 69911.0

The volumetric mean radius of Jupiter, expressed in kilometers.

### JUPITER_POLAR_RADIUS_KM = 66854.0

The polar radius of Jupiter, expressed in kilometers.

### KM_PER_AU = 1.4959787069098932e+8

The number of kilometers per astronomical unit.

## Classes

### class Apsis

An event where a satellite is closest to or farthest from the body it orbits.

For the Moon orbiting the Earth, or a planet orbiting the Sun, an apsis is an event where the orbiting body reaches its closest or farthest point from the primary body. The closest approach is called pericenter and the farthest point is apocenter. More specific terminology is common for particular orbiting bodies. The Moon's closest approach to the Earth is called perigee and its furthest point is called apogee. The closest approach of a planet to the Sun is called perihelion and the furthest point is called aphelion. This data structure is returned by SearchLunarApsis and NextLunarApsis to iterate through consecutive alternating perigees and apogees.

Type Attribute Description
Time time The date and time of the apsis.
ApsisKind kind Whether this is a pericenter or apocenter event.
float dist_au The distance between the centers of the bodies in astronomical units.
float dist_km The distance between the centers of the bodies in kilometers.

### class AxisInfo

Information about a body's rotation axis at a given time.

This structure is returned by RotationAxis to report the orientation of a body's rotation axis at a given moment in time. The axis is specified by the direction in space that the body's north pole points, using angular equatorial coordinates in the J2000 system (EQJ). Thus ra is the right ascension, and dec is the declination, of the body's north pole vector at the given moment in time. The north pole of a body is defined as the pole that lies on the north side of the Solar System's invariable plane, regardless of the body's direction of rotation. The spin field indicates the angular position of a prime meridian arbitrarily recommended for the body by the International Astronomical Union (IAU). The fields ra, dec, and spin correspond to the variables α0, δ0, and W, respectively, from Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2015. The field north is a unit vector pointing in the direction of the body's north pole. It is expressed in the equatorial J2000 system (EQJ).

Type Attribute Description
float ra The J2000 right ascension of the body's north pole direction, in sidereal hours.
float dec The J2000 declination of the body's north pole direction, in degrees.
float spin Rotation angle of the body's prime meridian, in degrees.
Vector north A J2000 dimensionless unit vector pointing in the direction of the body's north pole.

### class ConstellationInfo

Reports the constellation that a given celestial point lies within.

The Constellation function returns a ConstellationInfo object to report which constellation corresponds with a given point in the sky. Constellations are defined with respect to the B1875 equatorial system per IAU standard. Although the Constellation function requires J2000 equatorial coordinates as input, the returned object contains converted B1875 coordinates for reference.

Type Attribute Description
string symbol 3-character mnemonic symbol for the constellation, e.g. "Ori".
string name Full name of constellation, e.g. "Orion".
float ra1875 Right ascension expressed in B1875 coordinates.
float dec1875 Declination expressed in B1875 coordinates.

### class EclipseEvent

Holds a time and the observed altitude of the Sun at that time.

When reporting a solar eclipse observed at a specific location on the Earth (a "local" solar eclipse), a series of events occur. In addition to the time of each event, it is important to know the altitude of the Sun, because each event may be invisible to the observer if the Sun is below the horizon. If altitude is negative, the event is theoretical only; it would be visible if the Earth were transparent, but the observer cannot actually see it. If altitude is positive but less than a few degrees, visibility will be impaired by atmospheric interference (sunrise or sunset conditions).

Type Attribute Description
Time time The date and time of the event.
float altitude The angular altitude of the center of the Sun above/below the horizon, at time, corrected for atmospheric refraction and expressed in degrees.

### class EclipticCoordinates

Ecliptic angular and Cartesian coordinates.

Coordinates of a celestial body as seen from the center of the Sun (heliocentric), oriented with respect to the plane of the Earth's orbit around the Sun (the ecliptic).

Type Attribute Description
Vector vec Ecliptic cartesian vector with the following components: x: in the direction of the equinox along the ecliptic plane. y: Cartesian y-coordinate: in the ecliptic plane 90 degrees prograde from the equinox. z: Cartesian z-coordinate: perpendicular to the ecliptic plane. Positive is north.
float elat Latitude in degrees north (positive) or south (negative) of the ecliptic plane.
float elon Longitude in degrees around the ecliptic plane prograde from the equinox.

### class ElongationEvent

Contains information about the visibility of a celestial body at a given date and time.

See the Elongation function for more detailed information about the members of this class. See also SearchMaxElongation for how to search for maximum elongation events.

Type Attribute Description
Time time The date and time of the observation.
Visibility visibility Whether the body is best seen in the morning or the evening.
float elongation The angle in degrees between the body and the Sun, as seen from the Earth.
float ecliptic_separation The difference between the ecliptic longitudes of the body and the Sun, as seen from the Earth.

### class Equatorial

Equatorial angular coordinates

Coordinates of a celestial body as seen from the Earth. Can be geocentric or topocentric, depending on context. The coordinates are oriented with respect to the Earth's equator projected onto the sky.

Type Attribute Description
float ra Right ascension in sidereal hours.
float dec Declination in degrees.
float dist Distance to the celestial body in AU.
Vector vec The equatorial coordinates in cartesian form, using AU distance units. x = direction of the March equinox, y = direction of the June solstice, z = north.

### class GlobalSolarEclipseInfo

Reports the time and geographic location of the peak of a solar eclipse.

Returned by SearchGlobalSolarEclipse or NextGlobalSolarEclipse to report information about a solar eclipse event. The eclipse is classified as partial, annular, or total, depending on the maximum amount of the Sun's disc obscured, as seen at the peak location on the surface of the Earth. The kind field thus holds EclipseKind.Partial, EclipseKind.Annular, or EclipseKind.Total. A total eclipse is when the peak observer sees the Sun completely blocked by the Moon. An annular eclipse is like a total eclipse, but the Moon is too far from the Earth's surface to completely block the Sun; instead, the Sun takes on a ring-shaped appearance. A partial eclipse is when the Moon blocks part of the Sun's disc, but nobody on the Earth observes either a total or annular eclipse. If kind is EclipseKind.Total or EclipseKind.Annular, the latitude and longitude fields give the geographic coordinates of the center of the Moon's shadow projected onto the daytime side of the Earth at the instant of the eclipse's peak. If kind has any other value, latitude and longitude are undefined and should not be used.

Type Attribute Description
EclipseKind kind The type of solar eclipse: EclipseKind.Partial, EclipseKind.Annular, or EclipseKind.Total.
Time peak The date and time when the solar eclipse is darkest. This is the instant when the axis of the Moon's shadow cone passes closest to the Earth's center.
float distance The distance between the Sun/Moon shadow axis and the center of the Earth, in kilometers.
float latitude The geographic latitude at the center of the peak eclipse shadow.
float longitude The geographic longitude at the center of the peak eclipse shadow.

### class GravitySimulator

A simulation of zero or more small bodies moving through the Solar System.

This class calculates the movement of arbitrary small bodies, such as asteroids or comets, that move through the Solar System. It does so by calculating the gravitational forces on the bodies from the Sun and planets. The user of this class supplies a list of initial positions and velocities for the small bodies. Then the class can update the positions and velocities over small time steps.

### GravitySimulator.init(self, originBody, time, bodyStates)

Creates a gravity simulation object.

Type Parameter Description
Body originBody Specifies the origin of the reference frame. All position vectors and velocity vectors will use originBody as the origin of the coordinate system. This origin applies to all the input vectors provided in the bodyStates parameter of this function, along with all output vectors returned by GravitySimulator.Update. Most callers will want to provide one of the following: Body.Sun for heliocentric coordinates, Body.SSB for solar system barycentric coordinates, or Body.Earth for geocentric coordinates. Note that the gravity simulator does not correct for light travel time; all state vectors are tied to a Newtonian "instantaneous" time.
Time time The initial time at which to start the simulation.
StateVector[] bodyStates An array of zero or more initial state vectors (positions and velocities) of the small bodies to be simulated. The caller must know the positions and velocities of the small bodies at an initial moment in time. Their positions and velocities are expressed with respect to originBody, using equatorial J2000 orientation (EQJ). Positions are expressed in astronomical units (AU). Velocities are expressed in AU/day. All the times embedded within the state vectors must exactly match time, or this constructor will throw an exception.

### GravitySimulator.OriginBody(self)

Returns: Body

### GravitySimulator.SolarSystemBodyState(self, body)

Get the position and velocity of a Solar System body included in the simulation.

In order to simulate the movement of small bodies through the Solar System, the simulator needs to calculate the state vectors for the Sun and planets. If an application wants to know the positions of one or more of the planets in addition to the small bodies, this function provides a way to obtain their state vectors. This is provided for the sake of efficiency, to avoid redundant calculations. The state vector is returned relative to the position and velocity of the originBody parameter that was passed to this object's constructor.

Type Parameter Description
Body body The Sun, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, or Neptune.

Returns: StateVector The state vector of the requested Solar System body.

### GravitySimulator.Swap(self)

Exchange the current time step with the previous time step.

Sometimes it is helpful to "explore" various times near a given simulation time step, while repeatedly returning to the original time step. For example, when backdating a position for light travel time, the caller may wish to repeatedly try different amounts of backdating. When the backdating solver has converged, the caller wants to leave the simulation in its original state. This function allows a single "undo" of a simulation, and does so very efficiently. Usually this function will be called immediately after a matching call to GravitySimulator.Update. It has the effect of rolling back the most recent update. If called twice in a row, it reverts the swap and thus has no net effect. The constructor initializes the current state and previous state to be identical. Both states represent the time parameter that was passed into the constructor. Therefore, Swap will have no effect from the caller's point of view when passed a simulator that has not yet been updated by a call to GravitySimulator.Update.

### GravitySimulator.Time(self)

The time represented by the current step of the gravity simulation.

Returns: Time

### GravitySimulator.Update(self, time)

Advances the gravity simulation by a small time step.

Updates the simulation of the user-supplied small bodies to the time indicated by the time parameter. Returns an array of state vectors for the simulated bodies. The array is in the same order as the original array that was used to construct this simulator object. The positions and velocities in the returned array are referenced to the originBody that was used to construct this simulator.

Type Parameter Description
Time time A time that is a small increment away from the current simulation time. It is up to the developer to figure out an appropriate time increment. Depending on the trajectories, a smaller or larger increment may be needed for the desired accuracy. Some experimentation may be needed. Generally, bodies that stay in the outer Solar System and move slowly can use larger time steps. Bodies that pass into the inner Solar System and move faster will need a smaller time step to maintain accuracy. The time value may be after or before the current simulation time to move forward or backward in time.

Returns: StateVector[] An array of state vectors, one for each small body.

### class HorizontalCoordinates

Coordinates of a celestial body as seen by a topocentric observer.

Contains horizontal and equatorial coordinates as seen by an observer on or near the surface of the Earth (a topocentric observer). All coordinates are optionally corrected for atmospheric refraction.

Type Attribute Description
float azimuth The compass direction laterally around the observer's horizon, measured in degrees. North is 0 degrees, east is 90 degrees, south is 180 degrees, etc.
float altitude The angle in degrees above (positive) or below (negative) the observer's horizon.
float ra The right ascension in sidereal hours.
float dec The declination in degrees.

### class HourAngleEvent

Information about a celestial body crossing a specific hour angle.

Returned by the function SearchHourAngle to report information about a celestial body crossing a certain hour angle as seen by a specified topocentric observer.

Type Attribute Description
Time time The date and time when the body crosses the specified hour angle.
HorizontalCoordinates hor Apparent coordinates of the body at the time it crosses the specified hour angle.

### class IlluminationInfo

Information about the brightness and illuminated shape of a celestial body.

Returned by functions Illumination and SearchPeakMagnitude to report the visual magnitude and illuminated fraction of a celestial body at a given date and time.

Type Attribute Description
Time time The date and time of the observation.
float mag The visual magnitude of the body. Smaller values are brighter.
float phase_angle The angle in degrees between the Sun and the Earth, as seen from the body. Indicates the body's phase as seen from the Earth.
float phase_fraction A value in the range [0.0, 1.0] indicating what fraction of the body's apparent disc is illuminated, as seen from the Earth.
float helio_dist The distance between the Sun and the body at the observation time, in AU.
dist geo_dist The distance between the Earth and the both at the observation time, in AU.
Vector hc The body's heliocentric vector.
Vector gc The body's geocentric vector.
float ring_tilt For Saturn, the tilt angle in degrees of its rings as seen from Earth. When the ring_tilt is very close to 0, it means the rings are edge-on as seen from observers on the Earth, and are thus very difficult to see. For bodies other than Saturn, ring_tilt is None.

### class JupiterMoonsInfo

Holds the positions and velocities of Jupiter's major 4 moons.

The JupiterMoons function returns an object of this type to report position and velocity vectors for Jupiter's largest 4 moons Io, Europa, Ganymede, and Callisto. Each position vector is relative to the center of Jupiter. Both position and velocity are oriented in the EQJ system (that is, using Earth's equator at the J2000 epoch). The positions are expressed in astronomical units (AU), and the velocities in AU/day.

Type Attribute Description
StateVector io The position and velocity of Jupiter's moon Io.
StateVector europa The position and velocity of Jupiter's moon Europa.
StateVector ganymede The position and velocity of Jupiter's moon Ganymede.
StateVector callisto The position and velocity of Jupiter's moon Callisto.

### class LibrationInfo

Lunar libration angles, returned by Libration.

Contains lunar libration angles and lunar position information for a given moment in time. See Libration for more details.

Type Attribute Description
float elat Sub-Earth libration ecliptic latitude angle, in degrees.
float elon Sub-Earth libration ecliptic longitude angle, in degrees.
float mlat Moon's geocentric ecliptic latitude, in degrees.
float mlon Moon's geocentric ecliptic longitude, in degrees.
float dist_km Distance between the centers of the Earth and Moon in kilometers.
float diam_deg The apparent angular diameter of the Moon as seen from the center of the Earth.

### class LocalSolarEclipseInfo

Information about a solar eclipse as seen by an observer at a given time and geographic location.

Returned by SearchLocalSolarEclipse or NextLocalSolarEclipse to report information about a solar eclipse as seen at a given geographic location. When a solar eclipse is found, it is classified as partial, annular, or total. The kind field thus holds EclipseKind.Partial, EclipseKind.Annular, or EclipseKind.Total. A partial solar eclipse is when the Moon does not line up directly enough with the Sun to completely block the Sun's light from reaching the observer. An annular eclipse occurs when the Moon's disc is completely visible against the Sun but the Moon is too far away to completely block the Sun's light; this leaves the Sun with a ring-like appearance. A total eclipse occurs when the Moon is close enough to the Earth and aligned with the Sun just right to completely block all sunlight from reaching the observer. There are 5 "event" fields, each of which contains a time and a solar altitude. Field peak holds the date and time of the center of the eclipse, when it is at its peak. The fields partial_begin and partial_end are always set, and indicate when the eclipse begins/ends. If the eclipse reaches totality or becomes annular, total_begin and total_end indicate when the total/annular phase begins/ends. When an event field is valid, the caller must also check its altitude field to see whether the Sun is above the horizon at the time indicated by the time field. See EclipseEvent for more information.

Type Attribute Description
EclipseKind kind The type of solar eclipse: EclipseKind.Partial, EclipseKind.Annular, or EclipseKind.Total.
EclipseEvent partial_begin The time and Sun altitude at the beginning of the eclipse.
EclipseEvent total_begin If this is an annular or a total eclipse, the time and Sun altitude when annular/total phase begins; otherwise None.
EclipseEvent peak The time and Sun altitude when the eclipse reaches its peak.
EclipseEvent total_end If this is an annular or a total eclipse, the time and Sun altitude when annular/total phase ends; otherwise None.
EclipseEvent partial_end The time and Sun altitude at the end of the eclipse.

### class LunarEclipseInfo

Returns information about a lunar eclipse.

Returned by SearchLunarEclipse or NextLunarEclipse to report information about a lunar eclipse event. When a lunar eclipse is found, it is classified as penumbral, partial, or total. Penumbral eclipses are difficult to observe, because the Moon is only slightly dimmed by the Earth's penumbra; no part of the Moon touches the Earth's umbra. Partial eclipses occur when part, but not all, of the Moon touches the Earth's umbra. Total eclipses occur when the entire Moon passes into the Earth's umbra. The kind field thus holds one of the values EclipseKind.Penumbral, EclipseKind.Partial, or EclipseKind.Total, depending on the kind of lunar eclipse found. Field peak holds the date and time of the peak of the eclipse, when it is at its peak. Fields sd_penum, sd_partial, and sd_total hold the semi-duration of each phase of the eclipse, which is half of the amount of time the eclipse spends in each phase (expressed in minutes), or 0 if the eclipse never reaches that phase. By converting from minutes to days, and subtracting/adding with peak, the caller may determine the date and time of the beginning/end of each eclipse phase.

Type Attribute Description
EclipseKind kind The type of lunar eclipse found.
Time peak The time of the eclipse at its peak.
float sd_penum The semi-duration of the penumbral phase in minutes.
float sd_partial The semi-duration of the penumbral phase in minutes, or 0.0 if none.
float sd_total The semi-duration of the penumbral phase in minutes, or 0.0 if none.

### class MoonQuarter

A lunar quarter event along with its date and time.

An object of this type represents one of the four major lunar phases that appear on calendars: new moon, first quarter, full moon, or third quarter. Along with the quarter attribute that specifies the type of quarter, it contains a time field that indicates when the lunar quarter event happens.

Type Attribute Description
int quarter 0=new moon, 1=first quarter, 2=full moon, 3=third quarter.
Time time The date and time of the lunar quarter.

### class NodeEventInfo

Information about an ascending or descending node of a body.

This object is returned by SearchMoonNode and NextMoonNode to report information about the center of the Moon passing through the ecliptic plane.

Type Attribute Description
NodeEventKind kind Whether the node is ascending (south to north) or descending (north to south).
Time time The time when the body passes through the ecliptic plane.

### class Observer

Represents the geographic location of an observer on the surface of the Earth.

Type Parameter Description
float latitude Geographic latitude in degrees north of the equator.
float longitude Geographic longitude in degrees east of the prime meridian at Greenwich, England.
float height Elevation above sea level in meters.

### class PositionFunction

A function for which to solve a light-travel time problem.

This abstract class defines the contract for wrapping a position vector as a function of time. A class derived from PositionFunction must define a Position method that returns a position vector for a given time. The function CorrectLightTravel solves a generalized problem of deducing how far in the past light must have left a target object to be seen by an observer at a specified time. It is passed an instance of PositionFunction that expresses a relative position vector function.

### PositionFunction.Position(self, time)

Returns a relative position vector for a given time.

Type Parameter Description
Time time The time at which to evaluate a relative position vector.

Returns: Vector

### class RotationMatrix

Contains a rotation matrix that can be used to transform one coordinate system into another.

Type Parameter Description
float[3][3] rot A normalized 3x3 rotation matrix.

### class SeasonInfo

The dates and times of changes of season for a given calendar year.

Call Seasons to calculate this data structure for a given year.

Type Attribute Description
Time mar_equinox The date and time of the March equinox for the specified year.
Time jun_solstice The date and time of the June solstice for the specified year.
Time sep_equinox The date and time of the September equinox for the specified year.
Time dec_solstice The date and time of the December solstice for the specified year.

### class Spherical

Holds spherical coordinates: latitude, longitude, distance.

Type Parameter Description
float lat The latitude angle: -90..+90 degrees.
float lon The longitude angle: 0..360 degrees.
float dist Distance in AU.

### class StateVector

A combination of a position vector, a velocity vector, and a time.

The position (x, y, z) is measured in astronomical units (AU). The velocity (vx, vy, vz) is measured in AU/day. The coordinate system varies and depends on context. The state vector also includes a time stamp.

Type Attribute Description
float x The x-coordinate of the position, measured in AU.
float y The y-coordinate of the position, measured in AU.
float z The z-coordinate of the position, measured in AU.
float vx The x-component of the velocity, measured in AU/day.
float vy The y-component of the velocity, measured in AU/day.
float vz The z-component of the velocity, measured in AU/day.
Time t The date and time at which the position and velocity vectors are valid.

### class Time

Represents a date and time used for performing astronomy calculations.

All calculations performed by Astronomy Engine are based on dates and times represented by Time objects.

Type Parameter Description
float ut UT1/UTC number of days since noon on January 1, 2000. See the ut attribute of this class for more details.
Type Attribute Description
float ut The floating point number of days of Universal Time since noon UTC January 1, 2000. Astronomy Engine approximates UTC and UT1 as being the same thing, although they are not exactly equivalent; UTC and UT1 can disagree by up to 0.9 seconds. This approximation is sufficient for the accuracy requirements of Astronomy Engine. Universal Time Coordinate (UTC) is the international standard for legal and civil timekeeping and replaces the older Greenwich Mean Time (GMT) standard. UTC is kept in sync with unpredictable observed changes in the Earth's rotation by occasionally adding leap seconds as needed. UT1 is an idealized time scale based on observed rotation of the Earth, which gradually slows down in an unpredictable way over time, due to tidal drag by the Moon and Sun, large scale weather events like hurricanes, and internal seismic and convection effects. Conceptually, UT1 drifts from atomic time continuously and erratically, whereas UTC is adjusted by a scheduled whole number of leap seconds as needed. The value in ut is appropriate for any calculation involving the Earth's rotation, such as calculating rise/set times, culumination, and anything involving apparent sidereal time. Before the era of atomic timekeeping, days based on the Earth's rotation were often known as mean solar days.
float tt Terrestrial Time days since noon on January 1, 2000. Terrestrial Time is an atomic time scale defined as a number of days since noon on January 1, 2000. In this system, days are not based on Earth rotations, but instead by the number of elapsed SI seconds divided by 86400. Unlike ut, tt increases uniformly without adjustments for changes in the Earth's rotation. The value in tt is used for calculations of movements not involving the Earth's rotation, such as the orbits of planets around the Sun, or the Moon around the Earth. Historically, Terrestrial Time has also been known by the term Ephemeris Time (ET).

#### member functions

Calculates the sum or difference of a Time with a specified real-valued number of days.

Sometimes we need to adjust a given Time value by a certain amount of time. This function adds the given real number of days in days to the date and time in the calling object. More precisely, the result's Universal Time field ut is exactly adjusted by days and the Terrestrial Time field tt is adjusted for the resulting UTC date and time, using a best-fit piecewise polynomial model devised by Espenak and Meeus. The value of the calling object is not modified. This function creates a brand new Time object and returns it.

Type Parameter Description
float days A floating point number of days by which to adjust time. May be negative, 0, or positive.

Returns: Time

### Time.FromTerrestrialTime(tt)

Creates a Time object from a Terrestrial Time day value.

Type Parameter Description
float tt The number of days after the J2000 epoch.

Returns: Time

### Time.Make(year, month, day, hour, minute, second)

Creates a Time object from a UTC calendar date and time.

Type Parameter Description
int year The UTC 4-digit year value, e.g. 2019.
int month The UTC month in the range 1..12.
int day The UTC day of the month, in the range 1..31.
int hour The UTC hour, in the range 0..23.
int minute The UTC minute, in the range 0..59.
float second The real-valued UTC second, in the range [0, 60).

Returns: Time

### Time.Now()

Returns the computer's current date and time in the form of a Time object.

Uses the computer's system clock to find the current UTC date and time. Converts that date and time to a Time value and returns the result. Callers can pass this value to other Astronomy Engine functions to calculate current observational conditions.

Returns: Time

### Time.Parse(text)

Creates a Time object from a string of the form 'yyyy-mm-ddThh:mm:ss.sssZ'

Parses a UTC date and time from a string and returns a Time object. Permits a subset of ISO 8601 format. The year, month, and day are required. Hours, minutes, seconds, and fractions of a second are optional. If time is specified, there must be a 'T' between the date and the time and a 'Z' at the end of the time.

Type Parameter Description
string text A string of the following formats: yyyy-mm-dd yyyy-mm-ddThh:mmZ yyyy-mm-ddThh:mm:ssZ yyyy-mm-ddThh:mm:ss.sssZ

Returns: Time

### Time.Utc(self)

Returns the UTC date and time as a datetime object.

Uses the standard datetime class to represent the date and time in this Time object.

Returns: datetime

### class TransitInfo

Information about a transit of Mercury or Venus, as seen from the Earth.

Returned by SearchTransit or NextTransit to report information about a transit of Mercury or Venus. A transit is when Mercury or Venus passes between the Sun and Earth so that the other planet is seen in silhouette against the Sun. The calculations are performed from the point of view of a geocentric observer.

Type Attribute Description
Time start The date and time at the beginning of the transit. This is the moment the planet first becomes visible against the Sun in its background.
Time peak When the planet is most aligned with the Sun, as seen from the Earth.
Time finish The date and time at the end of the transit. This is the moment the planet is last seen against the Sun in its background.
float separation The minimum angular separation, in arcminutes, between the centers of the Sun and the planet. This angle pertains to the time stored in peak.

### class Vector

A Cartesian vector with 3 space coordinates and 1 time coordinate.

The vector's space coordinates are measured in astronomical units (AU). The coordinate system varies and depends on context. The vector also includes a time stamp.

Type Attribute Description
float x The x-coordinate of the vector, measured in AU.
float y The y-coordinate of the vector, measured in AU.
float z The z-coordinate of the vector, measured in AU.
Time t The date and time at which the coordinate is valid.

### Vector.Length(self)

Returns the length of the vector in AU.

### Vector.format(self, coord_format)

Returns a custom format string representation of the vector.

## Enumerated Types

### enum ApsisKind

Represents whether a satellite is at a closest or farthest point in its orbit.

An apsis is a point in a satellite's orbit that is closest to, or farthest from, the body it orbits (its primary). ApsisKind is an enumerated type that indicates which of these two cases applies to a particular apsis event.

Value Description
Pericenter The satellite is at its closest point to its primary.
Apocenter The satellite is at its farthest point from its primary.
Invalid A placeholder for an undefined, unknown, or invalid apsis.

### enum Body

The celestial bodies supported by Astronomy Engine calculations.

Value Description
Invalid An unknown, invalid, or undefined celestial body.
Mercury The planet Mercury.
Venus The planet Venus.
Earth The planet Earth.
Mars The planet Mars.
Jupiter The planet Jupiter.
Saturn The planet Saturn.
Uranus The planet Uranus.
Neptune The planet Neptune.
Pluto The planet Pluto.
Sun The Sun.
Moon The Earth's moon.
EMB The Earth/Moon Barycenter.
SSB The Solar System Barycenter.

### enum Direction

Indicates whether a body is rising above or setting below the horizon.

Specifies the direction of a rising or setting event for a body. For example, Direction.Rise is used to find sunrise times, and Direction.Set is used to find sunset times.

Value Description
Rise First appearance of a body as it rises above the horizon.
Set Last appearance of a body as it sinks below the horizon.

### enum EclipseKind

The different kinds of lunar/solar eclipses.

Value Description
Invalid No eclipse found.
Penumbral A penumbral lunar eclipse. (Never used for a solar eclipse.)
Partial A partial lunar/solar eclipse.
Annular An annular solar eclipse. (Never used for a lunar eclipse.)
Total A total lunar/solar eclipse.

### enum NodeEventKind

Indicates whether a crossing through the ecliptic plane is ascending or descending.

Value Description
Invalid A placeholder for an invalid or undefined node.
Ascending indicates a body passing through the ecliptic plane from south to north.
Descending indicates a body passing through the ecliptic plane from north to south.

### enum Refraction

Selects if/how to correct for atmospheric refraction.

Some functions allow enabling or disabling atmospheric refraction for the calculated apparent position of a celestial body as seen by an observer on the surface of the Earth.

Value Description
Airless No atmospheric refraction correction.
Normal Recommended correction for standard atmospheric refraction.
JplHorizons Used only for compatibility testing with JPL Horizons online tool.

### enum Visibility

Indicates whether a body (especially Mercury or Venus) is best seen in the morning or evening.

Value Description
Morning The body is best visible in the morning, before sunrise.
Evening The body is best visible in the evening, after sunset.

## Error Types

A vector magnitude is too small to have a direction in space.

### DateTimeFormatError

The syntax of a UTC date/time string was not valid, or it contains invalid values.

### EarthNotAllowedError

The Earth is not allowed as the celestial body in this calculation.

### Error

Indicates an error in an astronomical calculation.

### InternalError

An internal error occured that should be reported as a bug.

Indicates an unexpected and unrecoverable condition occurred. If you encounter this error using Astronomy Engine, it would be very helpful to report it at the Issues page on GitHub. Please include a copy of the stack trace, along with a description of how to reproduce the error. This will help improve the quality of Astronomy Engine for everyone! (Thank you in advance from the author.)

### InvalidBodyError

The celestial body is not allowed for this calculation.

### NoConvergeError

A numeric solver did not converge.

Indicates that there was a failure of a numeric solver to converge. If you encounter this error using Astronomy Engine, it would be very helpful to report it at the Issues page on GitHub. Please include a copy of the stack trace, along with a description of how to reproduce the error. This will help improve the quality of Astronomy Engine for everyone! (Thank you in advance from the author.)

## Functions

### AngleBetween(a, b)

Calculates the angle in degrees between two vectors.

Given a pair of vectors, this function returns the angle in degrees between the two vectors in 3D space. The angle is measured in the plane that contains both vectors.

Type Parameter Description
Vector a The first of a pair of vectors between which to measure an angle.
Vector b The second of a pair of vectors between which to measure an angle.

Returns: float The angle between the two vectors expressed in degrees. The value is in the range [0, 180].

### AngleFromSun(body, time)

Returns the angle between the given body and the Sun, as seen from the Earth.

This function calculates the angular separation between the given body and the Sun, as seen from the center of the Earth. This angle is helpful for determining how easy it is to see the body away from the glare of the Sun.

Type Parameter Description
Body body The celestial body whose angle from the Sun is to be measured. Not allowed to be Body.Earth.
Time time The time at which the observation is made.

Returns: float A numeric value indicating the angle in degrees between the Sun and the specified body as seen from the center of the Earth.

### BackdatePosition(time, observerBody, targetBody, aberration)

Solve for light travel time correction of apparent position.

When observing a distant object, for example Jupiter as seen from Earth, the amount of time it takes for light to travel from the object to the observer can significantly affect the object's apparent position. This function solves the light travel time correction for the apparent relative position vector of a target body as seen by an observer body at a given observation time. For geocentric calculations, GeoVector also includes light travel time correction, but the time t embedded in its returned vector refers to the observation time, not the backdated time that light left the observed body. Thus BackdatePosition provides direct access to the light departure time for callers that need it. For a more generalized light travel correction solver, see CorrectLightTravel.

Type Parameter Description
Time time The time of observation.
Body observerBody The body to be used as the observation location.
Body targetBody The body to be observed.
bool aberration True to correct for aberration, or False to leave uncorrected.

Returns: Vector The position vector at the solved backdated time. Its t field holds the time that light left the observed body to arrive at the observer at the observation time.

### BaryState(body, time)

Calculates barycentric position and velocity vectors for the given body.

Given a body and a time, calculates the barycentric position and velocity vectors for the center of that body at that time. The vectors are expressed in equatorial J2000 coordinates (EQJ).

Type Parameter Description
Body body The celestial body whose barycentric state vector is to be calculated. Supported values are Body.Sun, Body.SSB, Body.Moon, Body.EMB, and all planets: Body.Mercury, Body.Venus, Body.Earth, Body.Mars, Body.Jupiter, Body.Saturn, Body.Uranus, Body.Neptune, Body.Pluto.
Time time The date and time for which to calculate position and velocity.

Returns: StateVector An object that contains barycentric position and velocity vectors.

### BodyCode(name)

Finds the Body enumeration value, given the name of a body.

>>> astronomy.BodyCode('Mars')
<Body.Mars: 3>

Type Parameter Description
str name The common English name of a supported celestial body.

Returns: Body If name is a valid body name, returns the enumeration value associated with that body. Otherwise, returns Body.Invalid.

### CombineRotation(a, b)

Creates a rotation based on applying one rotation followed by another.

Given two rotation matrices, returns a combined rotation matrix that is equivalent to rotating based on the first matrix, followed by the second.

Type Parameter Description
RotationMatrix a The first rotation to apply.
RotationMatrix b The second rotation to apply.

Returns: RotationMatrix The combined rotation matrix.

### Constellation(ra, dec)

Determines the constellation that contains the given point in the sky.

Given J2000 equatorial (EQJ) coordinates of a point in the sky, determines the constellation that contains that point.

Type Parameter Description
float ra The right ascension (RA) of a point in the sky, using the J2000 equatorial system.
float dec The declination (DEC) of a point in the sky, using the J2000 equatorial system.

Returns: ConstellationInfo A structure that contains the 3-letter abbreviation and full name of the constellation that contains the given (ra,dec), along with the converted B1875 (ra,dec) for that point.

### CorrectLightTravel(func, time)

Solve for light travel time of a vector function.

When observing a distant object, for example Jupiter as seen from Earth, the amount of time it takes for light to travel from the object to the observer can significantly affect the object's apparent position. This function is a generic solver that figures out how long in the past light must have left the observed object to reach the observer at the specified observation time. It uses PositionFunction to express an arbitrary position vector as a function of time. This function repeatedly calls func.Position, passing a series of time estimates in the past. Then func.Position must return a relative state vector between the observer and the target. CorrectLightTravel keeps calling func.Position with more and more refined estimates of the time light must have left the target to arrive at the observer. For common use cases, it is simpler to use BackdatePosition for calculating the light travel time correction of one body observing another body. For geocentric calculations, GeoVector also backdates the returned position vector for light travel time, only it returns the observation time in the returned vector's t field rather than the backdated time. time : Time The observation time for which to solve for light travel delay.

Type Parameter Description
PositionFunction func An arbitrary position vector as a function of time.

Returns: Vector The position vector at the solved backdated time. The t field holds the time that light left the observed body to arrive at the observer at the observation time.

### DeltaT_EspenakMeeus(ut)

The default Delta T function used by Astronomy Engine.

Espenak and Meeus use a series of piecewise polynomials to approximate DeltaT of the Earth in their "Five Millennium Canon of Solar Eclipses". See: https://eclipse.gsfc.nasa.gov/SEhelp/deltatpoly2004.html This is the default Delta T function used by Astronomy Engine.

Type Parameter Description
float ut The floating point number of days since noon UTC on January 1, 2000.

Returns: float The estimated difference TT-UT on the given date, expressed in seconds.

### Ecliptic(equ)

Converts J2000 equatorial Cartesian coordinates to J2000 ecliptic coordinates.

Given coordinates relative to the Earth's equator at J2000 (the instant of noon UTC on 1 January 2000), this function converts those coordinates to J2000 ecliptic coordinates, which are relative to the plane of the Earth's orbit around the Sun.

Type Parameter Description
Equatorial equ Equatorial coordinates in the J2000 frame of reference.

Returns: EclipticCoordinates Ecliptic coordinates in the J2000 frame of reference.

### EclipticGeoMoon(time)

Calculates spherical ecliptic geocentric position of the Moon.

Given a time of observation, calculates the Moon's geocentric position in ecliptic spherical coordinates. Provides the ecliptic latitude and longitude in degrees, and the geocentric distance in astronomical units (AU). The ecliptic longitude is measured relative to the equinox of date. This algorithm is based on the Nautical Almanac Office's Improved Lunar Ephemeris of 1954, which in turn derives from E. W. Brown's lunar theories from the early twentieth century. It is adapted from Turbo Pascal code from the book Astronomy on the Personal Computer by Montenbruck and Pfleger. To calculate an equatorial J2000 vector instead, use GeoMoon.

Type Parameter Description
Time time The date and time for which to calculate the Moon's position.

Returns: Spherical The Moon's position as a distance, ecliptic latitude, and ecliptic longitude.

### EclipticLongitude(body, time)

Calculates heliocentric ecliptic longitude of a body based on the J2000 equinox.

This function calculates the angle around the plane of the Earth's orbit of a celestial body, as seen from the center of the Sun. The angle is measured prograde (in the direction of the Earth's orbit around the Sun) in degrees from the J2000 equinox. The ecliptic longitude is always in the range [0, 360).

Type Parameter Description
Body body A body other than the Sun.
Time time The date and time at which the body's ecliptic longitude is to be calculated.

Returns: float An angular value in degrees indicating the ecliptic longitude of the body.

### Elongation(body, time)

Determines visibility of a celestial body relative to the Sun, as seen from the Earth.

This function returns an ElongationEvent object, which provides the following information about the given celestial body at the given time:

• visibility is an enumerated type that specifies whether the body is more easily seen in the morning before sunrise, or in the evening after sunset.
• elongation is the angle in degrees between two vectors: one from the center of the Earth to the center of the Sun, the other from the center of the Earth to the center of the specified body. This angle indicates how far away the body is from the glare of the Sun. The elongation angle is always in the range [0, 180].
• ecliptic_separation is the absolute value of the difference between the body's ecliptic longitude and the Sun's ecliptic longitude, both as seen from the center of the Earth. This angle measures around the plane of the Earth's orbit, and ignores how far above or below that plane the body is. The ecliptic separation is measured in degrees and is always in the range [0, 180].
Type Parameter Description
Body body The celestial body whose visibility is to be calculated.
Time time The date and time of the observation.

Returns: ElongationEvent

### Equator(body, time, observer, ofdate, aberration)

Calculates equatorial coordinates of a celestial body as seen by an observer on the Earth's surface.

Calculates topocentric equatorial coordinates in one of two different systems: J2000 or true-equator-of-date, depending on the value of the ofdate parameter. Equatorial coordinates include right ascension, declination, and distance in astronomical units. This function corrects for light travel time: it adjusts the apparent location of the observed body based on how long it takes for light to travel from the body to the Earth. This function corrects for topocentric parallax, meaning that it adjusts for the angular shift depending on where the observer is located on the Earth. This is most significant for the Moon, because it is so close to the Earth. However, parallax corection has a small effect on the apparent positions of other bodies. Correction for aberration is optional, using the aberration parameter.

Type Parameter Description
Body body The celestial body to be observed. Not allowed to be Body.Earth.
Time time The date and time at which the observation takes place.
Observer observer A location on or near the surface of the Earth.
bool ofdate Selects the date of the Earth's equator in which to express the equatorial coordinates. If True, returns coordinates using the equator and equinox of date. If False, returns coordinates converted to the J2000 system.
bool aberration If True, corrects for aberration of light based on the motion of the Earth with respect to the heliocentric origin. If False, does not correct for aberration.

Returns: Equatorial Equatorial coordinates in the specified frame of reference.

### EquatorFromVector(vec)

Given an equatorial vector, calculates equatorial angular coordinates.

Type Parameter Description
Vector vec A vector in an equatorial coordinate system.

Returns: Equatorial Angular coordinates expressed in the same equatorial system as vec.

### GeoEmbState(time)

Calculates the geocentric position and velocity of the Earth/Moon barycenter.

Given a time of observation, calculates the geocentric position and velocity vectors of the Earth/Moon barycenter (EMB). The position (x, y, z) components are expressed in AU (astronomical units). The velocity (vx, vy, vz) components are expressed in AU/day.

Type Parameter Description
Time time The date and time for which to calculate the EMB's geocentric state.

Returns: StateVector The EMB's position and velocity vectors in J2000 equatorial coordinates.

### GeoMoon(time)

Calculates equatorial geocentric position of the Moon at a given time.

Given a time of observation, calculates the Moon's position as a vector. The vector gives the location of the Moon's center relative to the Earth's center with x-, y-, and z-components measured in astronomical units. The coordinates are oriented with respect to the Earth's equator at the J2000 epoch. In Astronomy Engine, this orientation is called EQJ. This algorithm is based on the Nautical Almanac Office's Improved Lunar Ephemeris of 1954, which in turn derives from E. W. Brown's lunar theories from the early twentieth century. It is adapted from Turbo Pascal code from the book Astronomy on the Personal Computer by Montenbruck and Pfleger.

Type Parameter Description
Time time The date and time for which to calculate the Moon's position.

Returns: Vector The Moon's position as a vector in J2000 Cartesian equatorial coordinates (EQJ).

### GeoMoonState(time)

Calculates equatorial geocentric position and velocity of the Moon at a given time.

Given a time of observation, calculates the Moon's position and velocity vectors. The position and velocity are of the Moon's center relative to the Earth's center. The position (x, y, z) components are expressed in AU (astronomical units). The velocity (vx, vy, vz) components are expressed in AU/day. The coordinates are oriented with respect to the Earth's equator at the J2000 epoch. In Astronomy Engine, this orientation is called EQJ. If you need the Moon's position only, and not its velocity, it is much more efficient to use GeoMoon instead.

Type Parameter Description
Time time The date and time for which to calculate the Moon's position and velocity.

Returns: StateVector The Moon's position and velocity vectors in J2000 equatorial coordinates (EQJ).

### GeoVector(body, time, aberration)

Calculates geocentric Cartesian coordinates of a body in the J2000 equatorial system.

This function calculates the position of the given celestial body as a vector, using the center of the Earth as the origin. The result is expressed as a Cartesian vector in the J2000 equatorial system: the coordinates are based on the mean equator of the Earth at noon UTC on 1 January 2000. If given an invalid value for body, this function will raise an exception. Unlike HelioVector, this function corrects for light travel time. This means the position of the body is "back-dated" by the amount of time it takes light to travel from that body to an observer on the Earth. Also, the position can optionally be corrected for aberration, an effect causing the apparent direction of the body to be shifted due to transverse movement of the Earth with respect to the rays of light coming from that body.

Type Parameter Description
Body body A body for which to calculate a heliocentric position: the Sun, Moon, or any of the planets.
Time time The date and time for which to calculate the position.
bool aberration A boolean value indicating whether to correct for aberration.

Returns: Vector A geocentric position vector of the center of the given body.

### HelioDistance(body, time)

Calculates the distance between a body and the Sun at a given time.

Given a date and time, this function calculates the distance between the center of body and the center of the Sun. For the planets Mercury through Neptune, this function is significantly more efficient than calling HelioVector followed by taking the length of the resulting vector.

Type Parameter Description
Body body A body for which to calculate a heliocentric distance: the Sun, Moon, or any of the planets.
Time time The date and time for which to calculate the heliocentric distance.

Returns: float The heliocentric distance in AU.

### HelioState(body, time)

Calculates heliocentric position and velocity vectors for the given body.

Given a body and a time, calculates the position and velocity vectors for the center of that body at that time, relative to the center of the Sun. The vectors are expressed in equatorial J2000 coordinates (EQJ). If you need the position vector only, it is more efficient to call HelioVector. The Sun's center is a non-inertial frame of reference. In other words, the Sun experiences acceleration due to gravitational forces, mostly from the larger planets (Jupiter, Saturn, Uranus, and Neptune). If you want to calculate momentum, kinetic energy, or other quantities that require a non-accelerating frame of reference, consider using BaryState instead.

Type Parameter Description
Body body The celestial body whose heliocentric state vector is to be calculated. Supported values are Body.Sun, Body.SSB, Body.Moon, Body.EMB, and all planets: Body.Mercury, Body.Venus, Body.Earth, Body.Mars, Body.Jupiter, Body.Saturn, Body.Uranus, Body.Neptune, Body.Pluto.
Time time The date and time for which to calculate position and velocity.

Returns: StateVector An object that contains heliocentric position and velocity vectors.

### HelioVector(body, time)

Calculates heliocentric Cartesian coordinates of a body in the J2000 equatorial system.

This function calculates the position of the given celestial body as a vector, using the center of the Sun as the origin. The result is expressed as a Cartesian vector in the J2000 equatorial system: the coordinates are based on the mean equator of the Earth at noon UTC on 1 January 2000. The position is not corrected for light travel time or aberration. This is different from the behavior of GeoVector. If given an invalid value for body, this function raises an exception.

Type Parameter Description
Body body The celestial body whose heliocentric position is to be calculated: The Sun, Moon, EMB, SSB, or any of the planets.
Time time The time at which to calculate the heliocentric position.

Returns: Vector A heliocentric position vector of the center of the given body at the given time.

### Horizon(time, observer, ra, dec, refraction)

Calculates the apparent location of a body relative to the local horizon of an observer on the Earth.

Given a date and time, the geographic location of an observer on the Earth, and equatorial coordinates (right ascension and declination) of a celestial body, this function returns horizontal coordinates (azimuth and altitude angles) for the body relative to the horizon at the geographic location. The right ascension ra and declination dec passed in must be equator of date coordinates, based on the Earth's true equator at the date and time of the observation. Otherwise the resulting horizontal coordinates will be inaccurate. Equator of date coordinates can be obtained by calling Equator, passing in True as its ofdate parameter. It is also recommended to enable aberration correction by passing in True for the aberration parameter. This function optionally corrects for atmospheric refraction. For most uses, it is recommended to pass Refraction.Normal in the refraction parameter to correct for optical lensing of the Earth's atmosphere that causes objects to appear somewhat higher above the horizon than they actually are. However, callers may choose to avoid this correction by passing in Refraction.Airless. If refraction correction is enabled, the azimuth, altitude, right ascension, and declination in the HorizontalCoordinates object returned by this function will all be corrected for refraction. If refraction is disabled, none of these four coordinates will be corrected; in that case, the right ascension and declination in the returned object will be numerically identical to the respective ra and dec values passed in.

Type Parameter Description
Time time The date and time for which to find horizontal coordinates.
Observer observer The location of the observer for which to find horizontal coordinates.
float ra Right ascension in sidereal hours of the celestial object, referred to the mean equinox of date for the J2000 epoch.
float dec Declination in degrees of the celestial object, referred to the mean equator of date for the J2000 epoch. Positive values are north of the celestial equator and negative values are south of it.
Refraction refraction The option for selecting whether to correct for atmospheric lensing. If Refraction.Normal, a well-behaved refraction model is used. If Refraction.None, no refraction correct is performed. Refraction.JplHorizons is used only for compatibility testing with the JPL Horizons online tool.

Returns: HorizontalCoordinates The horizontal coordinates (altitude and azimuth), along with equatorial coordinates (right ascension and declination), all optionally corrected for atmospheric refraction. See remarks above for more details.

### HorizonFromVector(vector, refraction)

Converts Cartesian coordinates to horizontal coordinates.

Given a horizontal Cartesian vector, returns horizontal azimuth and altitude. IMPORTANT: This function differs from SphereFromVector in two ways:

• SphereFromVector returns a lon value that represents azimuth defined counterclockwise from north (e.g., west = +90), but this function represents a clockwise rotation (e.g., east = +90). The difference is because SphereFromVector is intended to preserve the vector "right-hand rule", while this function defines azimuth in a more traditional way as used in navigation and cartography.
• This function optionally corrects for atmospheric refraction, while SphereFromVector does not. The returned object contains the azimuth in lon. It is measured in degrees clockwise from north: east = +90 degrees, west = +270 degrees. The altitude is stored in lat. The distance to the observed object is stored in dist, and is expressed in astronomical units (AU).
Type Parameter Description
Vector vector Cartesian vector to be converted to horizontal angular coordinates.
Refraction refraction See comments in the RefractionAngle function.

### IdentityMatrix()

Creates an identity rotation matrix.

Returns a rotation matrix that has no effect on orientation. This matrix can be the starting point for other operations, such as using a series of calls to Pivot to create a custom rotation matrix.

Returns: RotationMatrix The identity rotation matrix.

### Illumination(body, time)

Finds visual magnitude, phase angle, and other illumination information about a celestial body.

This function calculates information about how bright a celestial body appears from the Earth, reported as visual magnitude, which is a smaller (or even negative) number for brighter objects, and a larger number for dimmer objects. For bodies other than the Sun, it reports a phase angle, which is the angle in degrees between the Sun and the Earth, as seen from the center of the body. Phase angle indicates what fraction of the body appears illuminated as seen from the Earth. For example, when the phase angle is near zero, it means the body appears "full" as seen from the Earth. A phase angle approaching 180 degrees means the body appears as a thin crescent as seen from the Earth. A phase angle of 90 degrees means the body appears "half full". For the Sun, the phase angle is always reported as 0; the Sun emits light rather than reflecting it, so it doesn't have a phase angle. When the body is Saturn, the returned object contains a field ring_tilt that holds the tilt angle in degrees of Saturn's rings as seen from the Earth. A value of 0 means the rings appear edge-on, and are thus nearly invisible from the Earth. The ring_tilt holds 0 for all bodies other than Saturn.

Type Parameter Description
Body body The Sun, Moon, or any planet other than the Earth.
Time time The date and time of the observation.

Returns: IlluminationInfo

### InverseRefractionAngle(refraction, bent_altitude)

Calculates the inverse of an atmospheric refraction angle.

Given an observed altitude angle that includes atmospheric refraction, calculates the negative angular correction to obtain the unrefracted altitude. This is useful for cases where observed horizontal coordinates are to be converted to another orientation system, but refraction first must be removed from the observed position.

Type Parameter Description
Refraction refraction Refraction.Normal - corrects for atmospheric refraction (recommended). Refraction.Airless - no correction is performed. Refraction.JplHorizons - For JPL Horizons compatibility testing only.
float bent_altitude The apparent altitude that includes atmospheric refraction.

Returns: float The angular adjustment in degrees, to be added to the altitude angle to correct for atmospheric lensing. This will be less than or equal to zero.

### InverseRotation(rotation)

Calculates the inverse of a rotation matrix.

Given a rotation matrix that performs some coordinate transform, this function returns the matrix that reverses that transform.

Type Parameter Description
RotationMatrix rotation The rotation matrix to be inverted.

Returns: RotationMatrix The inverse rotation matrix.

### JupiterMoons(time)

Calculates jovicentric positions and velocities of Jupiter's largest 4 moons.

Calculates position and velocity vectors for Jupiter's moons Io, Europa, Ganymede, and Callisto, at the given date and time. The vectors are jovicentric (relative to the center of Jupiter). Their orientation is the Earth's equatorial system at the J2000 epoch (EQJ). The position components are expressed in astronomical units (AU), and the velocity components are in AU/day. To convert to heliocentric vectors, call HelioVector with Body.Jupiter to get Jupiter's heliocentric position, then add the jovicentric vectors. Likewise, you can call GeoVector to convert to geocentric vectors.

Type Parameter Description
Time time The date and time for which to calculate Jupiter's moons.

Returns: JupiterMoonsInfo The positions and velocities of Jupiter's 4 largest moons.

### LagrangePoint(point, time, major_body, minor_body)

Calculates one of the 5 Lagrange points for a pair of co-orbiting bodies.

Given a more massive "major" body and a much less massive "minor" body, calculates one of the five Lagrange points in relation to the minor body's orbit around the major body. The parameter point is an integer that selects the Lagrange point as follows: 1 = the Lagrange point between the major body and minor body. 2 = the Lagrange point on the far side of the minor body. 3 = the Lagrange point on the far side of the major body. 4 = the Lagrange point 60 degrees ahead of the minor body's orbital position. 5 = the Lagrange point 60 degrees behind the minor body's orbital position. The function returns the state vector for the selected Lagrange point in equatorial J2000 coordinates (EQJ), with respect to the center of the major body. To calculate Sun/Earth Lagrange points, pass in Body.Sun for major_body and Body.EMB (Earth/Moon barycenter) for minor_body. For Lagrange points of the Sun and any other planet, pass in just that planet (e.g. Body.Jupiter) for minor_body. To calculate Earth/Moon Lagrange points, pass in Body.Earth and Body.Moon for the major and minor bodies respectively. In some cases, it may be more efficient to call LagrangePointFast, especially when the state vectors have already been calculated, or are needed for some other purpose.

Type Parameter Description
int point An integer 1..5 that selects which of the Lagrange points to calculate.
Time time The time for which the Lagrange point is to be calculated.
Body major_body The more massive of the co-orbiting bodies: Body.Sun or Body.Earth.
Body minor_body The less massive of the co-orbiting bodies. See main remarks.

Returns: StateVector The position and velocity of the selected Lagrange point with respect to the major body's center.

### LagrangePointFast(point, major_state, major_mass, minor_state, minor_mass)

Calculates one of the 5 Lagrange points from body masses and state vectors.

Given a more massive "major" body and a much less massive "minor" body, calculates one of the five Lagrange points in relation to the minor body's orbit around the major body. The parameter point is an integer that selects the Lagrange point as follows: 1 = the Lagrange point between the major body and minor body. 2 = the Lagrange point on the far side of the minor body. 3 = the Lagrange point on the far side of the major body. 4 = the Lagrange point 60 degrees ahead of the minor body's orbital position. 5 = the Lagrange point 60 degrees behind the minor body's orbital position. The caller passes in the state vector and mass for both bodies. The state vectors can be in any orientation and frame of reference. The body masses are expressed as GM products, where G = the universal gravitation constant and M = the body's mass. Thus the units for major_mass and minor_mass must be au^3/day^2. Use MassProduct to obtain GM values for various solar system bodies. The function returns the state vector for the selected Lagrange point using the same orientation as the state vector parameters major_state and minor_state, and the position and velocity components are with respect to the major body's center. Consider calling LagrangePoint, instead of this function, for simpler usage in most cases.

Type Parameter Description
int point An integer 1..5 that selects which of the Lagrange points to calculate.
StateVector major_state The state vector of the major (more massive) of the pair of bodies.
float major_mass The mass product GM of the major body.
StateVector minor_state The state vector of the minor (less massive) of the pair of bodies.
float minor_mass The mass product GM of the minor body.

Returns: StateVector The position and velocity of the selected Lagrange point with respect to the major body's center.

### Libration(time)

Calculates the Moon's libration angles at a given moment in time.

Libration is an observed back-and-forth wobble of the portion of the Moon visible from the Earth. It is caused by the imperfect tidal locking of the Moon's fixed rotation rate, compared to its variable angular speed of orbit around the Earth. This function calculates a pair of perpendicular libration angles, one representing rotation of the Moon in eclitpic longitude elon, the other in ecliptic latitude elat, both relative to the Moon's mean Earth-facing position. This function also returns the geocentric position of the Moon expressed in ecliptic longitude mlon, ecliptic latitude mlat, the distance dist_km between the centers of the Earth and Moon expressed in kilometers, and the apparent angular diameter of the Moon diam_deg.

Type Parameter Description
Time time The date and time for which to calculate the Moon's libration angles.

Returns: LibrationInfo

### MassProduct(body)

Returns the product of mass and universal gravitational constant of a Solar System body.

For problems involving the gravitational interactions of Solar System bodies, it is helpful to know the product GM, where G = the universal gravitational constant and M = the mass of the body. In practice, GM is known to a higher precision than either G or M alone, and thus using the product results in the most accurate results. This function returns the product GM in the units au^3/day^2. The values come from page 10 of a JPL memorandum regarding the DE405/LE405 ephemeris.

Type Parameter Description
Body body The body for which to find the GM product. Allowed to be the Sun, Moon, EMB (Earth/Moon Barycenter), or any planet. Any other value will cause an exception to be thrown.

Returns: float The mass product of the given body in au^3/day^2.

### MoonPhase(time)

Returns the Moon's phase as an angle from 0 to 360 degrees.

This function determines the phase of the Moon using its apparent ecliptic longitude relative to the Sun, as seen from the center of the Earth. Certain values of the angle have conventional definitions:

• 0 = new moon
• 90 = first quarter
• 180 = full moon
• 270 = third quarter
Type Parameter Description
Time time The date and time of the observation.

Returns: float

### NextGlobalSolarEclipse(prevEclipseTime)

Searches for the next global solar eclipse in a series.

After using SearchGlobalSolarEclipse to find the first solar eclipse in a series, you can call this function to find the next consecutive solar eclipse. Pass in the peak value from the GlobalSolarEclipseInfo returned by the previous call to SearchGlobalSolarEclipse or NextGlobalSolarEclipse to find the next solar eclipse.

Type Parameter Description
Time prevEclipseTime A date and time near a new moon. Solar eclipse search will start at the next new moon.

Returns: GlobalSolarEclipseInfo

### NextLocalSolarEclipse(prevEclipseTime, observer)

Searches for the next local solar eclipse in a series.

After using SearchLocalSolarEclipse to find the first solar eclipse in a series, you can call this function to find the next consecutive solar eclipse. Pass in the peak value from the LocalSolarEclipseInfo returned by the previous call to SearchLocalSolarEclipse or NextLocalSolarEclipse to find the next solar eclipse.

Type Parameter Description
Time prevEclipseTime A date and time near a new moon. Solar eclipse search will start at the next new moon.
Observer observer The geographic location of the observer.

Returns: LocalSolarEclipseInfo

### NextLunarApsis(apsis)

Finds the next lunar perigee or apogee in a series.

This function requires an Apsis value obtained from a call to SearchLunarApsis or NextLunarApsis. Given an apogee event, this function finds the next perigee event, and vice versa. See SearchLunarApsis for more details.

Type Parameter Description
Apsis apsis

Returns: Apsis

### NextLunarEclipse(prevEclipseTime)

Searches for the next lunar eclipse in a series.

After using SearchLunarEclipse to find the first lunar eclipse in a series, you can call this function to find the next consecutive lunar eclipse. Pass in the peak value from the LunarEclipseInfo returned by the previous call to SearchLunarEclipse or NextLunarEclipse to find the next lunar eclipse.

Type Parameter Description
Time prevEclipseTime A date and time near a full moon. Lunar eclipse search will start at the next full moon.

Returns: LunarEclipseInfo

### NextMoonNode(prevNode)

Searches for the next time when the Moon's center crosses through the ecliptic plane.

Call SearchMoonNode to find the first of a series of nodes. Then call NextMoonNode to find as many more consecutive nodes as desired.

Type Parameter Description
NodeEventInfo prevNode The previous node find from calling SearchMoonNode or NextMoonNode.

Returns: NodeEventInfo

### NextMoonQuarter(mq)

Continues searching for lunar quarters from a previous search.

After calling SearchMoonQuarter, this function can be called one or more times to continue finding consecutive lunar quarters. This function finds the next consecutive moon quarter event after the one passed in as the parameter mq.

Type Parameter Description
MoonQuarter mq A value returned by a prior call to SearchMoonQuarter or NextMoonQuarter.

Returns: MoonQuarter

### NextPlanetApsis(body, apsis)

Finds the next planetary perihelion or aphelion event in a series.

This function requires an Apsis value obtained from a call to SearchPlanetApsis or NextPlanetApsis. Given an aphelion event, this function finds the next perihelion event, and vice versa. See SearchPlanetApsis for more details.

Type Parameter Description
Body body The planet for which to find the next perihelion/aphelion event. Not allowed to be Body.Sun or Body.Moon. Must match the body passed into the call that produced the apsis parameter.
Apsis apsis An apsis event obtained from a call to SearchPlanetApsis or NextPlanetApsis.

Returns: Apsis

### NextTransit(body, prevTransitTime)

Searches for another transit of Mercury or Venus.

After calling SearchTransit to find a transit of Mercury or Venus, this function finds the next transit after that. Keep calling this function as many times as you want to keep finding more transits.

Type Parameter Description
Body body The planet whose transit is to be found. Must be Body.Mercury or Body.Venus.
Time prevTransitTime A date and time near the previous transit.

Returns: TransitInfo

### ObserverGravity(latitude, height)

Calculates the gravitational acceleration experienced by an observer on the Earth.

This function implements the WGS 84 Ellipsoidal Gravity Formula. The result is a combination of inward gravitational acceleration with outward centrifugal acceleration, as experienced by an observer in the Earth's rotating frame of reference. The resulting value increases toward the Earth's poles and decreases toward the equator, consistent with changes of the weight measured by a spring scale of a fixed mass moved to different latitudes and heights on the Earth.

Type Parameter Description
float latitude The latitude of the observer in degrees north or south of the equator. By formula symmetry, positive latitudes give the same answer as negative latitudes, so the sign does not matter.
float height The height above the sea level geoid in meters. No range checking is done; however, accuracy is only valid in the range 0 to 100000 meters.

Returns: float The effective gravitational acceleration expressed in meters per second squared [m/s^2].

### ObserverState(time, observer, ofdate)

Calculates geocentric equatorial position and velocity of an observer on the surface of the Earth.

This function calculates position and velocity vectors of an observer on or near the surface of the Earth, expressed in equatorial coordinates. It takes into account the rotation of the Earth at the given time, along with the given latitude, longitude, and elevation of the observer. The caller may pass ofdate as True to return coordinates relative to the Earth's equator at the specified time, or False to use the J2000 equator. The returned position vector has components expressed in astronomical units (AU). To convert to kilometers, multiply the x, y, and z values by the constant value KM_PER_AU. The returned velocity vector has components expressed in AU/day.

Type Parameter Description
Time time The date and time for which to calculate the observer's position and velocity vectors.
Observer observer The geographic location of a point on or near the surface of the Earth.
bool ofdate Selects the date of the Earth's equator in which to express the equatorial coordinates. The caller may pass False to use the orientation of the Earth's equator at noon UTC on January 1, 2000, in which case this function corrects for precession and nutation of the Earth as it was at the moment specified by the time parameter. Or the caller may pass true to use the Earth's equator at time as the orientation.

Returns: StateVector An equatorial position vector and velocity vector relative to the center of the Earth.

### ObserverVector(time, observer, ofdate)

Calculates geocentric equatorial coordinates of an observer on the surface of the Earth.

This function calculates a vector from the center of the Earth to a point on or near the surface of the Earth, expressed in equatorial coordinates. It takes into account the rotation of the Earth at the given time, along with the given latitude, longitude, and elevation of the observer. The caller may pass ofdate as True to return coordinates relative to the Earth's equator at the specified time, or False to use the J2000 equator. The returned vector has components expressed in astronomical units (AU). To convert to kilometers, multiply the x, y, and z values by the constant value KM_PER_AU. The inverse of this function is also available: VectorObserver.

Type Parameter Description
Time time The date and time for which to calculate the observer's position vector.
Observer observer The geographic location of a point on or near the surface of the Earth.
bool ofdate Selects the date of the Earth's equator in which to express the equatorial coordinates. The caller may pass False to use the orientation of the Earth's equator at noon UTC on January 1, 2000, in which case this function corrects for precession and nutation of the Earth as it was at the moment specified by the time parameter. Or the caller may pass true to use the Earth's equator at time as the orientation.

Returns: Vector An equatorial vector from the center of the Earth to the specified location on (or near) the Earth's surface.

### PairLongitude(body1, body2, time)

Returns one body's ecliptic longitude with respect to another, as seen from the Earth.

This function determines where one body appears around the ecliptic plane (the plane of the Earth's orbit around the Sun) as seen from the Earth, relative to the another body's apparent position. The function returns an angle in the half-open range [0, 360) degrees. The value is the ecliptic longitude of body1 relative to the ecliptic longitude of body2. The angle is 0 when the two bodies are at the same ecliptic longitude as seen from the Earth. The angle increases in the prograde direction (the direction that the planets orbit the Sun and the Moon orbits the Earth). When the angle is 180 degrees, it means the two bodies appear on opposite sides of the sky for an Earthly observer. Neither body1 nor body2 is allowed to be Body.Earth. If this happens, the function throws an exception.

Type Parameter Description
Body body1 The first body, whose longitude is to be found relative to the second body.
Body body2 The second body, relative to which the longitude of the first body is to be found.
Time time The date and time of the observation.

Returns: float An angle in degrees in the range [0, 360).

### Pivot(rotation, axis, angle)

Re-orients a rotation matrix by pivoting it by an angle around one of its axes.

Given a rotation matrix, a selected coordinate axis, and an angle in degrees, this function pivots the rotation matrix by that angle around that coordinate axis. For example, if you have rotation matrix that converts ecliptic coordinates (ECL) to horizontal coordinates (HOR), but you really want to convert ECL to the orientation of a telescope camera pointed at a given body, you can use Pivot twice: (1) pivot around the zenith axis by the body's azimuth, then (2) pivot around the western axis by the body's altitude angle. The resulting rotation matrix will then reorient ECL coordinates to the orientation of your telescope camera.

Type Parameter Description
RotationMatrix rotation The input rotation matrix.
int axis An integer that selects which coordinate axis to rotate around: 0 = x, 1 = y, 2 = z. Any other value will cause an exception.
float angle An angle in degrees indicating the amount of rotation around the specified axis. Positive angles indicate rotation counterclockwise as seen from the positive direction along that axis, looking towards the origin point of the orientation system. Any finite number of degrees is allowed, but best precision will result from keeping angle in the range [-360, +360].

Returns: RotationMatrix A pivoted matrix object.

### RefractionAngle(refraction, altitude)

Calculates the amount of "lift" to an altitude angle caused by atmospheric refraction.

Given an altitude angle and a refraction option, calculates the amount of "lift" caused by atmospheric refraction. This is the number of degrees higher in the sky an object appears due to lensing of the Earth's atmosphere.

Type Parameter Description
Refraction refraction The option for selecting whether to correct for atmospheric lensing. If Refraction.Normal, a well-behaved refraction model is used. If Refraction.Airless, no refraction correct is performed. Refraction.JplHorizons is used only for compatibility testing with the JPL Horizons online tool. Any other value raises an exception.
float altitude The number of degrees above (positive) or below (negative) the horizon an object is, before being corrected for refraction.

Returns: float The number of additional degrees of altitude an object appears to have, due to atmospheric refraction, depending on the option selected by the refraction parameter.

### RotateState(rotation, state)

Applies a rotation to a state vector, yielding a rotated state vector.

This function transforms a state vector in one orientation to a state vector in another orientation. Both the position and velocity vectors are rotated the same way.

Type Parameter Description
RotationMatrix rotation A rotation matrix that specifies how the orientation of the vector is to be changed.
StateVector state The state vector whose orientation is to be changed.

Returns: StateVector A state vector in the orientation specified by rotation.

### RotateVector(rotation, vector)

Applies a rotation to a vector, yielding a rotated vector.

This function transforms a vector in one orientation to a vector in another orientation.

Type Parameter Description
RotationMatrix rotation A rotation matrix that specifies how the orientation of the vector is to be changed.
Vector vector The vector whose orientation is to be changed.

Returns: Vector A vector in the orientation specified by rotation.

### RotationAxis(body, time)

Calculates information about a body's rotation axis at a given time.

Calculates the orientation of a body's rotation axis, along with the rotation angle of its prime meridian, at a given moment in time. This function uses formulas standardized by the IAU Working Group on Cartographics and Rotational Elements 2015 report, as described in the following document: https://astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/WGCCRE2015reprint.pdf See AxisInfo for more detailed information.

Type Parameter Description
Body body One of the following values: Body.Sun, Body.Moon, Body.Mercury, Body.Venus, Body.Earth, Body.Mars, Body.Jupiter, Body.Saturn, Body.Uranus, Body.Neptune, Body.Pluto.
Time time The time at which to calculate the body's rotation axis.

Returns: AxisInfo The body's north pole direction and angle of its prime meridian.

### Rotation_ECL_EQD(time)

Calculates a rotation matrix from ecliptic J2000 (ECL) to equatorial of-date (EQD).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: ECL = ecliptic system, using equator at J2000 epoch. Target: EQD = equatorial system, using equator of date.

Type Parameter Description
Time time The date and time of the desired equator.

Returns: RotationMatrix A rotation matrix that converts ECL to EQD.

### Rotation_ECL_EQJ()

Calculates a rotation matrix from ecliptic J2000 (ECL) to equatorial J2000 (EQJ).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: ECL = ecliptic system, using equator at J2000 epoch. Target: EQJ = equatorial system, using equator at J2000 epoch.

Returns: RotationMatrix A rotation matrix that converts ECL to EQJ.

### Rotation_ECL_HOR(time, observer)

Calculates a rotation matrix from ecliptic J2000 (ECL) to horizontal (HOR).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: ECL = ecliptic system, using equator at J2000 epoch. Target: HOR = horizontal system. Use HorizonFromVector to convert the return value to a traditional altitude/azimuth pair.

Type Parameter Description
Time time The date and time of the desired horizontal orientation.
Observer observer A location near the Earth's mean sea level that defines the observer's horizon.

Returns: RotationMatrix A rotation matrix that converts ECL to HOR at time and for observer. The components of the horizontal vector are: x = north, y = west, z = zenith (straight up from the observer). These components are chosen so that the "right-hand rule" works for the vector and so that north represents the direction where azimuth = 0.

### Rotation_EQD_ECL(time)

Calculates a rotation matrix from equatorial of-date (EQD) to ecliptic J2000 (ECL).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: EQD = equatorial system, using equator of date. Target: ECL = ecliptic system, using equator at J2000 epoch.

Type Parameter Description
Time time The date and time of the source equator.

Returns: RotationMatrix A rotation matrix that converts EQD to ECL.

### Rotation_EQD_EQJ(time)

Calculates a rotation matrix from equatorial of-date (EQD) to equatorial J2000 (EQJ).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: EQD = equatorial system, using equator of the specified date/time. Target: EQJ = equatorial system, using equator at J2000 epoch.

Type Parameter Description
Time time The date and time at which the Earth's equator defines the source orientation.

Returns: RotationMatrix A rotation matrix that converts EQD at time to EQJ.

### Rotation_EQD_HOR(time, observer)

Calculates a rotation matrix from equatorial of-date (EQD) to horizontal (HOR).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: EQD = equatorial system, using equator of the specified date/time. Target: HOR = horizontal system. Use HorizonFromVector to convert the return value to a traditional altitude/azimuth pair.

Type Parameter Description
Time time The date and time at which the Earth's equator applies.
Observer observer A location near the Earth's mean sea level that defines the observer's location.

Returns: RotationMatrix A rotation matrix that converts EQD to HOR at time and for observer. The components of the horizontal vector are: x = north, y = west, z = zenith (straight up from the observer). These components are chosen so that the "right-hand rule" works for the vector and so that north represents the direction where azimuth = 0.

### Rotation_EQJ_ECL()

Calculates a rotation matrix from equatorial J2000 (EQJ) to ecliptic J2000 (ECL).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: EQJ = equatorial system, using equator at J2000 epoch. Target: ECL = ecliptic system, using equator at J2000 epoch.

Returns: RotationMatrix A rotation matrix that converts EQJ to ECL.

### Rotation_EQJ_EQD(time)

Calculates a rotation matrix from equatorial J2000 (EQJ) to equatorial of-date (EQD).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: EQJ = equatorial system, using equator at J2000 epoch. Target: EQD = equatorial system, using equator of the specified date/time.

Type Parameter Description
Time time The date and time at which the Earth's equator defines the target orientation.

Returns: RotationMatrix A rotation matrix that converts EQJ to EQD at time.

### Rotation_EQJ_GAL()

Calculates a rotation matrix from equatorial J2000 (EQJ) to galactic (GAL).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: EQJ = equatorial system, using the equator at the J2000 epoch. Target: GAL = galactic system (IAU 1958 definition).

Returns: RotationMatrix A rotation matrix that converts EQJ to GAL.

### Rotation_EQJ_HOR(time, observer)

Calculates a rotation matrix from equatorial J2000 (EQJ) to horizontal (HOR).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: EQJ = equatorial system, using the equator at the J2000 epoch. Target: HOR = horizontal system. Use HorizonFromVector to convert the return value to a traditional altitude/azimuth pair.

Type Parameter Description
Time time The date and time of the desired horizontal orientation.
Observer observer A location near the Earth's mean sea level that defines the observer's horizon.

Returns: RotationMatrix A rotation matrix that converts EQJ to HOR at time and for observer. The components of the horizontal vector are: x = north, y = west, z = zenith (straight up from the observer). These components are chosen so that the "right-hand rule" works for the vector and so that north represents the direction where azimuth = 0.

### Rotation_GAL_EQJ()

Calculates a rotation matrix from galactic (GAL) to equatorial J2000 (EQJ).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: GAL = galactic system (IAU 1958 definition). Target: EQJ = equatorial system, using the equator at the J2000 epoch.

Returns: RotationMatrix A rotation matrix that converts GAL to EQJ.

### Rotation_HOR_ECL(time, observer)

Calculates a rotation matrix from horizontal (HOR) to ecliptic J2000 (ECL).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: HOR = horizontal system. Target: ECL = ecliptic system, using equator at J2000 epoch.

Type Parameter Description
Time time The date and time of the horizontal observation.
Observer observer The location of the horizontal observer.

Returns: RotationMatrix A rotation matrix that converts HOR to ECL.

### Rotation_HOR_EQD(time, observer)

Calculates a rotation matrix from horizontal (HOR) to equatorial of-date (EQD).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: HOR = horizontal system (x=North, y=West, z=Zenith). Target: EQD = equatorial system, using equator of the specified date/time.

Type Parameter Description
Time time The date and time at which the Earth's equator applies.
Observer observer A location near the Earth's mean sea level that defines the observer's horizon.

Returns: RotationMatrix A rotation matrix that converts HOR to EQD at time and for observer.

### Rotation_HOR_EQJ(time, observer)

Calculates a rotation matrix from horizontal (HOR) to J2000 equatorial (EQJ).

This is one of the family of functions that returns a rotation matrix for converting from one orientation to another. Source: HOR = horizontal system (x=North, y=West, z=Zenith). Target: EQJ = equatorial system, using equator at the J2000 epoch.

Type Parameter Description
Time time The date and time of the observation.
Observer observer A location near the Earth's mean sea level that define's the observer's horizon.

Returns: RotationMatrix A rotation matrix that converts HOR to EQJ at time and for observer.

### Search(func, context, t1, t2, dt_tolerance_seconds)

Searches for a time at which a function's value increases through zero.

Certain astronomy calculations involve finding a time when an event occurs. Often such events can be defined as the root of a function: the time at which the function's value becomes zero. Search finds the ascending root of a function: the time at which the function's value becomes zero while having a positive slope. That is, as time increases, the function transitions from a negative value, through zero at a specific moment, to a positive value later. The goal of the search is to find that specific moment. The search function is specified by two parameters: func and context. The func parameter is a function itself that accepts a time and a context containing any other arguments needed to evaluate the function. The context parameter supplies that context for the given search. As an example, a caller may wish to find the moment a celestial body reaches a certain ecliptic longitude. In that case, the caller might create a type (class, tuple, whatever) that contains a Body member to specify the body and a numeric value to hold the target longitude. A different function might use a completely different context type. Every time it is called, func returns a float value or it raises an exception. If func raises an exception, the search immediately fails and the exception is propagated back to the caller. Otherwise, the search proceeds until it either finds the ascending root or fails for some reason. The search calls func repeatedly to rapidly narrow in on any ascending root within the time window specified by t1 and t2. The search never reports a solution outside this time window. Search uses a combination of bisection and quadratic interpolation to minimize the number of function calls. However, it is critical that the supplied time window be small enough that there cannot be more than one root (ascedning or descending) within it; otherwise the search can fail. Beyond that, it helps to make the time window as small as possible, ideally such that the function itself resembles a smooth parabolic curve within that window. If an ascending root is not found, or more than one root (ascending and/or descending) exists within the window t1..t2, Search will return None to indicate a normal search failure. If the search does not converge within 20 iterations, it will raise an Error exception.

Type Parameter Description
function(context, Time) func A function that takes an arbitrary context parameter and a Time parameter. Returns a float value. See remarks above for more details.
object context An arbitrary data structure needed to be passed to the function func every time it is called.
float t1 The lower time bound of the search window. See remarks above for more details.
float t2 The upper time bound of the search window. See remarks above for more details.
float dt_tolerance_seconds Specifies an amount of time in seconds within which a bounded ascending root is considered accurate enough to stop. A typical value is 1 second.

Returns: Time or None If the search is successful, returns a #Time object that is within dt_tolerance_seconds of an ascending root. In this case, the returned time value will always be within the inclusive range [t1, t2]. If there is no ascending root, or there is more than one ascending root, the function returns None.

### SearchAltitude(body, observer, direction, dateStart, limitDays, altitude)

Finds the next time a body reaches a given altitude.

Finds when the given body ascends or descends through a given altitude angle, as seen by an observer at the specified location on the Earth. By using the appropriate combination of direction and altitude parameters, this function can be used to find when civil, nautical, or astronomical twilight begins (dawn) or ends (dusk). Civil dawn begins before sunrise when the Sun ascends through 6 degrees below the horizon. To find civil dawn, pass Direction.Rise for direction and -6 for altitude. Civil dusk ends after sunset when the Sun descends through 6 degrees below the horizon. To find civil dusk, pass Direction.Set for direction and -6 for altitude. Nautical twilight is similar to civil twilight, only the altitude value should be -12 degrees. Astronomical twilight uses -18 degrees as the altitude value.

Type Parameter Description
Body body The Sun, Moon, or any planet other than the Earth.
Observer observer The location where observation takes place.
Direction direction Either Direction.Rise to find an ascending altitude event or Direction.Set to find a descending altitude event.
Time startTime The date and time at which to start the search.
float limitDays The fractional number of days after dateStart that limits when the altitude event is to be found. Must be a positive number.
float altitude The desired altitude angle of the body's center above (positive) or below (negative) the observer's local horizon, expressed in degrees. Must be in the range [-90, +90].

Returns: Time or None If the altitude event time is found within the specified time window, this function returns that time. Otherwise, it returns None.

### SearchGlobalSolarEclipse(startTime)

Searches for a solar eclipse visible anywhere on the Earth's surface.

This function finds the first solar eclipse that occurs after startTime. A solar eclipse may be partial, annular, or total. See GlobalSolarEclipseInfo for more information. To find a series of solar eclipses, call this function once, then keep calling NextGlobalSolarEclipse as many times as desired, passing in the peak value returned from the previous call.

Type Parameter Description
Time startTime The date and time for starting the search for a solar eclipse.

Returns: GlobalSolarEclipseInfo

### SearchHourAngle(body, observer, hourAngle, startTime)

Searches for the time when a celestial body reaches a specified hour angle as seen by an observer on the Earth.

The hour angle of a celestial body indicates its position in the sky with respect to the Earth's rotation. The hour angle depends on the location of the observer on the Earth. The hour angle is 0 when the body reaches its highest angle above the horizon in a given day. The hour angle increases by 1 unit for every sidereal hour that passes after that point, up to 24 sidereal hours when it reaches the highest point again. So the hour angle indicates the number of hours that have passed since the most recent time that the body has culminated, or reached its highest point. This function searches for the next time a celestial body reaches the given hour angle after the date and time specified by startTime. To find when a body culminates, pass 0 for hourAngle. To find when a body reaches its lowest point in the sky, pass 12 for hourAngle. Note that, especially close to the Earth's poles, a body as seen on a given day may always be above the horizon or always below the horizon, so the caller cannot assume that a culminating object is visible nor that an object is below the horizon at its minimum altitude. On success, the function reports the date and time, along with the horizontal coordinates of the body at that time, as seen by the given observer.

Type Parameter Description
Body body The celestial body, which can the Sun, the Moon, or any planet other than the Earth.
Observer observer Indicates a location on or near the surface of the Earth where the observer is located.
float hourAngle An hour angle value in the range [0.0, 24.0) indicating the number of sidereal hours after the body's most recent culmination.
Time startTime The date and time at which to start the search.

Returns: HourAngleEvent

### SearchLocalSolarEclipse(startTime, observer)

Searches for a solar eclipse visible at a specific location on the Earth's surface. This function finds the first solar eclipse that occurs after startTime. A solar eclipse may be partial, annular, or total. See LocalSolarEclipseInfo for more information. To find a series of solar eclipses, call this function once, then keep calling NextLocalSolarEclipse as many times as desired, passing in the peak value returned from the previous call. IMPORTANT: An eclipse reported by this function might be partly or completely invisible to the observer due to the time of day. See LocalSolarEclipseInfo for more information about this topic.

Type Parameter Description
Time startTime The date and time for starting the search for a solar eclipse.
Observer observer The geographic location of the observer.

Returns: LocalSolarEclipseInfo

### SearchLunarApsis(startTime)

Finds the time of the first lunar apogee or perigee after the given time.

Given a date and time to start the search in startTime, this function finds the next date and time that the center of the Moon reaches the closest or farthest point in its orbit with respect to the center of the Earth, whichever comes first after startTime. The return value (of type Apsis) also contains an indicator of whether the event is apogee or perigee. The closest point is called perigee and the farthest point is called apogee. The word apsis refers to either event. To iterate through consecutive alternating perigee and apogee events, call SearchLunarApsis once, then use the return value to call NextLunarApsis. After that, keep feeding the previous return value from NextLunarApsis into another call of NextLunarApsis as many times as desired.

Type Parameter Description
Time startTime The date and time at which to start searching for the next perigee or apogee.

Returns: Apsis

### SearchLunarEclipse(startTime)

Searches for a lunar eclipse.

This function finds the first lunar eclipse that occurs after startTime. A lunar eclipse may be penumbral, partial, or total. See LunarEclipseInfo for more information. To find a series of lunar eclipses, call this function once, then keep calling NextLunarEclipse as many times as desired, passing in the peak value returned from the previous call.

Type Parameter Description
Time startTime The date and time for starting the search for a lunar eclipse.

Returns: LunarEclipseInfo

### SearchMaxElongation(body, startTime)

Finds a date and time when Mercury or Venus reaches its maximum angle from the Sun as seen from the Earth.

Mercury and Venus are are often difficult to observe because they are closer to the Sun than the Earth is. Mercury especially is almost always impossible to see because it gets lost in the Sun's glare. The best opportunities for spotting Mercury, and the best opportunities for viewing Venus through a telescope without atmospheric interference, are when these planets reach maximum elongation. These are events where the planets reach the maximum angle from the Sun as seen from the Earth. This function solves for those times, reporting the next maximum elongation event's date and time, the elongation value itself, the relative longitude with the Sun, and whether the planet is best observed in the morning or evening. See ElongationEvent for more details about the returned object.

Type Parameter Description
Body body Either Body.Mercury or Body.Venus. Any other value will result in an exception. To find the best viewing opportunities for planets farther from the Sun than the Earth is (Mars through Pluto), use SearchRelativeLongitude to find the next opposition event.
Time startTime The date and time at which to begin the search. The maximum elongation event found will always be the first one that occurs after this date and time.

Returns: ElongationEvent

### SearchMoonNode(startTime)

Searches for a time when the Moon's center crosses through the ecliptic plane.

Searches for the first ascending or descending node of the Moon after startTime. An ascending node is when the Moon's center passes through the ecliptic plane (the plane of the Earth's orbit around the Sun) from south to north. A descending node is when the Moon's center passes through the ecliptic plane from north to south. Nodes indicate possible times of solar or lunar eclipses, if the Moon also happens to be in the correct phase (new or full, respectively). Call SearchMoonNode to find the first of a series of nodes. Then call NextMoonNode to find as many more consecutive nodes as desired.

Type Parameter Description
Time startTime The date and time for starting the search for an ascending or descending node of the Moon.

Returns: NodeEventInfo

### SearchMoonPhase(targetLon, startTime, limitDays)

Searches for the time that the Moon reaches a specified phase.

Lunar phases are conventionally defined in terms of the Moon's geocentric ecliptic longitude with respect to the Sun's geocentric ecliptic longitude. When the Moon and the Sun have the same longitude, that is defined as a new moon. When their longitudes are 180 degrees apart, that is defined as a full moon. This function searches for any value of the lunar phase expressed as an angle in degrees in the range [0, 360). If you want to iterate through lunar quarters (new moon, first quarter, full moon, third quarter) it is much easier to call the functions SearchMoonQuarter and NextMoonQuarter. This function is useful for finding general phase angles outside those four quarters.

Type Parameter Description
float targetLon The difference in geocentric longitude between the Sun and Moon that specifies the lunar phase being sought. This can be any value in the range [0, 360). Certain values have conventional names: 0 = new moon, 90 = first quarter, 180 = full moon, 270 = third quarter.
Time startTime The beginning of the time window in which to search for the Moon reaching the specified phase.
float limitDays The number of days after startTime that limits the time window for the search.

Returns: Time or None

### SearchMoonQuarter(startTime)

Finds the first lunar quarter after the specified date and time.

A lunar quarter is one of the following four lunar phase events: new moon, first quarter, full moon, third quarter. This function finds the lunar quarter that happens soonest after the specified date and time. To continue iterating through consecutive lunar quarters, call this function once, followed by calls to NextMoonQuarter as many times as desired.

Type Parameter Description
Time startTime The date and time at which to start the search.

Returns: MoonQuarter

### SearchPeakMagnitude(body, startTime)

Searches for the date and time Venus will next appear brightest as seen from the Earth.

This function searches for the date and time Venus appears brightest as seen from the Earth. Currently only Venus is supported for the body parameter, though this could change in the future. Mercury's peak magnitude occurs at superior conjunction, when it is virtually impossible to see from the Earth, so peak magnitude events have little practical value for that planet. Planets other than Venus and Mercury reach peak magnitude at opposition, which can be found using SearchRelativeLongitude. The Moon reaches peak magnitude at full moon, which can be found using SearchMoonQuarter or SearchMoonPhase. The Sun reaches peak magnitude at perihelion, which occurs each year in January. However, the difference is minor and has little practical value.

Type Parameter Description
Body body Currently only Body.Venus is allowed. Any other value results in an exception. See remarks above for more details.
Time startTime The date and time to start searching for the next peak magnitude event.

Returns: IlluminationInfo

### SearchPlanetApsis(body, startTime)

Finds the next planet perihelion or aphelion, after a given time.

Given a date and time to start the search in startTime, this function finds the next date and time that the center of the specified planet reaches the closest or farthest point in its orbit with respect to the center of the Sun, whichever comes first after startTime. The closest point is called perihelion and the farthest point is called aphelion. The word apsis refers to either event. To iterate through consecutive alternating perihelion and aphelion events, call SearchPlanetApsis once, then use the return value to call NextPlanetApsis. After that, keep feeding the previous return value from NextPlanetApsis into another call of NextPlanetApsis as many times as desired.

Type Parameter Description
Body body The planet for which to find the next perihelion/aphelion event. Not allowed to be Body.Sun or Body.Moon.
Time startTime The date and time at which to start searching for the next perihelion or aphelion.

Returns: Apsis

### SearchRelativeLongitude(body, targetRelLon, startTime)

Searches for when the Earth and another planet are separated by a certain ecliptic longitude.

Searches for the time when the Earth and another planet are separated by a specified angle in ecliptic longitude, as seen from the Sun. A relative longitude is the angle between two bodies measured in the plane of the Earth's orbit (the ecliptic plane). The distance of the bodies above or below the ecliptic plane is ignored. If you imagine the shadow of the body cast onto the ecliptic plane, and the angle measured around that plane from one body to the other in the direction the planets orbit the Sun, you will get an angle somewhere between 0 and 360 degrees. This is the relative longitude. Given a planet other than the Earth in body and a time to start the search in startTime, this function searches for the next time that the relative longitude measured from the planet to the Earth is targetRelLon. Certain astronomical events are defined in terms of relative longitude between the Earth and another planet:

• When the relative longitude is 0 degrees, it means both planets are in the same direction from the Sun. For planets that orbit closer to the Sun (Mercury and Venus), this is known as inferior conjunction, a time when the other planet becomes very difficult to see because of being lost in the Sun's glare. (The only exception is in the rare event of a transit, when we see the silhouette of the planet passing between the Earth and the Sun.)
• When the relative longitude is 0 degrees and the other planet orbits farther from the Sun, this is known as opposition. Opposition is when the planet is closest to the Earth, and also when it is visible for most of the night, so it is considered the best time to observe the planet.
• When the relative longitude is 180 degrees, it means the other planet is on the opposite side of the Sun from the Earth. This is called superior conjunction. Like inferior conjunction, the planet is very difficult to see from the Earth. Superior conjunction is possible for any planet other than the Earth.
Type Parameter Description
Body body A planet other than the Earth. If body is not a planet, or if it is Body.Earth, an error occurs.
float targetRelLon The desired relative longitude, expressed in degrees. Must be in the range [0, 360).
Time startTime The date and time at which to begin the search.

Returns: Time The date and time of the relative longitude event.

### SearchRiseSet(body, observer, direction, startTime, limitDays)

Searches for the next time a celestial body rises or sets as seen by an observer on the Earth.

This function finds the next rise or set time of the Sun, Moon, or planet other than the Earth. Rise time is when the body first starts to be visible above the horizon. For example, sunrise is the moment that the top of the Sun first appears to peek above the horizon. Set time is the moment when the body appears to vanish below the horizon. This function corrects for typical atmospheric refraction, which causes celestial bodies to appear higher above the horizon than they would if the Earth had no atmosphere. It also adjusts for the apparent angular radius of the observed body (significant only for the Sun and Moon). Note that rise or set may not occur in every 24 hour period. For example, near the Earth's poles, there are long periods of time where the Sun stays below the horizon, never rising. Also, it is possible for the Moon to rise just before midnight but not set during the subsequent 24-hour day. This is because the Moon sets nearly an hour later each day due to orbiting the Earth a significant amount during each rotation of the Earth. Therefore callers must not assume that the function will always succeed.

Type Parameter Description
Body body The Sun, Moon, or any planet other than the Earth.
Observer observer The location where observation takes place.
Direction direction Either Direction.Rise to find a rise time or Direction.Set to find a set time.
Time startTime The date and time at which to start the search.
float limitDays Limits how many days to search for a rise or set time. To limit a rise or set time to the same day, you can use a value of 1 day. In cases where you want to find the next rise or set time no matter how far in the future (for example, for an observer near the south pole), you can pass in a larger value like 365.

Returns: Time or None If the rise or set time is found within the specified time window, this function returns that time. Otherwise, it returns None.

### SearchSunLongitude(targetLon, startTime, limitDays)

Searches for the time when the Sun reaches an apparent ecliptic longitude as seen from the Earth.

This function finds the moment in time, if any exists in the given time window, that the center of the Sun reaches a specific ecliptic longitude as seen from the center of the Earth. This function can be used to determine equinoxes and solstices. However, it is usually more convenient and efficient to call Seasons to calculate all equinoxes and solstices for a given calendar year. The function searches the window of time specified by startTime and startTime+limitDays. The search will return None if the Sun never reaches the longitude targetLon or if the window is so large that the longitude ranges more than 180 degrees within it. It is recommended to keep the window smaller than 10 days when possible.

Type Parameter Description
float targetLon The desired ecliptic longitude in degrees, relative to the true equinox of date. This may be any value in the range [0, 360), although certain values have conventional meanings: 0 = March equinox, 90 = June solstice, 180 = September equinox, 270 = December solstice.
Time startTime The date and time for starting the search for the desired longitude event.
float limitDays The real-valued number of days, which when added to startTime, limits the range of time over which the search looks. It is recommended to keep this value between 1 and 10 days. See remarks above for more details.

Returns: Time or None

### SearchTransit(body, startTime)

Searches for the first transit of Mercury or Venus after a given date.

Finds the first transit of Mercury or Venus after a specified date. A transit is when an inferior planet passes between the Sun and the Earth so that the silhouette of the planet is visible against the Sun in the background. To continue the search, pass the finish time in the returned structure to NextTransit.

Type Parameter Description
Body body The planet whose transit is to be found. Must be Body.Mercury or Body.Venus.
Time startTime The date and time for starting the search for a transit.

Returns: TransitInfo

### Seasons(year)

Finds both equinoxes and both solstices for a given calendar year.

The changes of seasons are defined by solstices and equinoxes. Given a calendar year number, this function calculates the March and September equinoxes and the June and December solstices. The equinoxes are the moments twice each year when the plane of the Earth's equator passes through the center of the Sun. In other words, the Sun's declination is zero at both equinoxes. The March equinox defines the beginning of spring in the northern hemisphere and the beginning of autumn in the southern hemisphere. The September equinox defines the beginning of autumn in the northern hemisphere and the beginning of spring in the southern hemisphere. The solstices are the moments twice each year when one of the Earth's poles is most tilted toward the Sun. More precisely, the Sun's declination reaches its minimum value at the December solstice, which defines the beginning of winter in the northern hemisphere and the beginning of summer in the southern hemisphere. The Sun's declination reaches its maximum value at the June solstice, which defines the beginning of summer in the northern hemisphere and the beginning of winter in the southern hemisphere.

Type Parameter Description
int year The calendar year number for which to calculate equinoxes and solstices. The value may be any integer, but only the years 1800 through 2100 have been validated for accuracy: unit testing against data from the United States Naval Observatory confirms that all equinoxes and solstices for that range of years are within 2 minutes of the correct time.

Returns: SeasonInfo

### SiderealTime(time)

Calculates Greenwich Apparent Sidereal Time (GAST).

Given a date and time, this function calculates the rotation of the Earth, represented by the equatorial angle of the Greenwich prime meridian with respect to distant stars (not the Sun, which moves relative to background stars by almost one degree per day). This angle is called Greenwich Apparent Sidereal Time (GAST). GAST is measured in sidereal hours in the half-open range [0, 24). When GAST = 0, it means the prime meridian is aligned with the of-date equinox, corrected at that time for precession and nutation of the Earth's axis. In this context, the "equinox" is the direction in space where the Earth's orbital plane (the ecliptic) intersects with the plane of the Earth's equator, at the location on the Earth's orbit of the (seasonal) March equinox. As the Earth rotates, GAST increases from 0 up to 24 sidereal hours, then starts over at 0. To convert to degrees, multiply the return value by 15.

Type Parameter Description
Time time The date and time for which to find GAST. As an optimization, this function caches the sideral time value in time, unless it has already been cached, in which case the cached value is reused.

Returns: float GAST expressed in sidereal hours.

### SphereFromVector(vector)

Converts Cartesian coordinates to spherical coordinates.

Given a Cartesian vector, returns latitude, longitude, and distance.

Type Parameter Description
Vector vector Cartesian vector to be converted to spherical coordinates.

Returns: Spherical Spherical coordinates that are equivalent to the given vector.

### SunPosition(time)

Calculates geocentric ecliptic coordinates for the Sun.

This function calculates the position of the Sun as seen from the Earth. The returned value includes both Cartesian and spherical coordinates. The x-coordinate and longitude values in the returned object are based on the true equinox of date: one of two points in the sky where the instantaneous plane of the Earth's equator at the given date and time (the equatorial plane) intersects with the plane of the Earth's orbit around the Sun (the ecliptic plane). By convention, the apparent location of the Sun at the March equinox is chosen as the longitude origin and x-axis direction, instead of the one for September. SunPosition corrects for precession and nutation of the Earth's axis in order to obtain the exact equatorial plane at the given time. This function can be used for calculating changes of seasons: equinoxes and solstices. In fact, the function Seasons does use this function for that purpose.

Type Parameter Description
Time time The date and time for which to calculate the Sun's position.

Returns: EclipticCoordinates The ecliptic coordinates of the Sun using the Earth's true equator of date.

### VectorFromHorizon(sphere, time, refraction)

Given apparent angular horizontal coordinates in sphere, calculate horizontal vector.

Type Parameter Description
Spherical sphere A structure that contains apparent horizontal coordinates: lat holds the refracted azimuth angle, lon holds the azimuth in degrees clockwise from north, and dist holds the distance from the observer to the object in AU.
Time time The date and time of the observation. This is needed because the returned vector object requires a valid time value when passed to certain other functions.
Refraction refraction See remarks in function RefractionAngle.

Returns: Vector A vector in the horizontal system: x = north, y = west, and z = zenith (up).

### VectorFromSphere(sphere, time)

Converts spherical coordinates to Cartesian coordinates.

Given spherical coordinates and a time at which they are valid, returns a vector of Cartesian coordinates. The returned value includes the time, as required by all Time objects.

Type Parameter Description
Spherical sphere Spherical coordinates to be converted.
Time time The time that should be included in the returned vector.

Returns: Vector The vector form of the supplied spherical coordinates.

### VectorObserver(vector, ofdate)

Calculates the geographic location corresponding to an equatorial vector.

This is the inverse function of ObserverVector. Given a geocentric equatorial vector, it returns the geographic latitude, longitude, and elevation for that vector.

Type Parameter Description
Vector vector The geocentric equatorial position vector for which to find geographic coordinates. The components are expressed in astronomical units (AU). The time vector.t determines the Earth's rotation.
bool ofdate Selects the date of the Earth's equator in which vector is expressed. The caller may pass False to use the orientation of the Earth's equator at noon UTC on January 1, 2000, in which case this function corrects for precession and nutation of the Earth as it was at the moment specified by the the time vector.t. Or the caller may pass True to use the Earth's equator at vector.t as the orientation.

Returns: Observer The geographic latitude, longitude, and elevation above sea level that corresponds to the given equatorial vector.

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