pyorb 0.5.1

Keplerian orbit functions in Python

PyOrb

PyOrb is a lightweight package designed to convert back and forth between cartesian and kepler coordinates seamlessly and in a physically consistent manner, following defined rules. It provides a convenience class for handling orbits and is tested for special cases such as planar and circular orbits.

See full documentation here.

Feature list

Current features:

• Clear definition of an orbit, consistent throughout the code, including planar and circular orbits
• Kepler to Cartesian conversion
• Cartesian to Kepler conversion
• Can handle hyperbolic orbits
• All function handles all special cases (e.g. planar, circular and parabolic orbits)
• Convenient Orbit class or storing orbits and seamlessly convert between Kepler and Cartesian elements
• Access to all types of orbit anomalies
• Vectorized function for increased performance
• Access to alternative parameterizations such as Equinoctial elements

On the upcoming feature list:

• C-implementation of conversion function for performance
• Converting of orbits to a byte-stream
• Saving orbits to file (binary or HDFS 5)

To install

pip install pyorb

or to do the "nightly" build:

git clone https://github.com/danielk333/pyorb
cd pyorb
git checkout develop
pip install .

Alternatively, if you are following updates closely you can install using pip install -e . so that in the future a git pull will update the library.

Example

import pyorb

orb = pyorb.Orbit(M0 = pyorb.M_sol, degrees=True)
orb.update(a=1*pyorb.AU, e=0, i=0, omega=0, Omega=0, anom=0)

# Convert and get cartesian elements
print(orb.cartesian)

# Make eccentric and place at aphelion
orb.e = 0.2
orb.anom = 180

# print cartesian position in AU at aphelion after the above changes
print(orb.r/pyorb.AU)

Ellipse and angle definitions

Variables:

• a: Semi-major axis
• e: Eccentricity
• i: Inclination
• omega: Argument of perihelion
• Omega: Longitude of the ascending node
• nu: True anomaly
• E: Elliptic, parabolic or hyperbolic eccentric anomaly
• M: Mean anomaly

Orientation of the ellipse in the coordinate system and angle definitions:

• For zero inclination: the ellipse is located in the x-y plane.
• The direction of motion as True anomaly increases for a zero inclination orbit is anti-coockwise, i.e. from +x towards +y.
• If the eccentricity is increased for an unrotated orbit, the periapsis will lie in +x direction.
• If the inclination is increased, the ellipse will rotate around the x-axis, so that +y is rotated toward +z.
• An increase in Longitude of the ascending node corresponds to a rotation around the z-axis so that +x is rotated toward +y.
• Changing argument of perihelion will not change the plane of the orbit, it will rotate the orbit in the plane.
• Changing argument of perihelion will rotate the periapsis in the direction of motion.
• True anomaly measures from the +x axis, i.e nu = 0 is located at periapsis and nu = pi at apoapsis.
• All anomalies and orientation angles reach between 0 and 2pi
• If the inclination is 0 or pi the longitude of the ascending node is always zero (the rotation is described by only argument of perihelion).
• If the eccentricity is zero, the argument of perihelion is always zero (the rotation is described by only the longitude of the ascending node).
• If both e=0 and i=0 or i=pi: the position on the circle is only described by the anomaly.
• The eccentric anomaly is used for elliptic, parabolic and hyperbolic cases but the kepler equation changes accordingly.
• For parabolic and hyperbolic orbits the true and eccentric anomaly wraps at pi to the same trajectory, not the mirror version.

Shape definitions:

• The Semi-major axis is always positive.
• In the case of a parabolic orbit, as the Semi-major axis is undefined it is used as the periapsis distance instead.

Notes

Disabling direct conversion

There are two toggle flags in the pyorb.Orbit class for changing the conversion behavior: direct_update and auto_update that are True by default.

Disabling direct_update will stop automatic conversion between elements if any element is changed. This would allow for e.g.

orb.a = 1
orb.omega = 0

without any conversion to be done. However, as the kepler elements changed, the class has internally tracked this change and if auto_update=True once an access to a cartesian property is performed, e.g. print(orb.x), the conversion is performed so that the pair of cartesian-kepler elements are never contradictory.

If also auto_update is disabled, the update between kepler and cartesian needs to be manually by calling

orb.calculate_cartesian()

or

orb.calculate_kepler()

Using conversion functions directly

The pyorb.cart_to_kep or pyorb.kep_to_cart uses True anomaly and takes only numpy arrays ordered as per the function documentation.

Frames

Remember that an Keplerian orbit only makes sense in an inertial frame if gravitation dominated physics is your concern.

Array orbits

• Properties act on ALL orbits in the class
• Only way to update individual orbits of a set is to use self.update with the inds keyword
• Iterations are passive, the objects are copies from the array so the array itself is NOT modified

MIT License

Copyright (c) [2023] [Daniel Kastinen]

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.