Use a JPL ephemeris to predict planet positions.
This package can load and use a Jet Propulsion Laboratory (JPL) ephemeris for predicting the position and velocity of a planet or other Solar System body. It only needs NumPy, which pip will automatically attempt to install alongside pyephem when you run:
$ pip install jplephem
Note that jplephem offers only the logic necessary to produce plain three-dimensional vectors. Most programmers interested in astronomy will want to look at Skyfield instead, which uses jplephem but converts the numbers into more traditional measurements like right ascension and declination.
Most users will use jplephem with the Satellite Planet Kernel (SPK) files that the NAIF facility at NASA JPL offers for use with their own SPICE toolkit. They have collected their most useful kernels beneath the directory:
To learn more about SPK files, the official SPK Required Reading document is available from the NAIF facility’s web site under the NASA JPL domain.
Command Line Tool
If you have downloaded a .bsp file, you can run jplephem from the command line to display the data inside of it:
python -m jplephem comment de421.bsp python -m jplephem daf de421.bsp python -m jplephem spk de421.bsp
You can also take a large ephemeris and produce a smaller excerpt by limiting the range of dates that it covers:
python -m jplephem excerpt 2018/1/1 2018/4/1 de421.bsp excerpt421.bsp
You will get an error if your starting year is negative, because Unix commands expect a list of options when they see a dash. The fix is to provide a special argument -- which says “I’m done passing options, even if the next argument stars with a dash”:
python -m jplephem excerpt – -800/1/1 800/1/1 de422.bsp excerpt422.bsp
You can also filter by the integer codes for the targets you need. Unrecognized targets will not raise an error, to let you apply a master list of targets to a whole series of SPK files that might or might not each have all of the targets:
python -m jplephem excerpt --targets 1,2,3 2018/1/1 2018/4/1 de421.bsp excerpt421.bsp
If the input ephemeris is a URL, then jplephem will try to save bandwidth by fetching only the blocks of the remote file that are necessary to cover the dates you have specified. For example, the Jupiter satellite ephemeris jup310.bsp is famously large, weighing in a nearly a gigabyte. But if all you need are Jupiter’s satellites for a few months, you can download considerably less data:
$ python -m jplephem excerpt 2018/1/1 2018/4/1 \ https://naif.jpl.nasa.gov/pub/naif/generic_kernels/spk/satellites/jup310.bsp \ excerpt.bsp $ ls -lh excerpt.bsp -rw-r----- 1 brandon brandon 1.2M Feb 11 13:36 excerpt.bsp
In this case only about one-thousandth of the ephemeris’s data needed to be downloaded.
Getting Started With DE421
The DE421 ephemeris is a useful starting point. It weighs in at 17 MB, but provides predictions over the years 1900–2050:
After the kernel has downloaded, you can use jplephem to load this SPK file and learn about the segments it offers:
>>> from jplephem.spk import SPK >>> kernel = SPK.open('de421.bsp') >>> print(kernel) File type DAF/SPK and format LTL-IEEE with 15 segments: 2414864.50..2471184.50 Type 2 Solar System Barycenter (0) -> Mercury Barycenter (1) 2414864.50..2471184.50 Type 2 Solar System Barycenter (0) -> Venus Barycenter (2) 2414864.50..2471184.50 Type 2 Solar System Barycenter (0) -> Earth Barycenter (3) 2414864.50..2471184.50 Type 2 Solar System Barycenter (0) -> Mars Barycenter (4) 2414864.50..2471184.50 Type 2 Solar System Barycenter (0) -> Jupiter Barycenter (5) 2414864.50..2471184.50 Type 2 Solar System Barycenter (0) -> Saturn Barycenter (6) 2414864.50..2471184.50 Type 2 Solar System Barycenter (0) -> Uranus Barycenter (7) 2414864.50..2471184.50 Type 2 Solar System Barycenter (0) -> Neptune Barycenter (8) 2414864.50..2471184.50 Type 2 Solar System Barycenter (0) -> Pluto Barycenter (9) 2414864.50..2471184.50 Type 2 Solar System Barycenter (0) -> Sun (10) 2414864.50..2471184.50 Type 2 Earth Barycenter (3) -> Moon (301) 2414864.50..2471184.50 Type 2 Earth Barycenter (3) -> Earth (399) 2414864.50..2471184.50 Type 2 Mercury Barycenter (1) -> Mercury (199) 2414864.50..2471184.50 Type 2 Venus Barycenter (2) -> Venus (299) 2414864.50..2471184.50 Type 2 Mars Barycenter (4) -> Mars (499)
Since the next few examples involve vector output, let’s tell NumPy to make vector output attractive.
>>> import numpy as np >>> np.set_printoptions(precision=3)
Each segment of the file lets you predict the position of an object with respect to some other reference point. If you want the coordinates of Mars at 2457061.5 (2015 February 8) with respect to the center of the solar system, this ephemeris only requires you to take a single step:
>>> position = kernel[0,4].compute(2457061.5) >>> print(position) [2.057e+08 4.251e+07 1.394e+07]
But learning the position of Mars with respect to the Earth takes three steps, from Mars to the Solar System barycenter to the Earth-Moon barycenter and finally to Earth itself:
>>> position = kernel[0,4].compute(2457061.5) >>> position -= kernel[0,3].compute(2457061.5) >>> position -= kernel[3,399].compute(2457061.5) >>> print(position) [ 3.161e+08 -4.679e+07 -2.476e+07]
You can see that the output of this ephemeris is in kilometers. If you use another ephemeris, check its documentation to be sure of the units that it employs.
If you supply the date as a NumPy array, then each component that is returned will itself be a vector as long as your date:
>>> jd = np.array([2457061.5, 2457062.5, 2457063.5, 2457064.5]) >>> position = kernel[0,4].compute(jd) >>> print(position) [[2.057e+08 2.053e+08 2.049e+08 2.045e+08] [4.251e+07 4.453e+07 4.654e+07 4.855e+07] [1.394e+07 1.487e+07 1.581e+07 1.674e+07]]
Some ephemerides include velocity inline by returning a 6-vector instead of a 3-vector. For an ephemeris that does not, you can ask for the Chebyshev polynomial to be differentiated to produce a velocity, which is delivered as a second return value:
>>> position, velocity = kernel[0,4].compute_and_differentiate(2457061.5) >>> print(position) [2.057e+08 4.251e+07 1.394e+07] >>> print(velocity) [-363896.059 2019662.996 936169.773]
The velocity will by default be distance traveled per day, in whatever units for distance the ephemeris happens to use. To get a velocity per second, simply divide by the number of seconds in a day:
>>> velocity_per_second = velocity / 86400.0 >>> print(velocity_per_second) [-4.212 23.376 10.835]
Details of the API
Here are a few details for people ready to go beyond the high-level API provided above and read through the code to learn more.
Instead of reading an entire ephemeris into memory, jplephem memory-maps the underlying file so that the operating system can efficiently page into RAM only the data that your code is using.
Once the metadata has been parsed from the binary SPK file, the polynomial coefficients themselves are loaded by building a NumPy array object that has access to the raw binary file contents. Happily, NumPy already knows how to interpret a packed array of double-precision floats. You can learn about the underlying DAF “Double Precision Array File” format, in case you ever need to open other such array files in Python, through the DAF class in the module jplephem.daf.
An SPK file is made of segments. When you first create an SPK kernel object k, it examines the file and creates a list of Segment objects that it keeps in a list under an attribute named k.segments which you are free to examine in your own code by looping over it.
There is more information about each segment beyond the one-line summary that you get when you print out the SPK file, which you can see by asking the segment to print itself verbosely:
>>> segment = kernel[3,399] >>> print(segment.describe()) 2414864.50..2471184.50 Type 2 Earth Barycenter (3) -> Earth (399) frame=1 source=DE-0421LE-0421
Each Segment loaded from the kernel has a number of attributes that are loaded from the SPK file:
>>> from jplephem.spk import BaseSegment >>> help(BaseSegment) Help on class BaseSegment in module jplephem.spk: ... | segment.source - official ephemeris name, like 'DE-0430LE-0430' | segment.start_second - initial epoch, as seconds from J2000 | segment.end_second - final epoch, as seconds from J2000 | segment.start_jd - start_second, converted to a Julian Date | segment.end_jd - end_second, converted to a Julian Date | segment.center - integer center identifier | segment.target - integer target identifier | segment.frame - integer frame identifier | segment.data_type - integer data type identifier | segment.start_i - index where segment starts | segment.end_i - index where segment ends ...
If you want to access the raw coefficients, use the segment load_array() method. It returns two floats and a NumPy array:
>>> initial_epoch, interval_length, coefficients = segment.load_array() >>> print(coefficients.shape) (3, 14080, 13)
The square-bracket lookup mechanism kernel[3,399] is a non-standard convenience that returns only the last matching segment in the file. While the SPK standard does say that the last segment takes precedence, it also says that earlier segments for a particular center-target pair should be fallen back upon for dates that the last segment does not cover. So, if you ever tackle a complicated kernel, you will need to implement fallback rules that send some dates to the final segment for a given center and target, but that send other dates to earlier segments that are qualified to cover them.
If you are accounting for light travel time and require repeated computation of the position, but then need the velocity at the end, and want to avoid repeating the expensive position calculation, then try out the segment.generate() method - it will let you ask for the position, and then only proceed to the velocity once you are sure that the light-time error is now small enough.
Since all modern Julian dates are numbers larger than 2.4 million, a standard 64-bit Python or NumPy float necessarily leaves only a limited number of bits available for the fractional part. Technical Note 2011-02 from the United States Naval Observatory’s Astronomical Applications Department suggests that the precision possible with a 64-bit floating point Julian date is around 20.1 µs.
If you need to supply times and receive back planetary positions with greater precision than 20.1 µs, then you have two options.
First, you can supply times using the special float96 NumPy type, which is also aliased to the name longfloat. If you provide either a float96 scalar or a float96 array as your tdb parameter to any jplephem routine, you should get back a high-precision result.
Second, you can split your date or dates into two pieces, and supply them as a pair of arguments two tdb and tdb2. One popular approach for how to split your date is to use the tdb float for the integer Julian date, and tdb2 for the fraction that specifies the time of day. Nearly all jplephem routines accept this optional tdb2 argument if you wish to provide it, thanks to the work of Marten van Kerkwijk!
Support for Binary PCKs
You can also load and produce rotation matrices from a binary PCK file. Its segments are available through the segments attributes of the returned object.
>>> from jplephem.pck import PCK >>> p = PCK.open('moon_pa_de421_1900-2050.bpc') >>> p.segments.body 31006 >>> p.segments.frame 1 >>> p.segments.data_type 2
Given a solary system barycenter Julian date, the segment will return the three angles necessary to build a rotation matrix: right ascension of the pole, declination of the pole, and cumulative rotation of the body’s axis. Typically these will all be in radians.
>>> tdb = 2454540.34103 >>> print(p.segments.compute(tdb, 0.0, False)) [3.928e-02 3.878e-01 3.253e+03]
You can ask for velocity as well.
>>> r, v = p.segments.compute(tdb, 0.0, True) >>> print(r) [3.928e-02 3.878e-01 3.253e+03] >>> print(v) [6.707e-09 4.838e-10 2.655e-06]
Legacy Ephemeris Packages
Back before I learned about SPICE and SPK files, I had run across the text-file formatted JPL ephemerides at:
I laboriously assembled the data in these text files into native NumPy array files and wrapped them each in a Python package so that users could install an ephemeris with a simple command:
pip install de421
If you want to use one of these pip-installable ephemerides, you will be using a slightly older API, and will lose the benefit of the efficient memory-mapping that the newer SPK code performs. With the old API, here is how you would load DE421 and compute a position, given a barycentric dynamical time expressed as a Julian date:
import de421 from jplephem import Ephemeris eph = Ephemeris(de421) x, y, z = eph.position('mars', 2444391.5) # 1980.06.01
For more information about the legacy API, consult the jplephem entry on PyPI for the final release of the 1.x series:
The ephemerides that were made available as Python packages (the following links explain the differences between them) are:
- DE405 (May 1997) — 54 MB covering years 1600 through 2200
- DE406 (May 1997) — 190 MB covering years -3000 through 3000
- DE421 (February 2008) — 27 MB covering years 1900 through 2050
- DE422 (September 2009) — 531 MB covering years -3000 through 3000
- DE423 (February 2010) — 36 MB covering years 1800 through 2200
You can report any issues, bugs, or problems at the GitHub repository:
2021 July 3 — Version 2.16
- Fixed a ValueError raised in the excerpt command when an ephemeris segment needs to be entirely skipped because it has no overlap with the user-specified range of dates.
- Added a __version__ constant to the package’s top level.
2020 September 2 — Version 2.15
- The excerpt subcommand now accepts a --targets option to save space by copying only matching segments into the output SPK file.
- The Julian day fraction tdb2 is handled even more carefully than before, providing a smoother delta between successive positions when the difference between successive times is down around 0.1 µs.
2020 March 26 — Version 2.14
- Fall back to plain file I/O on platforms that support fileno() but that don’t support mmap(), like the Pyodide platform.
2020 February 22 — Version 2.13
- The exception raised when a segment is given a Julian date outside the segment’s date range is now an instance of the ValueError subclass OutOfRangeError that reminds the caller of the range of dates supported by the SPK segment, and carries an array attribute indicating which input dates were at fault.
2019 December 13 — Version 2.12
- Replaced use of NumPy flip() with a reverse slice [::-1] after discovering the function was a recent addition that some user installs of NumPy do not support.
2019 December 13 — Version 2.11
- Reverse the order in which Chebyshev polynomials are computed to slightly increase speed, to simplify the code, and in one case (comparing PCK output to NASA) to gain a partial digit of extra precision.
2019 December 11 — Version 2.10
- Document and release support for .bcp binary PCK kernel files through the new jplephem.pck module.
2019 January 3 — Version 2.9
- Added the load_array() method to the segment class.
2018 July 22 — Version 2.8
- Switched to a making a single memory map of the entire file, to avoid running out of file descriptors when users load an ephemeris with hundreds of segments.
2018 February 11 — Version 2.7
- Expanded the command line tool, most notably with the ability to fetch over HTTP only those sections of a large ephemeris that cover a specific range of dates, producing a smaller .bsp file.
2016 December 19 — Version 2.6
- Fixed the ability to invoke the module from the command line with python -m jplephem, and added a test to keep it fixed.
2015 November 9 — Version 2.5
- Move fileno() call out of the DAF constructor to support fetching at least summary information from StringIO objects.
2015 November 1 — Version 2.4
- Add Windows compatibility by switching mmap() from using PAGESIZE to ALLOCATIONGRANULARITY.
- Avoid a new NumPy deprecation warning by being careful to use only integers in the NumPy shape tuple.
- Add names “TDB” and “TT” to the names database for DE430.
2015 August 16 — Version 2.3
- Added auto-detection and support for old NAIF/DAF kernels like de405.bsp to the main DAF class itself, instead of requiring the awkward use of an entirely different alternative class.
2015 August 5 — Version 2.2
- You can now invoke jplephem from the command line.
- Fixes an exception that was raised for SPK segments with a coefficient count of only 2, like the DE421 and DE430 segments that provide the offset of Mercury from the Mercury barycenter.
- Supports old NAIF/DAF kernels like de405.bsp.
- The SPK() constructor is now simpler, taking a DAF object instead of an open file. This is considered an internal API change — the public API is the constructor SPK.open().
2015 February 24 — Version 2.1
- Switched from mapping an entire SPK file into memory at once to memory-mapping each segment separately on demand.
2015 February 8 — Version 2.0
- Added support for SPICE SPK kernel files downloaded directly from NASA, and designated old Python-packaged ephemerides as “legacy.”
2013 November 26 — Version 1.2
- Helge Eichhorn fixed the default for the position_and_velocity() argument tdb2 so it defaults to zero days instead of 2.0 days. Tests were added to prevent any future regression.
2013 July 10 — Version 1.1
- Deprecates the old compute() method in favor of separate position() and position_and_velocity() methods.
- Supports computing position and velocity in two separate phases by saving a “bundle” of coefficients returned by compute_bundle().
- From Marten van Kerkwijk: a second tdb2 time argument, for users who want to build higher precision dates out of two 64-bit floats.
2013 January 18 — Version 1.0
- Initial release
The Jet Propulsion Laboratory’s “Solar System Dynamics” page introduces the various options for doing solar system position computations: http://ssd.jpl.nasa.gov/?ephemerides
The plain ASCII format element sets from which the jplephem Python ephemeris packages are built, along with documentation, can be found at: ftp://ssd.jpl.nasa.gov/pub/eph/planets/ascii/
Equivalent FORTRAN code for using the ephemerides be found at the same FTP site: ftp://ssd.jpl.nasa.gov/pub/eph/planets/fortran/
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