# where to obtain ephemeris data for geodesy satellites?

Is anyone aware of where one can obtain ephemeris data in Geocentric Celestial Reference Systems (GCRS) coordinates for a geodesy satellite such as LAGEOS (It doesn't really matter which mission)? Or, alternatively, simulated data in GCRS coordinates. Specifically, Cartesian position and velocity coordinates. I can't seem to find them anywhere.

Update: My confusion has increased. I will try and rephrase my question.

Is it possible to obtain an ephemeris file and perform a transformation such that the ephemeris data can be expressed in GCRS coordinates? And if so, what is the process?

Purpose of question: What I am interested in is ephemeris data for a satellite (doesn't really matter which mission) that is subject to classical Newtonian acceleration plus relativistic corrections as recommended by the IERS such as Schwarzschild, Lense-Thirring and Geodetic accelerations.

• "Cartesian position and velocity coordinates" - these get outdated quickly. Instead, you want the orbital parameters - periapsis, apoapsis, inclination, longitude of the ascending node, argument of periapsis and true anomaly at T=0. – John Dvorak Sep 12 '17 at 2:47
• @JohnDvorak I would definitely like Cartesian coordinates. Unless it is easy to transform from one to the other? – Rumplestillskin Sep 12 '17 at 2:51
• Clarification: Cartesian coordinates are useless within minutes. Seconds, if you ignore satellite movement. Orbital parameters are good for ... weeks, I believe? – John Dvorak Sep 12 '17 at 3:48
• @JohnDvorak LAGEOS satellites orbits are both measured and predicted to centimeter accuracy. A good state vector and good propagator are how this is done. Keplerian orbital parameters are approximations and are not a good way to characterize real-world orbits. – uhoh Sep 12 '17 at 4:49
• – uhoh Sep 12 '17 at 13:00

## 1 Answer

The JPL Horizons website gives ephemerides for a large number of Earth satellites as well as deep space spacecraft, planets, moons, asteroids, etc.

If you configure it as shown below, selecting the units you'd like, the full state vectors (x, y, z, vx, vy, vz), use geocentric coordinates (@500) you will get the following output. You can choose various time step sizes (down to 1 minute) and time frames. You can choose direct download as csv text rather than HTML if you like - recommended for long files.

It looks to me that because of the special status and use of the LAGEOS satellites, the ephemeris only predicts a relatively short period into the future, unlike other spacecraft which have predictions for years sometimes.

This should get you started! If you have more questions about this post as comments and I or someone else will try to help.

Here are the Table settings. I believe that the ICRF/J2000.0 with Ecliptic and Mean Equinox settings will give you something close to GCRS but right now I am not sure how close. I'll keep reading and ask for help in comments.

Here is a sample output from the above configuration. It scrolls left-right and up-down.

Revised: Sep 11, 2017                 LAGEOS-2                         -122195

LAGEOS-2 (1992-070B, "Laser Geodynamics Satellite", NASA/ASI)
60-cm diameter sphere, 426 corner cube reflectors (VIS), 4 germanium (IR)
Deployed: 1993-Oct-22 from Space Shuttle Columbia (STS 52)

*******************************************************************************
Ephemeris / WWW_USER Mon Sep 11 21:51:05 2017 Pasadena, USA      / Horizons
*******************************************************************************
Target body name: LAGEOS-2 (spacecraft) (-122195) {source: LAGEOS-2}
Center body name: Earth (399)                     {source: DE431mx}
Center-site name: BODY CENTER
*******************************************************************************
Start time      : A.D. 2017-Jan-01 00:00:00.0000 TDB
Stop  time      : A.D. 2017-Jan-05 00:00:00.0000 TDB
Step-size       : 1440 minutes
*******************************************************************************
Center geodetic : 0.00000000,0.00000000,0.0000000 {E-lon(deg),Lat(deg),Alt(km)}
Center cylindric: 0.00000000,0.00000000,0.0000000 {E-lon(deg),Dxy(km),Dz(km)}
Center radii    : 6378.1 x 6378.1 x 6356.8 km     {Equator, meridian, pole}
Output units    : KM-S
Output type     : GEOMETRIC cartesian states
Output format   : 2 (position and velocity)
Reference frame : ICRF/J2000.0
Coordinate systm: Ecliptic and Mean Equinox of Reference Epoch
*******************************************************************************
JDTDB,            Calendar Date (TDB),                      X,                      Y,                      Z,                     VX,                     VY,                     VZ,
**************************************************************************************************************************************************************************************************
$$SOE 2457754.500000000, A.D. 2017-Jan-01 00:00:00.0000, 5.049112760756619E+03, 9.246781656953866E+03, 5.722633641721932E+03, -2.978199703429669E+00, 3.689975896939779E+00, -3.350502047340569E+00, 2457755.500000000, A.D. 2017-Jan-02 00:00:00.0000, -6.140907600397200E+03, -8.148707798015072E+03, -6.918983669661846E+03, 2.434461456961566E+00, -4.250750074318191E+00, 2.808377534161328E+00, 2457756.500000000, A.D. 2017-Jan-03 00:00:00.0000, 6.849580412560958E+03, 6.106324592083777E+03, 7.740446107133596E+03, -1.906840987637830E+00, 4.973834339923835E+00, -2.290764139470047E+00, 2457757.500000000, A.D. 2017-Jan-04 00:00:00.0000, -7.504132672898423E+03, -4.707277560275819E+03, -8.539479988453819E+03, 1.304309397636298E+00, -5.242849004192330E+00, 1.679103108590806E+00, 2457758.500000000, A.D. 2017-Jan-05 00:00:00.0000, 7.740851830184564E+03, 2.245705288312970E+03, 8.942780571589567E+03, -6.155844902136471E-01, 5.667380276723395E+00, -9.687665040214430E-01,$$EOE
**************************************************************************************************************************************************************************************************
Coordinate system description:

Ecliptic and Mean Equinox of Reference Epoch

Reference epoch: J2000.0
XY-plane: plane of the Earth's orbit at the reference epoch
Note: obliquity of 84381.448 arcseconds wrt ICRF equator (IAU76)
X-axis  : out along ascending node of instantaneous plane of the Earth's
orbit and the Earth's mean equator at the reference epoch
Z-axis  : perpendicular to the xy-plane in the directional (+ or -) sense
of Earth's north pole at the reference epoch.

Symbol meaning:

JDTDB    Julian Day Number, Barycentric Dynamical Time
X      X-component of position vector (km)
Y      Y-component of position vector (km)
Z      Z-component of position vector (km)
VX     X-component of velocity vector (km/sec)
VY     Y-component of velocity vector (km/sec)
VZ     Z-component of velocity vector (km/sec)

Geometric states/elements have no aberrations applied.

• @DavidHammen Does this generate something close to GCRS at least? Is there a straightforward way to transform this data to GCRS for epoch's other than J2000.0? – uhoh Sep 12 '17 at 5:14
• that's extremely helpful and a great place to start. I will read up on the IAU documentation regarding transforming between reference systems. – Rumplestillskin Sep 12 '17 at 5:24
• @Rumplestillskin found this looking through old answers in SXSE: PDF: iers.org/SharedDocs/Publikationen/EN/IERS/Publications/tn/… – uhoh Sep 12 '17 at 5:25
• @Rumplestillskin fyi I've just asked Have LAGEOS' germanium corner cube reflectors ever been used? – uhoh Sep 13 '17 at 10:24
• @Rumplestillskin If you look at the link in my comment above, it seems that they are not identical. If you are doing analysis of LAGEOS ranging data to centimeter accuracy, the difference may be huge, if you are making an animation or plot, the difference may be small. – uhoh Sep 14 '17 at 3:16