<p>The <a href="https://ssd.jpl.nasa.gov/horizons.cgi" rel="nofollow noreferrer">JPL Horizons</a> website gives ephemerides for a large number of Earth satellites as well as deep space spacecraft, planets, moons, asteroids, etc.</p>

<p>If you configure it as shown below, selecting the units you'd like, the full state vectors <code>(x, y, z, vx, vy, vz)</code>, use geocentric coordinates (<code>@500</code>) 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.</p>

<p>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.</p>

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

<p><a href="https://i.sstatic.net/BTVB3.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/BTVB3.png" alt="enter image description here"></a></p>

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

<p><a href="https://i.sstatic.net/bB6Ax.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/bB6Ax.png" alt="enter image description here"></a></p>

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

<pre><code>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.
</code></pre>

CC BY-SA 3.0
2017-09-12T05:14:36.817Z
@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
CC BY-SA 3.0
2017-09-12T05:24:27.277Z
that's extremely helpful and a great place to start. I will read up on the IAU documentation regarding transforming between reference systems.
Rumplestillskin
CC BY-SA 3.0
2017-09-12T05:25:54.720Z
@Rumplestillskin found this looking through old answers in [SXSE](https://space.stackexchange.com): PDF: https://www.iers.org/SharedDocs/Publikationen/EN/IERS/Publications/tn/TechnNote29/tn29_031.pdf?__blob=publicationFile&v=1
uhoh
CC BY-SA 3.0
2017-09-13T10:24:55.900Z
@Rumplestillskin fyi I've just asked [Have LAGEOS' germanium corner cube reflectors ever been used?](https://space.stackexchange.com/q/22999/12102)
uhoh
CC BY-SA 3.0
2017-09-14T01:48:49.890Z
That's fantastic stuff!! I have previously used the JPL site for a three body problem with a satellite, Earth and the Moon but I completely forgot. Hopefully this gives what I need. I struggle to realise the need for so many different reference systems!
Rumplestillskin
CC BY-SA 3.0
2017-09-14T02:18:36.590Z
So I do have a question - - - Isn't GCRS a geocentric form in the ICRF? I mean aren't they equivalent? So shouldn't the data be spot on ? Or am I misunderstanding something?
Rumplestillskin
CC BY-SA 3.0
2017-09-14T03:16:00.700Z
@Rumplestillskin If you look at [the link](https://www.iers.org/SharedDocs/Publikationen/EN/IERS/Publications/tn/TechnNote29/tn29_031.pdf?__blob=publicationFile&v=1) 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
CC BY-SA 3.0
2017-09-14T03:23:42.663Z
The difference is that GCRS is defined to apply best *inside the gravitational field of the Earth* whereas ICRF is not. So the difference seems to be in how general relativity is handled.
uhoh
CC BY-SA 3.0
2017-09-14T03:24:30.117Z
ahhh I see!! Wow, it is certainly non-trivial!
Rumplestillskin
CC BY-SA 3.0
2017-09-14T07:50:25.730Z
I wonder if it is possible just to get a list of positional/velocity data transformed in GCRS coordinates for any mission? I am not specifically looking for LAGEOS. It is something that obviously sounds like it should be very easy to find but my googling abilities and lack of knowledge is stopping me :) I will read your document tonight.
Rumplestillskin
CC BY-SA 3.0
2017-09-14T08:00:02.493Z
@Rumplestillskin [PyEphem](http://rhodesmill.org/pyephem/) seems to have a rich vocabulary of coordinate frames. It's possible that converting between ICRF and GCRS is just a few lines of script. A better solution might be to use [Astropy](http://docs.astropy.org/en/stable/coordinates/). See for example http://docs.astropy.org/en/stable/api/astropy.coordinates.GCRS.html#astropy.coordinates.GCRS I don't know if you are active in python or not. If not, I think you'll find it opens a lot of doors. I'd suggest staring with an Ananconda installation; start by using [CONDA](https://conda.io/docs/).
uhoh
CC BY-SA 3.0
2017-09-14T08:01:44.897Z
I am most certainly not active in Python at all. However, technical details should not stop progress! I will be sure to have a look at it.
Rumplestillskin
CC BY-SA 3.0
2017-09-20T07:50:59.320Z
I have read the paper you have attached and I must admit I am still very confused!! Maybe even more confused. I was hoping for something like the following situation: You have an ephemeris file for a GPS satellite who's position is calculated in ECEF coordinates. You run each position through a rotation/coordinate transformation program and you have ECI coordinates. Does such an operation exist to obtain GCRS coordinates? I am doubting myself as to whether this question even makes sense now.
Rumplestillskin
CC BY-SA 3.0
2017-09-20T08:01:47.947Z
@DavidHammen have you had any experience with this? Looking at your profile it seems right up your alley!
Rumplestillskin
CC BY-SA 3.0
2017-09-20T08:05:39.980Z
@Rumplestillskin For many artificial satellites in orbit around the Earth, and for Earth's natural satellite the Moon, motion is calculated and regularly confirmed to an accuracy of centimeters. Yes, accuracy. For this to happen, *the small effects on space and time* predicted by General Relativity (GR) must be properly included. If you don't need that level of accuracy, just use the ephemeris from Horizons as shown above; you can call those coordinates Earth Centered Inertial (ECI) as-is, without catching too much flak.
uhoh
CC BY-SA 3.0
2017-09-20T08:07:05.847Z
@Rumplestillskin This is rocket science so the details are sometimes quite challenging; *it's not exactly brain surgery* after all! https://youtu.be/THNPmhBl-8I
uhoh
CC BY-SA 3.0
2017-09-20T08:17:12.010Z
thanks for the quick response!! So what I am dealing with is Eq. (10.12)  in  [link](http://iers-conventions.obspm.fr/2010officialinfo.php).. Hmm maybe it won't matter that much so long as the coordinates aren't in a rotation frame?? I am completely lost on this reference frame business but thanks for the help. I think I will stick to mathematics in future :)
Rumplestillskin
CC BY-SA 3.0
2017-09-20T08:44:37.213Z
@Rumplestillskin [Eq. 10.12](http://iers-conventions.obspm.fr/2010/2010_official/chapter10/tn36_c10.pdf) is acceleration, something you would integrate to calculate an orbit from scratch (thus General relativistic models for space-time coordinates *and
equations of motion*), not to transform an existing ephemeris from one coordinate system to another. At first glance it seems to be the same as the equation in [this question](https://physics.stackexchange.com/q/313146/83380). There's certainly nothing wrong with asking a related question in physics stackexchange, as long as it's not identical.
uhoh
CC BY-SA 3.0
2017-09-20T09:00:08.070Z
suggestion 1) ping @MarkAdler suggestion 2) migrate this, or ask a related but not identical question in [SXSE](https://space.stackexchange.com/)
uhoh
CC BY-SA 3.0
2017-09-20T10:06:09.683Z
ah so that's exactly what I want to do but for some reason I thought I would need to perform some transformation or something to that effect in GCRS. So I am interested in trying to improve this equation and hence my need to get an ephemeris so I can compare but it might be easier said than done. So if I integrate those equations plus a Newtonian acceleration are the coordinates automatically in GCRS?
Rumplestillskin
CC BY-SA 3.0
2017-09-20T10:07:15.517Z
Also are you aware of an integrator that is pre designed that I can pick from a list of forces. Specifically newton and relativity? Otherwise I would need to write a script to it myself.
Rumplestillskin
CC BY-SA 3.0
2017-09-20T10:08:01.807Z
I am aware of GMAT but the selection for reference frame is another reason for my question! It is confusing.
Rumplestillskin
CC BY-SA 3.0
2017-09-20T10:25:35.370Z
Let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/65887/discussion-between-rumplestillskin-and-uhoh).
Rumplestillskin
CC BY-SA 3.0
2017-09-12T05:00:25.187Z
2017-09-12T05:34:31.247Z
2017-09-12T05:34:31.247Z
uhoh
<p>Is anyone aware of where one can obtain <strong>ephemeris data in Geocentric Celestial Reference Systems (GCRS) coordinates</strong> for a geodesy satellite such as LAGEOS (It doesn't really matter which mission)? Or, alternatively, simulated data in <strong>GCRS coordinates</strong>. Specifically, Cartesian position and velocity coordinates. I can't seem to find them anywhere. </p>

<p><strong>Update:</strong> My confusion has increased. I will try and rephrase my question.</p>

<p>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?</p>

<p><strong>Purpose of question:</strong>
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.</p>

CC BY-SA 3.0
2017-09-12T02:47:32.260Z
"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
CC BY-SA 3.0
2017-09-12T02:51:19.397Z
@JohnDvorak I would definitely like Cartesian coordinates. Unless it is easy to transform from one to the other?
Rumplestillskin
CC BY-SA 3.0
2017-09-12T03:48:52.283Z
Clarification: Cartesian coordinates are useless within minutes. Seconds, if you ignore satellite movement. Orbital parameters are good for ... weeks, I believe?
John Dvorak
CC BY-SA 3.0
2017-09-12T04:49:10.373Z
@JohnDvorak [LAGEOS satellites](https://en.wikipedia.org/wiki/LAGEOS) 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
CC BY-SA 3.0
2017-09-12T13:00:02.740Z
fyi I've asked [Have LAGEOS' germanium corner cube reflectors ever been used?](https://space.stackexchange.com/q/22999/12102)
uhoh
<data-analysis><satellite><artificial-satellite><near-earth-object><ephemeris>
where to obtain ephemeris data for geodesy satellites?
Rumplestillskin
# where to obtain ephemeris data for geodesy satellites?

(Asked by: username_0 on 2017-09-12)

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.

**Tags:** data-analysis, satellite, artificial-satellite, near-earth-object, ephemeris

> **Comments:**
> **username_1**: "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.  
> **username_0**: @username_1 I would definitely like Cartesian coordinates. Unless it is easy to transform from one to the other?  
> **username_1**: Clarification: Cartesian coordinates are useless within minutes. Seconds, if you ignore satellite movement. Orbital parameters are good for ... weeks, I believe?  
> **username_2**: @username_1 [LAGEOS satellites](https://en.wikipedia.org/wiki/LAGEOS) 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.  
> **username_2**: fyi I've asked [Have LAGEOS' germanium corner cube reflectors ever been used?](https://space.stackexchange.com/q/22999/12102)  

---

## 1 answers

### Answer by username_2 on 2017-09-12. Score: 2

The [JPL Horizons](https://ssd.jpl.nasa.gov/horizons.cgi) 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.

[![enter image description here](https://i.sstatic.net/BTVB3.png)](https://i.sstatic.net/BTVB3.png)

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.

[![enter image description here](https://i.sstatic.net/bB6Ax.png)](https://i.sstatic.net/bB6Ax.png)

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.

```

> **Comments:**
> **username_2**: @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?  
> **username_0**: that's extremely helpful and a great place to start. I will read up on the IAU documentation regarding transforming between reference systems.  
> **username_2**: @username_0 found this looking through old answers in [SXSE](https://space.stackexchange.com): PDF: https://www.iers.org/SharedDocs/Publikationen/EN/IERS/Publications/tn/TechnNote29/tn29_031.pdf?__blob=publicationFile&v=1  
> **username_2**: @username_0 fyi I've just asked [Have LAGEOS' germanium corner cube reflectors ever been used?](https://space.stackexchange.com/q/22999/12102)  
> **username_0**: That's fantastic stuff!! I have previously used the JPL site for a three body problem with a satellite, Earth and the Moon but I completely forgot. Hopefully this gives what I need. I struggle to realise the need for so many different reference systems!  
> **username_0**: So I do have a question - - - Isn't GCRS a geocentric form in the ICRF? I mean aren't they equivalent? So shouldn't the data be spot on ? Or am I misunderstanding something?  
> **username_2**: @username_0 If you look at [the link](https://www.iers.org/SharedDocs/Publikationen/EN/IERS/Publications/tn/TechnNote29/tn29_031.pdf?__blob=publicationFile&v=1) 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.  
> **username_2**: The difference is that GCRS is defined to apply best *inside the gravitational field of the Earth* whereas ICRF is not. So the difference seems to be in how general relativity is handled.  
> **username_0**: ahhh I see!! Wow, it is certainly non-trivial!  
> **username_0**: I wonder if it is possible just to get a list of positional/velocity data transformed in GCRS coordinates for any mission? I am not specifically looking for LAGEOS. It is something that obviously sounds like it should be very easy to find but my googling abilities and lack of knowledge is stopping me :) I will read your document tonight.  
> **username_2**: @username_0 [PyEphem](http://rhodesmill.org/pyephem/) seems to have a rich vocabulary of coordinate frames. It's possible that converting between ICRF and GCRS is just a few lines of script. A better solution might be to use [Astropy](http://docs.astropy.org/en/stable/coordinates/). See for example http://docs.astropy.org/en/stable/api/astropy.coordinates.GCRS.html#astropy.coordinates.GCRS I don't know if you are active in python or not. If not, I think you'll find it opens a lot of doors. I'd suggest staring with an Ananconda installation; start by using [CONDA](https://conda.io/docs/).  
> **username_0**: I am most certainly not active in Python at all. However, technical details should not stop progress! I will be sure to have a look at it.  
> **username_0**: I have read the paper you have attached and I must admit I am still very confused!! Maybe even more confused. I was hoping for something like the following situation: You have an ephemeris file for a GPS satellite who's position is calculated in ECEF coordinates. You run each position through a rotation/coordinate transformation program and you have ECI coordinates. Does such an operation exist to obtain GCRS coordinates? I am doubting myself as to whether this question even makes sense now.  
> **username_0**: @DavidHammen have you had any experience with this? Looking at your profile it seems right up your alley!  
> **username_2**: @username_0 For many artificial satellites in orbit around the Earth, and for Earth's natural satellite the Moon, motion is calculated and regularly confirmed to an accuracy of centimeters. Yes, accuracy. For this to happen, *the small effects on space and time* predicted by General Relativity (GR) must be properly included. If you don't need that level of accuracy, just use the ephemeris from Horizons as shown above; you can call those coordinates Earth Centered Inertial (ECI) as-is, without catching too much flak.  
> **username_2**: @username_0 This is rocket science so the details are sometimes quite challenging; *it's not exactly brain surgery* after all! https://youtu.be/THNPmhBl-8I  
> **username_0**: thanks for the quick response!! So what I am dealing with is Eq. (10.12)  in  [link](http://iers-conventions.obspm.fr/2010officialinfo.php).. Hmm maybe it won't matter that much so long as the coordinates aren't in a rotation frame?? I am completely lost on this reference frame business but thanks for the help. I think I will stick to mathematics in future :)  
> **username_2**: @username_0 [Eq. 10.12](http://iers-conventions.obspm.fr/2010/2010_official/chapter10/tn36_c10.pdf) is acceleration, something you would integrate to calculate an orbit from scratch (thus General relativistic models for space-time coordinates *and equations of motion*), not to transform an existing ephemeris from one coordinate system to another. At first glance it seems to be the same as the equation in [this question](https://physics.stackexchange.com/q/313146/83380). There's certainly nothing wrong with asking a related question in physics stackexchange, as long as it's not identical.  
> **username_2**: suggestion 1) ping @MarkAdler suggestion 2) migrate this, or ask a related but not identical question in [SXSE](https://space.stackexchange.com/)  
> **username_0**: ah so that's exactly what I want to do but for some reason I thought I would need to perform some transformation or something to that effect in GCRS. So I am interested in trying to improve this equation and hence my need to get an ephemeris so I can compare but it might be easier said than done. So if I integrate those equations plus a Newtonian acceleration are the coordinates automatically in GCRS?  
> **username_0**: Also are you aware of an integrator that is pre designed that I can pick from a list of forces. Specifically newton and relativity? Otherwise I would need to write a script to it myself.  
> **username_0**: I am aware of GMAT but the selection for reference frame is another reason for my question! It is confusing.  
> **username_0**: Let us [continue this discussion in chat](http://chat.stackexchange.com/rooms/65887/discussion-between-username_0-and-username_2).  

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