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I am using SPICE to read and store Chebyshev coefficients to then compute position of Solar System bodies in my navigation software (see this post).

The coefficients are defined with respect to the frame center definition : Earth-Moon barycenter for the Earth and Moon and Solar System barycenter for other planets. Example for de440.bsp :

BRIEF -- Version 4.1.0, September 17, 2021 -- Toolkit Version N0067
Summary for: de440.bsp

Bodies: MERCURY BARYCENTER (1) w.r.t. SOLAR SYSTEM BARYCENTER (0)
        VENUS BARYCENTER (2) w.r.t. SOLAR SYSTEM BARYCENTER (0)
        EARTH BARYCENTER (3) w.r.t. SOLAR SYSTEM BARYCENTER (0)
        MARS BARYCENTER (4) w.r.t. SOLAR SYSTEM BARYCENTER (0)
        JUPITER BARYCENTER (5) w.r.t. SOLAR SYSTEM BARYCENTER (0)
        SATURN BARYCENTER (6) w.r.t. SOLAR SYSTEM BARYCENTER (0)
        URANUS BARYCENTER (7) w.r.t. SOLAR SYSTEM BARYCENTER (0)
        NEPTUNE BARYCENTER (8) w.r.t. SOLAR SYSTEM BARYCENTER (0)
        PLUTO BARYCENTER (9) w.r.t. SOLAR SYSTEM BARYCENTER (0)
        SUN (10) w.r.t. SOLAR SYSTEM BARYCENTER (0)
        MERCURY (199) w.r.t. MERCURY BARYCENTER (1)
        VENUS (299) w.r.t. VENUS BARYCENTER (2)
        MOON (301) w.r.t. EARTH BARYCENTER (3)
        EARTH (399) w.r.t. EARTH BARYCENTER (3)
        Start of Interval (ET)              End of Interval (ET)
        -----------------------------       -----------------------------
        1549 DEC 31 00:00:00.000            2650 JAN 25 00:00:00.000

I want to have all coefficients defined in the same frame center.

So, is there a way to change the frame center definition of Chebyshev coefficients without compute bodies position ?

For example is it possible to have Chebyshev coefficients of the Earth w.r.t the Solar System barycenter ?

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  • $\begingroup$ If the plane of all the coordinates is the same (which I'm pretty sure it is), it's just a vector addition problem. $\endgroup$
    – Barry Carter
    Sep 12, 2022 at 13:24
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    $\begingroup$ For positions yes, but for Chebyshev coefficients I am not sure we can add them like a vector ! $\endgroup$
    – GuillaumeJ
    Sep 12, 2022 at 13:30
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    $\begingroup$ I think the reason they center the Moon on the Earth is that if they hadn't, the expressions for the Moon would be a lot larger as there would be both very large scale, and very small scale variances. AFAIK, there is no trick, you'd have to re-do the interpolation with the SSB as the center. And I would expect the resulting coefficient list for the same accuracy to be at least what is already given for the Earth plus those for the Moon. $\endgroup$
    – Greg Miller
    Sep 12, 2022 at 17:51
  • $\begingroup$ I concur with what @GregMiller says. $\endgroup$
    – ChrisR
    Sep 12, 2022 at 23:50
  • $\begingroup$ My mistake-- because the polynomials are valid for a different number of days, you'd need to convert them to the shorter periods for the moon and earth and then add $\endgroup$
    – Barry Carter
    Sep 13, 2022 at 11:13

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I want to have all coefficients defined in the same frame center.

That's not a good ask, for many reasons (see below).

For example is it possible to have Chebyshev coefficients of the Earth w.r.t the Solar System barycenter ?

Not unless you are on the team that creates the Chebyshev coefficients in a JPL Development Ephemeris file -- and that won't happen. There are multiple reasons why those Development Ephemerides are represented the way they are, with the Earth and Moon at the center of the reason.

  • The Earth-Moon system and the Pluto-Charon system are the only two planetary systems in the solar system that comprise multiple bodies of somewhat comparable mass. Humanity has had one mission to Pluto.

  • Humanity has had thousands of missions to low Earth orbit and geosynchronous Earth orbit, plus many more to the Moon. Predicting where the Moon is with respect to the Earth is important. Tracking the Earth and Moon as separate bodies with respect to the solar system barycenter would inevitably result in precision loss for this key usage.

  • The Earth-Moon barycenter has a frequency of one cycle per year with respect to the Sun, and hence roughly one cycle per year with respect to the solar system barycenter. The Earth and Moon individually have a monthly variation on top of this. The Chebyshev coefficient sets would have to have much finer steps to track the Earth and Moon separately.

  • In fact, the Earth itself is not represented in the JPL Development Ephemerides. Instead, the Earth-Moon barycenter with respect to the solar system barycenter and Moon with respect to Earth are represented -- plus the Earth to Moon mass ratio. That gives enough information to calculate the position of (for example) Mars with respect to Earth as Mars is also represented in the JPL Development Ephemerides.

If you use SPICE, all of the nastiness of how bodies are represented in different ephemeris models that SPICE uses disappears. SPICE takes care of that for you. If you want to use the Development Ephemerides directly (plus other ephemerides) and not use SPICE, that is a bit of a pain. More than a bit. Use SPICE unless there are compelling reasons not to do so.

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  • $\begingroup$ Thanks. I'm not using SPICE to compute positions because the navigation software will be embedded onboard a spacecraft, so I can't use SPICE library onboard. And due to the fact that onboard memory is limited, I can't store directly bodies positions. So I am storing Chebyshev coefficients and then compute bodies position thanks to Chebyshev polynom. I know I can have Earth and Moon positions from Earth-Moon barycenter and Earth to Moon ratio, but the idea was to create a more generical function in which all Chebyshev coefficients are given in the same center frame. $\endgroup$
    – GuillaumeJ
    Sep 13, 2022 at 13:58
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    $\begingroup$ You can't do that, @GuillaumeJ, sorry. You'll have to have your onboard software replicate some of what SPICE does. You'll probably also want to load only key portions of a Development Ephemeris model. You do not need the whole enchilada, as it is rather large. $\endgroup$
    – David Hammen
    Sep 13, 2022 at 14:00
  • $\begingroup$ Yes that's what I'm doing, I extract only a small portion of a Development Ephemeris file with SPICE (for a body and period of time selected) and then store this portion in the software. With this I am able to compute bodies positions, but I have to create specific cases for Earth/ Moon position computation. And it would be the same for Phobos for example, where Chebyshev coefficients are given w.r.t. Mars Barycenter. So I wanted to have all the coefficients in the same center frame so that the processing would be easier, but as you said it seems not possible. $\endgroup$
    – GuillaumeJ
    Sep 13, 2022 at 14:14
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    $\begingroup$ (Continued) When rendezvousing with Phobos, it would be a very bad idea to represent the position of Phobos and the position of the spacecraft with respect to the solar system barycenter. The precision loss would be immense. $\endgroup$
    – David Hammen
    Sep 13, 2022 at 14:39
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    $\begingroup$ What one person considers a "pain" is a matter of preference. I consider working with SPICE a pain, and instead have implemented DE libraries in a few different languages which might be of help to others heading down this path: github.com/gmiller123456/jpl-development-ephemeris (granted SPICE does a lot more than just access DE files). $\endgroup$
    – Greg Miller
    Sep 13, 2022 at 21:02

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