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In the JPL Horizons there are Earth mean equator and ecliptic reference planes. The ecliptic is an apparent path of the Sun's motion as seen from Earth and tilted 23.5deg with respect to the Earth equator. So, both ecliptic and equatorial planes are directly connected with the Earth.

If I calculate the trajectory of a satellite relative to the Sun (let's say, flying to the Mars) is it appropriate to do it relative to the plane, connected with the Earth, and specifically, the equatorial plane? Is there an other plane, which is more appropriate for calculations of interplanetary missions?

I know, that any reference frame may be chosen for calculations (even with the center in Vesta asteroid), however for any case there is always the most appropriate reference frame exists.

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You are correct - and the choice is pretty simple (although might not be if your satellite is to interact with different bodies).

There's a number of celestial coordinate systems, and they differ by a couple features. And the choice is based on where you go and what is your observation target.

If your satellite is to observe Earth, Equatorial system is most natural; it will help with tricks like Sun-synchronous satellites which exploit Earth oblateness etc. If you're building an interplanetary probe, you'll want Ecliptic, as the inclinations of all important trajectories will be close to zero. If you're building a space telescope, it may be brought to target orbit with these two, but afterwards should operate with Galactic or Supergalactic system of coordinates to make things easier to its users.

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  • $\begingroup$ The Wiki says that both equatorial and ecliptic have the primary direction to the Vernal equinox. How is it possible for planes with different inclination? $\endgroup$ – Leeloo Jul 22 '18 at 18:52
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    $\begingroup$ @Leeloo: The plane of Ecliptic is the plane of Earth orbit, so the Earth center-Sun center line always lies in the plane of Ecliptic, at moment of Equinox too. At time of equinox, though, the line between center of Earth and the Sun passes through Earth equator (Sun is in zenith at noon on the equator), so it works for the equatorial coords too. Regardless, that's just a minor convenience, a positive quirk; the primary role of direction of Vernal Equinox is to establish the prime meridian for both systems; the equatorial planes are derived from other properties, just happen to intersect there. $\endgroup$ – SF. Jul 22 '18 at 19:56
  • $\begingroup$ An argument to the contrary: JPL uses the ICRF (Earth equatorial, circa noon on 1 Jan 2000) as the basis for planetary ephemerides and for position and velocity of interplanetary spacecraft. For spacecraft /probes that are close to / on another planet, they'll use an appropriate planet-centric frame of reference that is tied to the ICRF. $\endgroup$ – David Hammen Jul 23 '18 at 9:30
  • $\begingroup$ @DavidHammen: The most convenient data format for observatories, Deep Space Network antennas, etc is Earth-centric. Besides, the difference between Equatorial and Ecliptic systems is so small (convenience of picking the "better one" small enough), that in many cases it will be less of a headache to stick to one of them consistently, than to switch between the two depending on specific situation. $\endgroup$ – SF. Jul 23 '18 at 9:56

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