NASA interplanetary missions

SUDOnym

Do NASA use Einsteinian corrections (either SR or GR) when doing interplanetary missions? or is it purely Newtonian calculations?
-I'm almost certain that it was purely Newtonian mechanics for the moon missions...

Vorde

While I can't answer for a fact, I would be very surprised if they didn't use GR, considering that they are shooting a hunk of metal that could cost upwards of a $100 million and hoping to hit a target millions of miles away, besides the fact that they are all physicists...

Nabeshin

Fairly sure only Newtonian mechanics is used for flight paths. The velocities are far too low for special relativistic corrections to come into play, and the bodies in question are either not very massive (planets) or at quite a distance away (the sun).

I do not even know if someone has in practice calculated geodesics in a multi-body system using full GR. It's certainly absurd. It's conceivable to include post-Newtonian corrections, but likely these would still be swamped by normal uncertainties. At any rate, the calculation in full GR is very much overkill.

Vorde

Really? I'm surprised, while I can't even begin to imagine the complexity of the equations, it seems that with the expenses and time involved it would be worth it.

Chronos

They probably ran the numbers just to be sure, but, as Nabeshin noted any deviation from standard newtonian mechanics would be negligible and easily compensated for by attitude control rockets.

D H

To accurate model the orbits of the planets for a long period of time one must look beyond Newtonian physics to some extent. JPL uses a post-Newtonian correction to develop its planetary ephemerides. JPL may well employ a post-Newtonian correction for the paths of their interplanetary missions, but only because they already have this mechanism in place. (They almost certainly do not have it in place in the spacecraft flight software. If they do use a post-Newtonian correction, it would be in the best estimate of trajectory (BET) calculations performed after the fact.)

Those corrections are not truly needed for interplanetary missions. As Nabeshin mentioned, the errors in the sensors, effectors, and control algorithms on the spacecraft and in the errors in the external measurements used to anchor the spacecraft's state will vastly overwhelm the tiny errors that result from ignoring relativistic effects. The time spans are too short, and except for missions to Mercury, the gravitational effects are too small, for GR to result in any noticeable deviation from Newtonian gravity.