I have always wondered about this with regard to Newton's Third law:
For every action there is an equal and opposite reaction.
I ask because Earth is an third body scenario between the sun and Jupiter. Jupiter has enough gravity to occasionally pull the Earth slightly (not significantly) out of orbit from the Sun, but Earth's orbit to the Sun is self-correcting due to the difference in mass between the Sun and Jupiter. Quick web searching reveals Jupiter's pull on Earth is only approximately 0.005% of the Sun's after accounting for both mass and distance, but that number rises to 0.011% after accounting for syzygy with the moon.
> So if a craft departs from rendezvous with another craft it must do so by pushing away from that other craft.
More commonly we push away propellant, but pushing on the other craft is an option.
> If the rendezvous was in orbit does that mean departing from rendezvous pushes both crafts out of orbit?
Assuming we're pushing on the other craft, it means both crafts will change orbits, but in opposite directions. If we're talking about an instantaneous push in the direction of travel one craft will move to an orbit where it is closer to earth one half rotation later, and the other craft will move to an orbit where it is farther from earth one half rotation later.
Both, either, or neither craft could exit orbit like this, but one would be exiting orbit by crashing into the thing its orbiting around (e.g. earth) and the other would exit by reaching escape velocity and flying off into the distance.
> I ask because Earth is an third body scenario between the sun and Jupiter. Jupiter has enough gravity to occasionally pull the Earth slightly (not significantly) out of orbit from the Sun, but Earth's orbit to the Sun is self-correcting due to the difference in mass between the Sun and Jupiter. Quick web searching reveals Jupiter's pull on Earth is only approximately 0.005% of the Sun's after accounting for both mass and distance, but that number rises to 0.011% after accounting for syzygy with the moon.
Yes, Jupiter constantly (not occasionally) perturbs earths orbit, and technically earth constantly perturbs jupiters orbit (though the influence in that direction is completely negligible), but as you note its not enough for either to reach escape velocity or crash into the sun, and it appears to more or less even out over time.
Orbits are essentially non-euclidean geometry. The opposite reaction is adding or shedding velocity. That still works exactly as Newton predicted. What doesn’t work is throwing something left making you go right. It makes you go right and up, or right and down.
the "push" is generated by escaping gas from burning fuel. it's possible that if the gas impacts the other craft it could affect that craft's orbit but I can't imagine that 60 years after people walked on the moon you and I are the first to think about that, so I presume its been accounted for