Time dilation on fast massive objects

[scienalc]

The popular thought experiment states, that if of two identical twins one is left on Earth an the other is embarked on a spaceship and sent into open space at near-c velocity, time for the traveling one will pass slower than for the one left on earth, due to the speed.
On the other hand, time passes faster for objects outside the influence of gravity.

What would be the extremes of those situations? Say the spaceship in the above example has the same mass as Earth, or a greater mass, e.g. the Sun, and the extreme case, a supermassive space ship, how would that affect the thought experiment?

Furthermore, I would ask for some clarification regarding reference points: consider the original thought experiment (mass of spaceship is negligible compared to the mass of the Earth), but shift the reference point to the cockpit of the space ship, i.e. to the pilot it would seem that the Earth is moving with great velocity, therefore, he would conclude that time on Earth would pass slower than for him, amplified additionally by the fact of the greater gravitational influence for the twin on Earth. In other words, what provides the absolute outcome of the experiment (regardless of reference points)?


Thanks a lot

PS: I assume of course time validation based on identical, precise clocks placed on the Earth and on the spaceship and the, somewhat subjective, statements "time passes slower/faster [for x]" refer to the difference these clocks would show after the performed experiment.

 

[Nugatory]

Furthermore, I would ask for some clarification regarding reference points: consider the original thought experiment (mass of spaceship is negligible compared to the mass of the Earth), but shift the reference point to the cockpit of the space ship, i.e. to the pilot it would seem that the Earth is moving with great velocity, therefore, he would conclude that time on Earth would pass slower than for him, amplified additionally by the fact of the greater gravitational influence for the twin on Earth. In other words, what provides the absolute outcome of the experiment (regardless of reference points)?

Start by reading this FAQ: http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

Once you have that down, we can work you through the more complicated case you started with.

 

[scienalc]

Thanks for providing this link, I found it really useful. Basically, the reference points aboard the ship and on Earth can't be treated as equivalent, because the ship has to change inertial frames when turning around, so, after the turn is completed, it needs to readjust its clock. Particularly interesting is the fact that the time gap (i.e. the "aging" of the Earth twin) happens during the turning. Being and electrical engineer, I found the explanation using the path integral especially appealing, which states that the time difference comes from the fact that the same integral was integrated along a different path.

Based on these insights, I can conclude that the mass difference between the objects doesn't contribute to the time dilation which is the result of relative motion. Along that train of thought, I assume that the gravity induced time dilation is specific to the observed objects, meaning that this time difference would exist regardless of motion and that even after the ordeal of traveling of one of the objects, the gravity induced time difference would be a constant which would need to be incorporated in the time dilation after the travel. Is this correct? (By gravity induced time difference I mean that the time on the surface of an asteroid would "flow faster" than the time on the surface of a star)

I would be still interested in the discussion of the extreme cases, mentioned in my first post. I would find it hard to believe, even if I was correct in the above argument, that the time difference induced by gravity and time dilation generated by speed of motion are a "simple" superposition.