Explaining Relativity: Motion in a Gravity Field

[hprog]

Suppose we have two objects A and B in uniform motion according to each other with velocity v (A claims B to in motion with velocity v and B claims A to be in motion with velocity v).
After a while a big gravity field G appears on the site, and the escape velocity of objects in the field of G is u, where u < v.
As such the object at rest would naturally fall into the gravity field while the object in motion would escape since v > u.
But relativity says that each one of A and B can claim itself to be at rest while claiming the other in motion, which means that both of them claim that they will fall into the gravity field while the other one is to escape.
Clearly only one of them can be right, so how is this being explained with relativity?

 

[Dale]

Escape velocities are always measured relative to the planet.

 

[hprog]

Escape velocities are always measured relative to the planet.

Thanks for your answer.
Is this also true for a planet in acceleration? probably yes (although an object in acceleration cannot claim itself to be at rest as it is evident by the twin paradox, still here it makes sense that the point is not rest or motion but rather the planet's view).

 

[Naty1]

yes.

In RELATIVITY, most things (observations) depend on your frame of reference...all frames are equally valid, none reigns supreme...they are all 'relative', meaning the frame you choose largely determines the obervations you make...even time and space are not fixed and immutable...only the speed of light is fixed for all (inertial) observers. One frame measurement doesn't usually agree with another...but each is equally valid.

So when A and B claim the other guy is moving at velocity v, that's ONLY true for those two frames...From the earth, for example, one observes different velocities for A and B, and from the moon, yet another set.

And the above comments apply also to time, for example, not just velocity: Time passes differently for each of the A and B objects, on the earth, and on the moon. The passage of time depends on velocity AND gravity (potential)...

 

[hprog]

Is this also true for a planet in acceleration? probably yes (although an object in acceleration cannot claim itself to be at rest as it is evident by the twin paradox, still here it makes sense that the point is not rest or motion but rather the planet's view).

yes.

In RELATIVITY, most things (observations) depend on your frame of reference...all frames are equally valid, none reigns supreme...they are all 'relative', meaning the frame you choose largely determines the obervations you make...even time and space are not fixed and immutable...only the speed of light is fixed for all (inertial) observers. One frame measurement doesn't usually agree with another...but each is equally valid.

So when A and B claim the other guy is moving at velocity v, that's ONLY true for those two frames...From the earth, for example, one observes different velocities for A and B, and from the moon, yet another set.

And the above comments apply also to time, for example, not just velocity: Time passes differently for each of the A and B objects, on the earth, and on the moon. The passage of time depends on velocity AND gravity (potential)...

My question is that since the principle of relativity is said for inertial frames only is it is evident by the twin paradox, as such what would be if the planet is in acceleration? (actually a gravitational field is anyway considered non-inertial even when not in acceleration).

 

[Dale]

Is this also true for a planet in acceleration?

Yes. For example, the Earth's velocity relative to the sun is less than the solar escape velocity, therefore the Earth orbits the sun rather than escaping.