Twins in opposing Orbit Paradox - Time dilation

[deinseins]

Hi all,

this is my first post and I know that there are a lot of posts on the twin paradox already but I could not find one that helps me solve my thought experiment. Sadly I am no physisist but an engineer. Here goes my problem:

 

Orbit mechanics allows for two spaceships to orbit a massive body at high velocity in such a way that they pass each other closely after every revolution, i.e. they have roughly opposing orbits. Each Spacecraft has a clock on board and has no windows. There is only a sort of near field communication when they pass each other to compare clocks. With a very large massive body in the center; no atmosphere and a low orbit a relative speed of about 50 km per second could be reached. I know that this is small compared to the speed of light but it should be possible to measure the time dilation with appropriate clocks.

 

Each man in their spacecraft will not feel any accleretation because they are in a free fall position. I assume that this counts as enough reason to declare it an inertial frame (maybe this is the point where it goes wrong but I dont see anything against it) . Now when they pass each other they can both propose that the other is moving and they themselves are at rest and the other mans clock should be ticking more slowly, which could then be verified when they next pass each other. This would remove the usual way out of the problem that to compare the clocks one of the parties has to accelerate and lose symmetry.

 

When they next pass each other what will happen? Shouldnt they both expect that the other person has experienced less time?

 

Sorry if this is hard to read but I am not practised at posing these sort of questions.

 

Looking forward to your reply!

deinseins

Edited January 28, 2011 by deinseins

[swansont]

Not feeling an acceleration is not the same thing as being in an inertial frame (we're discounting general relativistic gravitational effects here); the fact that their paths are circular means they are accelerating and not in inertial frames. However, a carefully situated observer in an inertial frame can see them each moving at some speed v, and would conclude that their clocks are running equally slow as a result. However, what an observer on each spacecraft cannot do is assume s/he is at rest, since they are in an accelerating frame of reference, so one cannot simply apply the corrections of special relativity to the clocks on the spacecraft using the relative speed. The calculation of what an observer on the craft sees is probably not trivial.

[deinseins]

Thank you for the quick reply.

Now that you say so I remember knowing that a circular motion of a frame makes it non inertial even if it seems to feel that way for the man on the spacecraft. I think you could devise an experiment which proves that you are on a circular motion and so the man cannot say he is at rest. Ok. I think I got it. Thank you for your help