jbriggs444
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Right. So you can arrange for the orbital period of a satellite moving at 0.5c to be anything you want by simply selecting the right altitude. And arranging for the requisite centripetal acceleration.Steeve Leaf said:The farther the ship is the longer it takes for it to complete an orbit doing the same speed 0.5c.
In one case it is 12 sec and in the other 90 min.
It would help if, instead of mentioning "Marcela" you had referenced the question you were trying to answer: One common technique in these forums is to mention the post number where the referenced passage exists. In this case, that would be #27:
Steeve Leaf said:A spaceship named "Marcela" circle kilometers (maybe about 129e6 km) away at 0.5c.
It has synchronized its time of orbit with IS that it sees it all the time at the same position and distance.
What is the speed of Marcela relative to IS and how the optic clocks explain this time dilation ?
Here you have postulated a spacecraft which is still moving at 0.5c relative to earth. You have varied its orbital radius so that it remains directly above the ISS at all times (this seems to assume that the ISS is in an equatorial orbit -- which it is not). You proceed to ask about its speed relative to the ISS.
The answer is obviously 0.5c. The velocity of the ISS is negligible compared to 0.5c. So the velocity of the 0.5c orbiter is still 0.5c in any inertial frame where the ISS is momentarily at rest, just as it is in an Earth-centered inertial frame.
However, there is a potential ambiguity. You have said that "it sees it all the time at the same position and distance". This suggests that you are adopting a frame of reference that rotates with the orbit of the ISS. In this reference frame, you have stipulated that Marcela is motionless.
The answer now is obviously 0.
But changing the reference frame does not change anything about the situation. The time dilation formula based on an object moving in an inertial frame still applies. The fast orbiter is still moving at 0.5c and its time dilation is the same as before.