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Imagine a person sitting on a very high chair. To be more specific, on a chair that has the same height as a satellite with a person aboard and which orbits the earth in a circular path. Let's say the (arbitrary) height is 400 kilometer.

The person in the chair feels an upward e.m. force, while the person in the satellite feels no force at all. Is there a difference between the pace of time which the person on the chair experiences and the one which the person in the satellite experiences? Of course, the person on the chair has taken proper precautions. Let's not consider centrifugal forces.

This is not the same as asking for the pace of time in a satellite orbiting the earth in a circular orbit. The satellite is in free fall and tries to maximize the time passed, just like any other object in free fall (this is an approximation for low velocities; at high velocities, the curvature of space also comes into play). As the satellite is moving in an orbit of which every point has the same pace of time (faster as on the surface of the earth), the time moves at the same pace as the time at the height at which the satellite moves.

The extra thing I ask is if the pace of time for the man in the chair is different from the pace of time in the satellite. Since the man stays put at the height of the orbiting satellite, he is finding himself in a point in space where the time has the same pace as in all the points through which the satellite travels, so one is tempted to think there is no difference in the pace of time for both persons.

Is the slowing of time for the person in the free falling satellite due to its speed (if no gravity were present it would travel in a straight line with the same velocity as in the circular orbit) so it would in that case be a special relativistic effect, while the slower pace in time for the man on the chair would be a general relativistic effect? In other words, can you use the special relativistic time dilation formula for a person (in a satellite) traveling in flat space with the same speed as the circular orbiting satellite (for low velocities)?

Deschele Schilder
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  • If they have different velocities, then yes. But if the satellite were in geo-synchronous orbit, then no... – DilithiumMatrix Dec 14 '16 at 16:33
  • Hi descheleschilder. The linked question specifically compares the time dilation of an orbitting satellite to a satellite hovering stationary at the same amplitude. – John Rennie Dec 15 '16 at 06:50

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They are at the same gravitational potential, so the only difference is time dilation. The orbiter will have time elapse more slowly.

Ken G
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