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I am trying to understand time dilation w.r.t velocity. Its said that when a satellite travels around earth (at speed more than a synchronized clock on earth which is stationary w.r.t earth), it experiences time slower in comparison to a clock on earth.

first of all, if you say, the time slows down with increase in velocity, that velocity is in reference to what?? how can you say that the satellite experiences time slower and not otherwise, because from each one's perspective the other is moving and itself is at rest.

consider this... mind the revolution of earth around the sun.. (the frame reference here is sun). now, a rocket goes in outer space for one year such that, wrt sun it is stationary and the earth is actually moving. after one year, as earth comes at the same place again... the rocket meets earth surface... now here its the earth who was moving, so will the astronaut in rocket age more or less than its companions on earth?

another question I had was regarding the velocity. Earth revolves around sun at a particular velocity, sun again revolves around the center of galaxy. and the galaxy is also not stationary.. so when you say nothing can exceed speed of light, how can you know earth is not actually revolving at some speed greater than light....and what is the reference when you calculate speed for anything?

I am sorry i couldn't articulate better. can someone help me with these doubts?

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    $\begingroup$ I think you want to read/look up videos about the Twin Paradox: en.wikipedia.org/wiki/Twin_paradox. There are also many questions on this site about this paradox. Two things to keep in mind when you are reading about the Twin Paradox. First, the twin paradox is not actually a paradox. It is a puzzle with a well-defined answer. Second, you do NOT need to understand general relativity to understand the answer to the twin paradox, although some sources on the web will claim you do. $\endgroup$
    – Jahan Claes
    Feb 8, 2021 at 16:35
  • $\begingroup$ There's a nice satellite time dilation diagram here. Notice how time dilation due to speed and time dilation due to gravitational potential (relative to an observer on Earth's surface) cancel each other at an altitude of ~3000 km. $\endgroup$
    – PM 2Ring
    Feb 8, 2021 at 17:49

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You are right that when dealing with such real examples things look messy.

The results of standard relativity formally requires no gravitational field and a inertial frame of reference.

In order to find time dilation of an orbit satelite, it is necessary to use general relativity. A good approximation is the Schwarzschild metric. It is valid for non rotating bodies, what is not the case of the Earth, but our angular velocity is not so fast.

If we deal with objects far from gravitational fields, from each frame the clock in the other frame ticks slower.

It must be so, because the movement is relative. Each frame is inertial and from its perspective the other one is moving.

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  • $\begingroup$ if the clock in other frame seems ticking slower, how come when they two meet.. one is younger than other.. I mean if A is younger than B after some relative displacement or motion, where they were same age at first... why didn't A see B''s clock tick faster (bcz it should see that way or else it cant be younger that B if it observes b's clock ticking slower) $\endgroup$
    – Dipanshu Jain
    Feb 8, 2021 at 16:36
  • $\begingroup$ That is the point. If both are inertial frames, their relative velocities are constant and they will never meet again. In order to have a meeting, one of them changes velocity. That breaks the symmetry and leads to different ages on the meeting. If both changes velocities equally, they will have the same age on meeting. $\endgroup$
    – Claudio Saspinski
    Feb 8, 2021 at 17:28

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