Atomic Clocks and General Reliativity

[TJH]

Hello!

I have a question about general relativity and the space-time continuum. If two atomic clocks were started at the same time and one was sent to Jupiter and back and one was kept at sea level on Earth, what would the time difference be when the Jupiter clock returned? According to general relativity, the time difference should be very substantial. Can anyone explain the maths on how to reach the answer to this question? Would be much appreciated

[cubinator]

Well, technically it depends on how fast the Jupiter clock goes to Jupiter. If it's going at, say, .1 c, it'll show a much different time than a clock that went there at .00001 c. It also would change depending on how long it was at Jupiter. Being in interplanetary space with no planets nearby means time would run "faster" for the space clock than the Earth clock. But then the space clock gets close to a really big planet for a while. If it stayed there long enough, Jupiter's time dilation would compensate for the clock's being in interplanetary space and the clock on Earth would catch up. But if you did it just right, you could put the clock in interplanetary space (it speeds up) leave it in orbit near Jupiter for a while (it slows down) then bring it back to Earth (it speeds up again then slows down a little bit) so that the two clocks, although having shown different times before, show exactly the same time when the space clock gets back to Earth. I've no idea on the math, but it really depends on how long the space clock's trip is.

[TJH]

Thanks  

[Tex_NL]

To summarize and simplify what @cubinator said for those that still have trouble understanding this tricky subject:

The faster you move, the slower time will pass. The deeper you are inside a strong gravity well, the faster time will progress.