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For a given speed, is the time dilation of a space traveler different if moving radially toward the earth as compared with moving radially away from the earth? Is the time dilation of a space traveler moving tangentially to the earth always less than radial motion for a given speed?

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    $\begingroup$ Don't confuse the effects of time dilation with those of signal retardation. The direction of travell affects tha latter but not the former. $\endgroup$ Sep 10, 2019 at 23:26
  • $\begingroup$ I am only interested in time dilation. $\endgroup$ Sep 15, 2019 at 23:36
  • $\begingroup$ How ever would the space traveler's clock know whether it was moving toward the earth or away from the earth? And why would it care any more about this than whether it was moving toward or away from Mars? $\endgroup$
    – WillO
    Sep 27, 2019 at 15:41
  • $\begingroup$ Assuming that the space traveler is at earth's geosync orbit radius moving toward or away from the earth is relevant since gravitational potential is either increasing or decreasing. Does the direction of movement against the gravitational field affect the space traveler's clock with respect to a clock at rest? I think that the answer requires considering general relativistic effects. $\endgroup$ Sep 28, 2019 at 18:21

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Time dilation only depends on the magnitude of the relative velocity between the two observers. Therefore, it doesn't matter if the two observers are moving towards or away from each other.

This becomes especially clear when you realize when we discuss reference frames we are are talking about, well, frames of reference. At this point then there really is no sense of two frames moving towards or away from each other. There is just relative motion between the two frames, and this relative motion is what causes time dilation when comparing time intervals between two events between the two frames.

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  • $\begingroup$ See: physics.stackexchange.com/questions/174694/… It appears that the direction matters for how the time dilation responds; or does it? I like your answer, but I would like to reconcile it with the former stack exchange response on this topic. $\endgroup$ Sep 15, 2019 at 23:08
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Gravitational time dilation is a name given to the observation that the higher clock in a gravitational field runs faster than a lower clock. It is a poor name.

The observation is between clocks.

The same observation is made between two accelerating clocks, one ahead of the other. It can be calculated from the times each clock shows to the other observer after the acceleration stops, when they are moving inertially. Both observers then agree the leading clock shows a later time than the trailing clock.

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There are two separate effects to keep track of here- namely time dilation caused by the relative motion of the space traveller, and time dilation due to gravity.

The first effect is dependent only on the relative speeds of the reference frames of the space-traveller and the observer on Earth- the direction of motion has no effect. You can convince yourself of this if you imagine observations made in deep space where there is no local large spherical body (ie Earth) beneath you- you would have no way of judging direction, and nothing to be tangential to.

The second effect is governed by the space-traveller's relative distance from the centre of the Earth, and so a traveller approaching Earth will experience a gradually reducing gravitational frequency shift, whereas a traveller moving away from Earth will experience a gradually increasing one. The space-traveller moving tangentially to the Earth will experience a variation in gravitational time shift in proportion to the component of their motion normal to the Earth's centre, which will be zero in the case of a traveller orbiting the Earth, but will vary for a traveller on a straight path tangential to the Earth.

These effects have to be taken into account when calibrating GPS systems. You can read an interesting summary here: https://en.wikipedia.org/wiki/Error_analysis_for_the_Global_Positioning_System#Relativity

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