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This question already has an answer here:

I am trying to understand and clarify the way time dilation occurs due to general and special relativity and for which reason. In the case where an object is approaching a planet in free-fall how does the gravitational field affect time dilation in the object? I have set out the case below is this correct? I have ignored the effect of the object on the planet.

  1. If an object is approaching a planet, for example, in a straight line from a distance due to gravity it will only experience time dilation due to its velocity and this will increase according to its velocity and SR. It would not experience time dilation due to proximity of the larger body as it is in free fall.
  2. If the object is then stationary on the surface of the planet it will experience time dilation due to being in an accelerated frame as it can no longer fall freely, it would only experience time dilation due to motion of the planet.
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marked as duplicate by John Rennie special-relativity Apr 12 '16 at 9:41

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  • $\begingroup$ Hi user36093; could you rephrase your question a bit so that you're only asking one main thing, and that it's clear what that one main thing is? Right now it's hard to pick out a single conceptual issue from your four situations. $\endgroup$ – David Z Apr 11 '16 at 11:56
  • $\begingroup$ Hi user36093. See the question I've linked. In my answer to it I do exactly the calculation you describe. Time dilation is calculated from the metric and is affected by both the velocity of the moving object and the spacetime curvature. $\endgroup$ – John Rennie Apr 11 '16 at 16:35
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In general relativity both the motional time dilation (usually associated with special relativity) and the gravitational time dilation should be calculated together. It is not strictly correct to break the problem apart into two pieces.

To calculate time dilation you need to calculate the proper time elapsed for an observer, then compare that to the coordinate time as measured by a distant stationary observer.

A freely falling object will experience time dilation from both the gravitational field (space-time metric) and their motion. Even though they are in an inertial frame, they still measure time differently, because the local space-time is curved.

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  • $\begingroup$ @Paul.T; that's a helpful explanation, I see that even for an object heading directly towards the larger body space-time is curved. $\endgroup$ – user36093 Apr 12 '16 at 8:16

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