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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.
user36093
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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.

Paul T.
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