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In special relativity we get a time dilation for high velocities near by c and in general relativity we get also a time dilation near by strong gravity fields.

But what about a combination of these two effects? So if a object has a high velocity and is in a strong gravity field, would the effect of time dilation higher or will the effects cancle each other?

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marked as duplicate by Rob Jeffries, Kyle Kanos, ACuriousMind, Gert, hft Nov 5 '15 at 3:17

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Both effects operate independently.

A good example is the GPS signal. The GPS clocks need to be accurate to within $30ns$ to achieve the required positioning accuracy. However, GPS satellites orbit the earth; in other words they go fast, and at high altitude. Their speeds slows down time, and the reduced gravity makes it flow faster. Hence there are 2 adjustments that need to be made.

  1. Their speed (almost $14,000km/h$)implies the clocks will be slow by about $7\mu$$s$
  2. Because of their altitude (about $20,000km$), their clocks will run fast by about $45\mu$$s$ per day.

As a result, the adjustment required is $45-7=38\mu$$s$ per day. This might not sound like much, but remember that light travels at $300,000km/s$, or $11.4km$ in $38\mu$$s$. In other words, without this adjustment, your position would drift more than $300km$ per month!

See here for more information about GPS satellites.

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