Ni,

In general artificial satellites do not have terribly accurate clocks on board.

The average commsat or Earth reconsat has no need for 'synchronized' clocks (whatever that means).

And certainly the average satellite has no need to correct *anything* for general relativity.

Could you perhaps rephrase your question?

Then it is a theoretical question. We know that at high altitudes time ticks faster due to gravitational time dilation.

And some sources try to explain it theoretically.

http://relativity.livingreviews.org/Articles/lrr-2003-1/

Ni,

I'm still puzzled. Are you asking for an explanation of gravitational redshift/time dilation?

Or are you asking about satellite technologies?

Good question,

It seems to me that satellite technologies incorporates gravitational redshift/time dilation (in scientific researches for example).

The Hubble telescope needs to perform any task within a given interval on a clock onboard.

GPS satellites are required to return the time on its clocks. All these clocks must be synchronized.

Телескоп Хаббла должен выполнять любую задачу в течение заданного интервала по часам на борту. 

GPS спутники обязаны вернуть показания времени на своих часах. Все эти часы должны быть синхронизированы.

Satellites achieve a high accuracy of time through communication with ground stations.

Why do we need to synchronize satellites?

The pace of time the satellite is more than the surface of the Earth (the speed of the satellite gives the slowing of the clock is smaller than the Earth gravitation gives you the acceleration of the clock), so for comparison with the earth clock, we need to synchronize the pace of the clock on the satellite. You also need to consider variable gravity from the Sun and the moon.

However, you also need to sync the digital clock readings, as without it not working, for example, GPS.

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Темп времени на спутнике больше, чем на поверхности Земли (скорость спутника дает замедление хода часов меньше, чем гравитация Земли дает ускорение хода часов), поэтому для сравнения с земными часами нам необходима синхронизация темпа хода часов на спутнике. Необходимо учесть также переменную гравитацию от Солнца и Луны.

Однако нужно еще и синхронизация цифровых показаний часов, поскольку без этого не работает, например, GPS.