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When reading about Astra satellites on Wikipedia (https://en.wikipedia.org/wiki/Astra_1KR), I saw that the period of the Astra 1KR satellite, positioned at 19.2° E, is 1,436.1 minutes (source: NORAD data).

That is 3.9 minutes short of a day (1440 minutes), how is that possible with the satellite still being geostationary?

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A day, i.e. 24 hours, isn't how long the Earth takes to rotate. It's the time between the Sun being in the same place in the sky, but that isn't the same as the time it take the Earth to rotate 360° because the Earth moves around the Sun at the same time as rotating on its axis. Strictly speaking what we call a day is a solar day.

The time the Earth takes to rotate by 360° is called a sidereal day, and it's 23 hours, 56 minutes and 4.1 seconds i.e. about 3.9 minutes less than a solar day. The period of a geostationary satellite is a sidereal day not a solar day, and that's why it too is 3.9 minutes shorter than a solar day.

If you are interested in reading more about this you'll find lots of articles about sidereal time on the web. I found a good introductory article on the Astronomy Essentials web site.

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    $\begingroup$ @Exocytosis not as far as I know. It's expensive to put a satellite in a geostationary orbit because it's a relatively large distance from the Earth for satellites. The only reason for doing it is if you really want it to be geostationary. $\endgroup$ Sep 17 '20 at 15:01
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    $\begingroup$ @Exocytosis It would be possible to make a satellite follow the mean solar day, but that would not make it appear in the sky in a fixed position relative to the sun, because the earth's orbit is elliptical. The difference between "time as defined by the sun's position in the sky" and the mean solar day is called the equation of time and it varies by about $\pm20$ minutes during the year. $\endgroup$
    – alephzero
    Sep 17 '20 at 15:26
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    $\begingroup$ There are satellite(s) at the L1 point for the Earth/Sun system. This is a semi-stable orbit between the Earth and the Sun, explained by NASA here: solarsystem.nasa.gov/resources/754/what-is-a-lagrange-point These satellites effectively orbit the Sun, but have the same effect of being in a orbit around the Earth that has the same period as the solar day. $\endgroup$
    – ManicDee
    Sep 17 '20 at 23:01
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    $\begingroup$ @Exocytosis do you mean a sun-synchronous orbit ? en.wikipedia.org/wiki/Sun-synchronous_orbit where the orbiter is in 24 hour sunlight? Not geostationary or anything like it though. $\endgroup$
    – Criggie
    Sep 18 '20 at 2:00
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    $\begingroup$ It might be insightful to point out that the difference is approximately 1440/365.25 minutes. $\endgroup$
    – MSalters
    Sep 18 '20 at 8:23

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