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If a satellite is revolving in a GEO orbit, then what will be the eclipse duration for it? How to calculate when the satellite will enter the dark side of the Earth?

Any formula or online tool would be appreciated.

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  • $\begingroup$ You could try using HORIZONS or CSPICE for this (see astronomy.stackexchange.com/questions/13488 for links), and I think it would depend on the satellite. Feel free to contact me directly (contact info in profile) if you'd like. $\endgroup$ – barrycarter Jul 27 '18 at 17:38
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At the equinox this is quite easy to calculate, at least approximately.

A geostationary orbit is 265000km long, but the Earth's shadow is only 12700km wide (since the Earth-Sun distance is much larger than the orbit).

At an equinox, the sun is in the plane of the equator, and since GEO satellites orbit on the equator, the satellite passes through the middle of the shadow. So it spends 12700/265000 of its orbit in shadow. Each orbit takes 1 day, so that fraction of one day is about 1 hour 10 minutes.

At a solstice, the shadow deviates by 23.5 degrees = 0.41 radians from the equator. This means that at solstice the centre of the shadow will pass about 0.41\times 36000km =15000km from the satellite, and the satellite won't pass through the shadow at all.

At dates in between the calculation is harder. Approximations can be calculated with trigonometry if required.

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