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Satellite in eclipse



At great risk of being thwapped with a clue bat, I'm going to ask this
newbie sort of question that may seem stupid but it has me stumped.

I read/hear about satellites being in eclipse for too long and running out
of battery/shutting down/whatever.  Now, since most of the LEO satellites
are in orbits of 100 minutes +/-, I don't understand how they could be in
eclipse for more than ~50 minutes.  So the question is...

For the satellites that have this eclipse issue, is it that their batteries
are essentially expired and can't power the satellite for ~50 minutes (that
makes sense to me) based on the charge they get from having the solar panels
exposed for ~50 minutes, or is there some mechanism that is totally
non-obvious to me that allows a LEO satellite to be in the dark for periods
of time much longer than half of each orbit thereby creating a situation
where the batteries have to power it in the dark for a very long period of
time relative to the orbital period?

If it's the former, well, that's obvious enough I guess.  If it's the
latter, could someone draw me a picture or point me to a URL that explains
how that is possible?

Thanks.

Darin
VE3OIJ
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