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[i]Imagine the earth with its shadow (umbra) cone projecting behind it, away from the sun. The shadow moves up and down 24 degrees with the season due to the tilt of the earth's axis. Now take a hula hoop which represents the orbit. You can rotate it up and down (inclination) and around the earth's axis (right ascension of the ascending node, RAAN, if you must know). Under some rotations the entire hoop is outside of the umbra cone. However, it is impossible for the entire hoop to be INSIDE of the umbra cone, which is what is required for a period of constant night. According to my handy SMAD book (Space Mission Analysis and Design) the longest eclipse (night) period for a satellite at space station altitude is a little over 36 minutes. This is regardless of inclination or RAAN. This happens when the orbit (hula hoop) crosses right through the middle of the umbra cone.[/i]
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