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How long is a satellite above the horizon?

The Hubble Space Telescope is on a circular, low-Earth orbit, at an elevation h= 600km above the Earth’s surface. For an observer who sees HST pass through the zenith, how long is HST above the horizon during each orbit?

The part of the orbit is 2t/360 where t is the angle given by cos t=R/R+h. R is the radius of the Earth, h the height.
So cos t = 6,378.5/6,978.5=0.914 => t=24 degree => part of orbit 48/360 = 0.1333

The total length of the orbit can be found from Kepler’s third law and is 96 minutes. So each orbit Hubble is 12.8 min above the horizon.

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