1.A synchronous satellite, which always remains above the same point on a planet
ID: 2265591 • Letter: 1
Question
1.A synchronous satellite, which always remains above the same point on a planet's equator, is put in orbit around Jupiter to study that planet's famous red spot. Jupiter rotates once every 9.84 h. Use the following data to find the altitude of the satellite above the surface of the planet. Jupiter has a mass of
A synchronous satellite, which always remains above the same point on a planet's equator, is put in orbit around Jupiter to study that planet's famous red spot. Jupiter rotates once every 9.84 h. Use the following data to find the altitude of the satellite above the surface of the planet. Jupiter has a mass of 1.90 Times 1027 kg, and a mean radius of 6.99 Times 107 m. kmExplanation / Answer
In circular orbit, gravitational acceleration g is in equilibrium with centripetal acceleration Ac.
That is, g = GM/r^2 = Ac = omega^2*r
Thus r^3 = GM/omega^2 ==> r = (GM/omega^2)^(1/3)
= (6.674E-11*1.9E27 / (2pi/(9.84*3600)^2))^(1/3) = 159144544.3 m
Altitude = r-r(Jupiter) = 89244544.3 m
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