A synchronous satellite, which always remains above the same point on a planet\'

Question

A synchronous satellite, which always remains above the same point on a planet's equator, is put in orbit around Saturn so that scientists can study a surface feature. Saturn rotates once every 10.5 h. Use the data of Table 13.2 to find the altitude of the satellite.

______ km

Table 13.2:

A synchronous satellite, which always remains above the same point on a planet's equator, is put in orbit around Saturn so that scientists can study a surface feature. Saturn rotates once every 10.5 h. Use the data of Table 13.2 to find the altitude of the satellite. ______ km Table 13.2:

Explanation / Answer

Period of Saturn T = 10.5 h = 10.5 x 60 x 60 s = 37800 s Mass of Saturn M = 5.69 x 10 26 kg Radius of saturn R = 5.9 x 10 7 m We know T = 2p v[r^ 3 / GM ] r ^3 = GM (T/2p) ^2 Where G = Gravitational constant = 6.67 x 10 ^-11 Nm ^2/ kg ^2 Subsitute the values we get r 3 = 1.373 x 10 ^24 r = 111.161 x 10^ 6 m We know orbital radius r = R+h From this altitude h = r-R = 5.216 x 10 ^7 m The altitude of the satellite h = 5.216 x 10 ^7 m

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