Satellite - 1 moves around planet -1 in a circular orbit of radius 384000 km and period 27.32 days whereas satellite - 2 moves around planet - 2 in another circular orbit of radius 1883000 km and period 16.69 days. Then, mass of planet - 2, M2 and that of planet-1 ie M1 are related by
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Answer:
At what height above the Earth's surface would you find a geosynchronously (P = 24 hours) orbiting satellite?
[Answer] The simplest way to calculate this answer is to compare a geosynchronous orbit with that of the moon:
(P2)moon (a3)moon
------------- = --------
(P2)geosyn (a3)geosyn
(27.32 days)2 (384,000 km)3
------------- = -----
(1 day)2 (a3)geosyn
(a3)geosyn = 5.66 x 1016/ 7.46 x 102 km3 = 7.58 x 1013 km3
ageosyn = 4.23 x 104 km
alternatively, one could use the Newton's form of Kepler's third law:
a3/ p2 = G (MEarth + Msatellite) / 4 pi2
a3 = (24 hr x 3600 s/hr)2 * 6.67 x 10-11 N m2 / kg2 * (5.97 x 1024 kg + 1000 kg) / 39.5
a3 = 7.53 x 1022 m3
a = 4.22 x 107 m = 4.22 x 104 km
to get our final answer, we have to subtract the radius of the Earth:
height = 4.22 x 104 km - 6.4 x 103 km = 3.6 x 104 km