question archive A spacecraft orbits an unknown planet at a distance of 5
A spacecraft orbits an unknown planet at a distance of 5
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A spacecraft orbits an unknown planet at a distance of 5.2x10 to the seventh power meters from the center. The period of its orbit is 52 hours. What is the mass of the planet?
2.4 x10 to the 24 kg,3.5x10 to the 22,9.2x10 to the 25,6.1x10 to the 26,1.9x10 to the 20.
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Answer:
According to keplers law, the square of the time period of a satellite moving round the planet is proportional to the cube of the distance.
T^2 = 4 π^2 R^3 / G M
mass of the planet is
M = 4 π^2 R^3 / G T^2
= 4 π^2 (5.2x10^7)^3 / (6.67x10^-11) [( 56)(3600)]^2
= 2.04x10^24 kg
