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fireyking19
21.09.2019 •
Physics
You have been visiting a distant planet. your measurements have determined that the planet's mass is three times that of earth but the free-fall acceleration at the surface is only one-fourth as large.
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Ответ:
g = (G*m) *M / (RE^2),where G and m are constants. G is Universal Gravitational Constant and m is your mass, which is the same everywhere.
Then, if ME is the mass of the planet Earth, RE is the radius of planet Earth, MP is the mass of the distant planet and RE is the radius of the distant planet you can write:
g on Earth / g on distant planet = [ME/(RE^2)] / [MP/(RP^2)] = 4
And MP = 3ME
Then you can obtain the ratio of RP/RE
[ME / (RE^2) ] / [3ME / (RP)^2 ] = 4
=> (RP)^2 / (RE)^2 = 4*3 = 12
=> (RP)^2 = 12*(RE)^2
=> RP = (√12) RE
This is the radius of the distant planet is √12 or about 3.46 times the radius of the Earth.
Ответ: