If the masses of Earth and the Moon were both doubled, by how much would the radius of the Moon's orbit about Earth have to change if its speed did not change? (Assume that rEMrEM is the mean distance between Earth and the Moon before changing of the mass, r′EMrEM′ is the mean distance between Earth and the Moon after changing of the mass.)

Question

Geography

Johanna Bailey

1 November, 01:52

If the masses of Earth and the Moon were both doubled, by how much would the radius of the Moon's orbit about Earth have to change if its speed did not change? (Assume that rEMrEM is the mean distance between Earth and the Moon before changing of the mass, r′EMrEM′ is the mean distance between Earth and the Moon after changing of the mass.)

+2

Answers (1)

Know the Answer?

Maurice Erickson · Answer 1

doubled

Explanation:

for speed to remain same, the gravitational force must remain same

F = GMeMm/r²

Me: Mass of Earth

Mm: Mass of Moon

F = G*2*Me*2*Mm/r²

if r is doubled

F = G*2*Me*2*Mm / (4r²)

F = GMeMm/r²