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.)

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

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