Let’s assume that the radius of the Earth has decreased by 3 times. How should its mass change
| December 20, 2020 | education
Let’s assume that the radius of the Earth has decreased by 3 times. How should its mass change so that the acceleration of gravity on the surface remains the same?
Acceleration of gravity:
g = G * M / R ^ 2
When changing the radius by 3 times
g₁ = G * M / (R / 3) ^ 2 = G * (9 * M) / R ^ 2
This means that in order for g to remain unchanged, the mass must be reduced by a factor of 9.
Let’s check:
g = G * (M / 9) / (R / 3) ^ 2 = G * M / R ^ 2
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