Gravity Hypothetical planet again
A hypothetical planet has a density radius and surface gravitational acceleration
If the radius of the planet were doubled but the planetary density stayed the same, the acceleration due to gravity at the planet's surface would be _ _ __ ?
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1 solution
R is doubled, thus the volume becomes 8 times (4/3* pi * r^3). volume * density = mass, thus mass becomes 8 times. by the formula for gravitational acceleration: G * M/(r^2), thus G * 8M/4(R^2) gives twice the earlier acceleration. therefore 2g.