A hypothetical planet has density $ρ$ , radius R, and surface gravitational acceleration g. If the radius of the planet is doubled, but the planetary density stayed the same, the acceleration due to gravity at the planet’s surface would be ___ times g.

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Solution

$g = \frac{G M}{R^{2}} = \frac{G \frac{4}{3} π R^{3} ρ}{R^{2}} = \frac{4}{3} π G ρ R$
Now since R is doubled, the new g will also be doubled

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A hypothetical planet has density ρ, radius R, and surface gravitational acceleration g. If the radius of the planet is doubled, but the planetary density stayed the same, the acceleration due to gravity at the planet’s surface would be ___ times g.

g=GMR2=G43πR3ρR2=43πGρR Now since R is doubled, the new g will also be doubled

A hypothetical planet has density $ρ$ , radius R, and surface gravitational acceleration g. If the radius of the planet is doubled, but the planetary density stayed the same, the acceleration due to gravity at the planet’s surface would be ___ times g.

$g = \frac{G M}{R^{2}} = \frac{G \frac{4}{3} π R^{3} ρ}{R^{2}} = \frac{4}{3} π G ρ R$
Now since R is doubled, the new g will also be doubled