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"By the same token, the force of gravity scales linearly with a planet’s diameter. Half the diameter of a planet and you get half the gravitational force at the
by snake_plissken 11y ago
"By the same token, the force of gravity scales linearly with a planet’s diameter. Half the diameter of a planet and you get half the gravitational force at the surface..."
Wait, what? Assuming the mass of the planet remains constant, wouldn't you get 4 times the gravitational force at the surface?
- ISL 11y agoThe linearity result assumes constant density, not constant mass.
- useless 11y agoI think the assumption is the density remains the same (rho=M/(r^3)) stays the same so GM/(r^2) becomes G rho r.
- derobert 11y agoThe article isn't presuming mass stays constant, but rather that density does. (That's a much more realistic assumption—a world made out of similar stuff will have similar density, for reasonable amounts of gravity)
- aaron695 11y ago> Assuming the mass of the planet remains constant, wouldn't you get 4 times the gravitational force at the surface? No idea why you'd ask this question but yes. But the original statement is wrong isn't it, if you half the diameter you 1/8 the gravity [1/8 the mass] [edit] But you'd also be twice closer, which is 4 times the force, got it.