Gravity and the Inverse-Square Rule

Reason with proportional changes in mass and center-to-center distance.

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For two point masses, F = G m1 m2 / r^2. The same external result applies to nonoverlapping spherically symmetric bodies using center distances. Keep unmentioned quantities fixed. Do not replace r with height above a surface.

Worked example

If distance doubles, the denominator becomes four times larger, so force becomes one quarter. If one mass doubles at the same distance, force doubles.

For a spherical source, gravitational field strength outside it is proportional to one divided by squared center distance. Relative values are one at r, one quarter at 2r, and one ninth at 3r.

Would you believe it?

Earth is in orbit too: it moves around the Sun under gravity. An orbit combines motion with a continually changing direction.

NASA: gravity and mechanics

Question 1 One mass doubles, with the other mass and r fixed. The force becomes what? Twice as large Four times as large Half as large

Question 2 Both masses double while r stays fixed. The force becomes what? Twice as large Unchanged Four times as large

Question 3 An initial force is 36 N. If r triples, the new force is what? 108 N 4 N 12 N

Question 4 A satellite is at height h above a spherical planet of radius R. Which distance enters GM/r^2? R + h h alone R - h

Question 5 At twice a spherical planet's radius from its center, g is what fraction of its surface value? One half Zero One quarter

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