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How does gravitational attraction fall off with distance?


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November 18, 2012 8:48PM

The size of the gravitational attraction between two masses depends on two things:

The masses of both objects, and the distance between their centers of mass.

-- Regarding the masses, the strength of the force between them is proportional to

the product of the masses. It doesn't matter how big one is or how small the other

one is. All that matters is the product . . . (mass-#1) multiplied by (mass-#2).

When that product doubles, the force doubles.

-- Your question is regarding the distance. The strength of the force between the

two objects is inversely proportional to the square of the distance between them.

This tells you two things about how the distance affects the force.

First, the relationship is inverse, so greater distance means less force.

Second, it's the square of the distance. So triple the distance means 1/32 = 1/9 as much force.

Ten times the distance means 1/102 = 1/100 as much force, and so on.

Talking about the distance, we also need to understand that the 'distance' is the

distance between the 'center of mass' or the 'center of gravity' of the objects. For

purposes of gravity, an object behaves as of all of its mass is right there at the

center. So, for example, your weight on Earth depends on your distance from the

center of the Earth, and that's about 4,000 miles.