Newton's Law of Universal Gravitation - Examples

Newton's Law of Universal Gravitation































Suppose that the force between two objects, one with a mass of 2kg and the other with a much larger mass, is 20N. Replacing the 2kg mass by a 4kg mass --- doubling one mass --- will double the force. The force between the objects would then be 40N. In this case, the larger mass could be the earth.



How would your weight change if the mass of the earth were increased to three times its present value while its radius stayed the same?

Your weight would go up by a factor of three.



What would happen to your weight if the mass of the earth increased to three times its present value while your mass doubled?

Your weight would go up by a factor of 3 times 2 or a factor of 6. You would weigh six times what you do now.



What would happen to the force between two objects if the masses of both were doubled while the distance between them stayed the same?

The force is proportional to the product of the masses, so it would go up by a factor of 2 times 2 or a factor of 4.

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Edmund Halley asked Sir Robert Hooke what form of force law could account for Kepler's Laws.

Hooke guessed that an inverse square law would do it but was never able to prove it.

When Halley asked Newton what sort of orbit would result from an inverse square law of force, Newton replied "ellipsis".

He had worked it all out twenty years earlier.


What happens to the gravitational force between two objects when the distance between them increases from 2m to 6m?

The distance is multiplied by a factor of 3. The force is inversly proportional to the square of the distance, to it is divided by 3 times 3 or 9. The force becomes 1/9 of what it was.



The moon is about 1/4 the size of the earth. If it had the same total mass as the earth, how much would a 100kg man weigh when standing on its surface?

On the earth, the man would weigh 1000N. In this example, both masses remain the same but the distance between their centers has been divided by 4. The force is therefore multiplied by 4 times 4 or 16. The man would weigh 16000N on the surface of the Moon.



Since a man standing on the moon really weighs only 1/6 of what he weighs on the surface of the earth, there is something wrong with the previous example. Fix it.

The size of the moon is OK, so the distance can't be changed. The man's mass does not change. The only thing that could be wrong is the mass of the moon. The example assumed that it was the same as the earth. That gave the man much too much weight --- 16 times the earth value or 96 times the correct value for the real moon. Evidently the assumed mass for the moon was 96 times what it should be. The mass of the moon is 1/96 the mass of the earth.

We have just weighed the moon.

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Objects falling to the earth, the moon falling around the earth, are being attracted by the earth's mass.

Planets in their elliptical orbits are all accelerating directly toward the sun which is attracting them.

Tides are caused by the moon's gravitational attraction for the earth's oceans.

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Uranus showed small deviations from its predicted orbit. Newton's laws located the undiscovered planet which was attracting it. Telescopes found Neptune there.

Sir Edmund Halley used Newton's laws to predict the return of a comet.

Distant stars orbit each other exactly according to Newton's laws.

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