Question

The weight of a body on earth is 1000 n. Determine its weight on a planet whose 1 1 mass is 10 and radius 2 that of the earth.

Answer 1

According to Newton, F = G * m1 * m2 / R^2

Where m1 and m2 are the two masses and R is the distance between them.

You can certainly do a three dimensional integral of the above force to find out the answer, but all you really need to know are the scaling laws that apply.

First, if m2 is the planet, and it has a different mass than Earth, the resulting force will be proportional to the planetary mass. So 1/7 the mass will lead to 1/7 the force.

Second, if the radius is different, the force will be proportional to the square of the the radius. If the radius goes from 1 to 1/2 the force will go from 1 to 4.

Combining the two effects gives 1/7 * 4 = 4/7.

If the original weight was 700g force, the new weight will be 400 g force.