Question

A spy satellite is orbiting earth and experiences a gravitation Force F if a similar satellite with one half the mass is placed in an orbit that is twice as far from the earths center the gravitational force between the earth and the second satellite will be what multiple of F?

Answer 1

The gravitational force on the second satellite is 1/8 of the force exerted on the 1st satellite.

Explanation:

The magnitude of the gravitational force exerted by the Earth on the satellite is given by:

$F=G\frac{Mm}{r^2}$

where

G is the gravitational constant

M is the Earth's mass

m is the mass of the satellite

r is the radius of the orbit of the satellite

Let's call F the gravitational force on the first satellite, of mass m, with an orbit of radius r.

The second satellite has mass

$m'=\frac{m}{2}$

and the radius of its orbit is

$r'=2r$

So, the gravitational force exerted on the second satellite is

$F'=G\frac{M(\frac{m}{2})}{(2r)^2}=\frac{1}{8}(\frac{GMm}{r^2})=\frac{1}{8}F$

Therefore, the force on the second satellite is 1/8 of the force exerted on the 1st satellite.

Learn more about gravitational force:

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