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:
[tex]F=G\frac{Mm}{r^2}[/tex]
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
[tex]m'=\frac{m}{2}[/tex]
and the radius of its orbit is
[tex]r'=2r[/tex]
So, the gravitational force exerted on the second satellite is
[tex]F'=G\frac{M(\frac{m}{2})}{(2r)^2}=\frac{1}{8}(\frac{GMm}{r^2})=\frac{1}{8}F[/tex]
Therefore, the force on the second satellite is 1/8 of the force exerted on the 1st satellite.
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