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Earth has a mass of 5.97 x 10^24 kg and a radius of 6.37 x 10^6 meters. What would be

the force of gravity between the Earth and a 29 kg satellite that is orbiting 65,000
m above the surface of Earth?

1 Answer

5 votes
The force of gravity between the Earth and the satellite can be calculated using the following formula:

F = G x (m1 x m2) / r^2

where F is the force of gravity, G is the gravitational constant (6.67 x 10^-11 Nm^2/kg^2), m1 is the mass of the Earth, m2 is the mass of the satellite, and r is the distance between the centers of the Earth and the satellite.

First, we need to calculate the distance between the satellite and the center of the Earth:

r = radius of the Earth + altitude of the satellite
r = 6.37 x 10^6 m + 6.5 x 10^4 m
r = 6.433 x 10^6 m

Now we can calculate the force of gravity:

F = G x (m1 x m2) / r^2
F = (6.67 x 10^-11 Nm^2/kg^2) x (5.97 x 10^24 kg x 29 kg) / (6.433 x 10^6 m)^2
F = 8.76 x 10^3 N

Therefore, the force of gravity between the Earth and the satellite is approximately 8,760 N.
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