Question

A satellite is in circular orbit around an unknown planet. A second, different, satellite also travels in a circular orbit around this same planet, but with an orbital radius four times larger than the first satellite. Sue-Bob, the bad physics student, says: "The gravitational force of the planet depends inversely on the orbital radius squared. Since the second satellite's orbitai radius is four times that of the first satellite, the second satellite experiences on-sixteenth the gravitational force that is exerted on the first satellite. Explain what is right, and wrong, with Sue-Bob's explanation.

Answer 1

According to sue-Bob's explanation the gravitational force is Inversly promotional to the radius of the orbit

So F=k/r here k is the constant and r is the radius of the orbit

Let the first satellite experiences the force F = k/r

So for the second satellite r'= 4*r

So F' = k /r' = k/4r = F/4

So F'= F/4 . ( The on-fourth of first force )

But in real the second satellite experience the Force on-sixteenth the force experienced by first satellite

Which is wrong according to suehbob's explanation.

But as we know the force Inversly Perpotional to the squre of the radius of the orbit

F = k/r²

So the on -sixteenth os right according Newton, but wrong according the bad physics student.