How Do Kepler's Laws Explain Satellite Orbits and Gravity Points?

[Steven-]

1) Satellite X and Satellite Y orbit the earth. The distance between X and the Earth is 8 times greater than the distance between Y and the earth. Using Kepler's Laws, the period of satellite X is what factor times the period of satellite Y?

R is the distance between satellite Y and the earth

I used Kepler's third law:

T^2=R^3 for Y
T^2=(8R)^3 for X

So T for Y would be R^(3/2)
and T for X would be 22.6*R^(3/2)

So the factor is 22.6 right? But the answer key says "4.0" So am I right?

2) There is a point between the Earth and the moon where the net force of gravity on an object located at that point would be zero. I have no idea which formula to use on this problem, please help.

 

[member 553083]

Thank you!This is known as the Lagrange point, and it is determined by a combination of Newton's law of gravity and the equations of motion. You can find more information about it here: https://en.wikipedia.org/wiki/Lagrangian_point