A satellite circling the earth completes each orbit in 5.10x10^3 seconds. What is the gravitational field strength at the location of the satellite's orbit?

A. 3.08 m/s^2
B. 9.68 m/s^2
C. 9.72 m/s^2
D. 9.80 m/s^2

Any help would be appreciated!

Question

A satellite circling the earth completes each orbit in 5.10x10^3 seconds. What is the gravitational field strength at the location of the satellite's orbit?

A. 3.08 m/s^2
B. 9.68 m/s^2
C. 9.72 m/s^2
D. 9.80 m/s^2

Any help would be appreciated!

anonymous · Answer

The period of an orbit is given by:$$T=2 \pi \sqrt{\frac{ r ^{3} }{ GM }}$$where T is period; r is the mean orbital radius; G is the gravitational constant; and M is the mass of the body orbited (Earth in this case).

anonymous · Answer

The value the looking for is the acceleration of gravity on the satellite.  That is given by:$$a=\frac{ GM }{ r ^{2} }$$

anonymous · Answer

Things that are given are T, G, and M.  Well, G and M can be looked up.  

Does this help you see how to solve the problem?

anonymous · Answer

It did help, thank you!

Where I was going wrong was I didn't know the formula for finding the period of an orbit so I kept trying to derive it from other equations (while making many mistakes). I finally have it figured out now though.

Thanks again.

anonymous · Answer

You're welcome.