Please help me??

Question

Use the mass of the sun and its distance to the Earth to compute the time it takes the earth to circle the sun? Express your answer in years.

What equation do I use to slolve this and what is the answer. I think I did it incorrectly. Not sure if the answer is one year.

Answer 1

The force of gravity, Fg, goes as: GM1M2/r^2, where G is the gravitational constant, M1 and M2 are the two masses (of the Sun and the Earth), and r is the distance between them.

http://en.wikipedia.org/wiki/Gravitational_constant

This induces an acceleration on the Earth of Fg/M

If any object is traveling in a circular arc at constant speed, it experiences an acceleration of V^2/r.

Since the orbit is stable, we have:

V^2/r = Fg/M = GM1/r^2

or

V^2 = GMs/r

Since we know G (from wikipedia), Ms (the mass of the Sun), and r (the distance from the earth to the Sun), we can solve this for V^2 and then V.

The total distance traveled in one orbit is (2)(pi)(r) and the total time for an orbit is distance/speed or

orbit time = 2(pi)(r)/V

Just make sure you get all the units right. (60 seconds/minute, kilometers vs. meters, etc.)