Calculating the Period of a Planet Orbiting the Sun

[tnutty]

Homework Statement

A planet moves in an elliptical orbit around the sun. The mass of the sun is M_s. The minimum and maximum distances of the planet from the sun are R_1 and R_2 , respectively.


Using Kepler's 3rd law and Newton's law of universal gravitation, find the period of revolution ,P, of the planet as it moves around the sun. Assume that the mass of the planet is much smaller than the mass of the sun.

Express the period in terms of G, M_s, R_1, R_2.

Homework Equations

T^2 = 4(pi)^2(r)^3 / GM

The Attempt at a Solution

r = (R_1 + R_2 ) / 2

T^2 = [ 4 pi^2 * ( 1/2 (R_1+R_2) ) ^3 ] / GM

T = sqrt ( " the above" );


I guess I went wrong somewhere. any help?

 

[tnutty]

any help?

 

[nlightner]

Hello,

I would like to clarify that the formula you have used is correct. However, there is a small mistake in your calculation. The formula for the period, T, in terms of G, M_s, R_1, and R_2 is:

T^2 = (4*pi^2 / G*M_s) * (R_1+R_2)^3

Therefore, the correct solution would be:

T = sqrt [(4*pi^2 / G*M_s) * (R_1+R_2)^3]

I hope this helps you with your homework. Keep up the good work!