# Finding Dimensions for Period of a Planet

1. Feb 3, 2010

### clark1089

1. The problem statement, all variables and given/known data
Hi! This is from Physics for Scientists and Engineers, Vol. 6 by Tipler and Mosca.

44. Kepler's third law relates the period of a planet to its orbital radius r, the constant G in Newton's law of gravitation, and the mass of the Sun Ms . What combination of these factors gives the correct dimensions for the period of a planet?

2. Relevant equations
F = Gm1m2/r2
G = [L3/MT2]
T=C*ra*Mb*Gc
3. The attempt at a solution

I'm trying to solve for C in the final equation given.

The big problem I'm having here comes after solving for the exponents in the third equation there...

[T] = [L]a[M]b[[L3/MT2]c

Next I distribute exponents and combine the like terms...

[T] = La+3cMb-cT-2c

Okay, now I solve for C using the T1 on the left side of the equation...

-2c = 1
c = -1/2

Now I have C, the other variables come to me... eheAHEUAEU

a+3(-1/2) = 0
b-c = 0
a = 3/2
b = -1/2

T=C*ra*Mb*Gc

Only now, I sub them in.

T=C*r3/2*M-1/2*G-1/2

THIS is where I have a problem! :( The answer given to this set was C = sqrt(GM)*r3/2.

Can someone tell me what I'm doing wrong? I don't see how T gets removed or why the negative squareroots become positive while the 3/2 remains the same

ANY HELP IS APPRECIATED !!! :( So stuck :(

Last edited: Feb 3, 2010
2. Feb 3, 2010

### clark1089

Made a mistake with T^(-2a).. it's actually T^(-2c)! Fixed that mistake. Sorry :X

Still need help though... :(

Last edited: Feb 3, 2010