(adsbygoogle = window.adsbygoogle || []).push({}); 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 radiusr, the constantGin Newton's law of gravitation, and the mass of the SunM_{s}. What combination of these factors gives the correct dimensions for the period of a planet?

2. Relevant equations

F = Gm_{1}m_{2}/r^{2}

G = [L^{3}/MT^{2}]

T=C*r^{a}*M^{b}*G^{c}

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}[[L^{3}/MT^{2}]^{c}

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

[T] = L^{a+3c}M^{b-c}T^{-2c}

Okay, now I solve for C using the T^{1}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

With the exponents solved for, I return to my original equation:

T=C*r^{a}*M^{b}*G^{c}

Only now, I sub them in.

T=C*r^{3/2}*M^{-1/2}*G^{-1/2}

THIS is where I have a problem! :( The answer given to this set was C = sqrt(GM)*r^{3/2}.

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 :(

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# Homework Help: Finding Dimensions for Period of a Planet

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