# Answer to Question #11608 in Mechanics | Relativity for parth

Question #11608
A planet moves around the sun in nearly circulas orbit.its period of revolution &quot;T&quot; depends upon 1)radius &quot;r&quot; of the orbit 2)mass &quot;M&quot; OF THE SUN 3) the gravitational constant &quot;G&quot;.SHOW DIMENSIONALLY THAT T SQUARE IS DIRETLY PROPOTIONAL TO r cube
1
2012-07-05T11:27:45-0400
Using

a = GM/R&sup2;,

where R is the radius from the center of the planet to the center of a sun, M is the mass of the sun and G is the Gravitational constant and also using the centripetal force equation

a = W&sup2;R

where W is the radians / second velocity of the planet. Combining these equations above and cancelling the a (acceleration) gives

GM/R&sup2; = W&sup2;R ==&gt; GM/R&sup3; = W&sup2;.

Assuming that W = 1/T we get

GM/R&sup3; = 1/T&sup2; ==&gt; T&sup2; = R&sup3;/GM.

So, T depends upon the radius &quot;R&quot; of the orbit, mass &quot;M&quot; of the sun and the gravitational constant &quot;G&quot; and T&sup2; is directly proportional TO R&sup3;.

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