A planet moves around the sun in nearly circulas orbit.its period of revolution "T" depends upon 1)radius "r" of the orbit 2)mass "M" OF THE SUN 3) the gravitational constant "G".SHOW DIMENSIONALLY THAT T SQUARE IS DIRETLY PROPOTIONAL TO r cube
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Expert's answer
2012-07-05T11:27:45-0400
Using
a = GM/R²,
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 = W²R
where W is the radians / second velocity of the planet. Combining these equations above and cancelling the a (acceleration) gives
So, T depends upon the radius "R" of the orbit, mass "M" of the sun and the gravitational constant "G" and T² is directly proportional TO R³.
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