An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kelper's Third law about the period of a satellite around a common central body, square of the period of revolution T is proportional to the cube of the radius of the orbit r. Show usnig dimensional analysis, that `T = (k)/(R ) sqrt((r^3)/(g)),` Where k is a dimensionless constant and g is acceleration due to gravity.

Explanation

To show that the period of revolution \( T \) of an artificial satellite is given by the equation

\[ T = \frac{k}{R} \sqrt{\frac{r^3}{g}}, \]

where \( k \) is a dimensionless constant, \( R \) is the radius of the planet, \( r \) is the radius of the orbit, and \( g \) is the acceleration due to gravity, we will use dimensional analysis.

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