**Question:**

**An artificial satellite is revolving around a planet of mass M and radius R, in a circular orbit of radius r. From Kepler’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 using dimensional analysis, that T = k/R √r3/g where k is a dimensionless constant and g is acceleration due to gravity.**

**Solution:**

From Kepler’s third law, we know that

T2 a3 where T2 is the square of time period of the satellite revolving around a planet and is proportional to the cube of the radius of the orbit r3.

T2 r3

T r3/2

T depends on R and g

T r3/2gaRb