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.

Answer 1

Given T² α r³ ⇒ T α r^3/2 is also function of g and 

R ⇒ T α g^x R^y