The effective potential energy, E, of a lunar satellite of mass, m, moving in an. elliptical orbit around the moon of mass, m, is given by
E = \(\frac{K^{2}}{2m_{1}r^{2}} – \frac{Gm_{1}m_{2}}{r}\) where r is the distance of the satellite from the mooΕ and G is the universal gravitational constant of dimensions, M\(^{-1}\)L\(^{3}\)T\(^{2}\).
Δetermine the dimensions of the angular momentum, K, of the satellite using dimensional analysis.
Explanation
Dimensions of the angular momentum, K =
\(\frac{[K]^{2}}{[m_{1}][r]^{2}} = \frac{[G][m_{1}][m_{2}]}{[r]}\)
\(\frac{[k]^{2}}{ML^{2}} = \frac{M^{-1} L^{3} T^{-2}M^{2}}{L}\)
[K] = (M\(^{2}\)L4T\(^{-2}\))Β½
\(\therefore\) [k] = ML\(^{2}T^{-1}\)
(NOTE: the dimension of E = dimension of gravitational force.)