Mass of earth = Me
Mass of satellite = m
Radius of orbit of satellite = R
Orbital Velocity vo = \(\sqrt{\frac{GM}{R}}\)
(a) K.E. versus orbital radius R
K.E. = \(\frac{1}{2}mm_0^2\) = \(\frac{1}{2}m.\frac{GM}{R}\)
= \(\frac{GMm}{2R}\)
K.E \(\propto\) \(\frac{1}{R}\) (It decreases with R)
(b) P.E. versus orbital radius R.
P.E. = −\(\frac{GMm}{R}\) or P.E.\(\propto\) \(\frac{-1}{R}\)
(c) Total energy versus Orbital radius R
K.E = +\(\frac{1}{2}\)\(\frac{GMm}{R}\) - \(\frac{GMm}{R}\)
T.E = \(\frac{1}{2}\) \(\frac{GMm}{R}\) - \(\frac{GMm}{R}\)
T.E = -\(\frac{1}{2}\)\(\frac{GMm}{R}\)
