A star like the sun has serveral bodies moving around it at different distance. Consider that all of them are moving in circular orbits. Let `r` be the distance of the body from the centre of the star and let its linear velocity be `upsilon`, angular velocity `omega`, kinetic energy `K`, gravitational potential energy `U`, total energy `E` and angular momentum `L`. As the radius `r` of the orbit increase, determine which of the above quantities increase and which ones decrease.

Explanation

Linear velocity of a body orbiting a star is, `upsilon = sqrt((GM)/(r ))`, when `r` increases, `upsilon` decrease.
Angular velocity, `omega = (2pi)/(T ) = (2pi)/(kr^(3//2))` , When `r` increases, `omega` decrease.
Kinetic energy, `K = (1)/(2) m upsilon^(2) = (1)/(2) m (GM)/(r)` , When `r` increases, `KE` decrease.
Gravitational `PE`, `U = - (GM m)/(r)`, When `r` increases, `PE` becomes less negative i.e., increases.
Total energy, `E = KE + PE = (GM m)/(2r) + ((-GM m)/(r)) = (-GM m)/(2r)` , When `r` increase, `E` increases.
Angular momentum `L = m upsilon r = mr sqrt((GM)/(r)) = m sqrt(GM r)` , When `r` increases, `L` increases.