Question #fa936

1 Answer
Joaquín M.
May 9, 2016

The only magnitude which changes is the linear momentum. Angular momentum and kinetic energy are constant.

Explanation:

The satellite which is revolving in a circular orbit around the Earth has gravity force, pulling towards the Earth, in balance with the centrifuge force, pulling towards the space,

F_g = F_c => G*M*m/r^2 = m*v^2/r => v^2 = G*M/r

where

M = mass of Earth ; m= mass of satellite ; r= distance from the satellite to the centre of Earth ; G= gravitation constant

Therefore, the module of speed of satellite is constant, so the module of linear momentum is constant but not its direction. A satellite in circular orbit has as linear momentum

vec p = m * vec v = mv* ( -vec i *costheta + vec j*sentheta) where theta is the angle of the satellite in relation with axis X.

The kinetic energy is defined as E_k =m*v^2/2, thus as the module of speed is constant, E_k is contant.

As the orbit of the satellite is flat the angular momentum is conserved, consequently, does not change.

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