# Question fa936

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,

${F}_{g} = {F}_{c} \implies G \cdot M \cdot \frac{m}{r} ^ 2 = m \cdot {v}^{2} / r \implies {v}^{2} = G \cdot \frac{M}{r}$

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}$$= m \cdot$$\vec{v}$= mv* ( -$\vec{i}$$\cdot \cos \theta +$$\vec{j}$*sentheta)# where $\theta$ is the angle of the satellite in relation with axis $X$.

The kinetic energy is defined as ${E}_{k} = m \cdot {v}^{2} / 2$, 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.