Question #fa936

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Question #fa936

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Answer 1 · 2016-05-09T21:07:53

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,

$F_{g} = F_{c} \Rightarrow G \cdot M \cdot \frac{m}{r^{2}} = m \cdot \frac{v^{2}}{r} \Rightarrow v^{2} = G \cdot \frac{M}{r}$ $F_g = F_c => G*M*m/r^2 = m*v^2/r => v^2 = G*M/r$

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

$\to p$ $vec p$ $= m \cdot$ $= m *$ $\to v$ $vec v$ $= m v \cdot ($ $= mv* ($ - $\to i$ $vec i$ $\cdot cos θ +$ $*costheta +$ $\to j$ $vec j$ $\cdot s e n θ)$ $*sentheta)$ where $θ$ $theta$ is the angle of the satellite in relation with axis $X$ $X$ .

The kinetic energy is defined as $E_{k} = m \cdot \frac{v^{2}}{2}$ $E_k =m*v^2/2$ , thus as the module of speed is constant, $E_{k}$ $E_k$ is contant.

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

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Question #fa936

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