Satellite

Classical Mechanics Level 3

A satellite of mass $m_s$ is revolving in a circular orbit of radius $r_s$ around the Earth of mass $M$ has a total energy $E$ .

Find its angular momentum.

\sqrt{2Em_s r_s}

\frac{\sqrt E}{m_s r_s ^2}

\frac E{2m_s r_s ^2}

(2Em_s r_s ^2 )^{1/2}

1 solution

Md Zuhair
Mar 7, 2017

We know $E = \dfrac{I{\omega}^2}{2}$ , Now $I= m_s * r_s^2$

So $\sqrt{\dfrac{2E}{I}}$ = $\sqrt{\dfrac{2E}{m_s * r_s^2}} = \omega$

We know Angular Momentum $J = I\omega$

So putting $\sqrt{\dfrac{2E}{m_s * r_s^2}} = \omega$ in the equation we get

$(2Em_s r_s ^2 )^{1/2}$ on simplification

So answer $\boxed{J = (2Em_s r_s ^2 )^{1/2}}$