The orbital angular momentum of a satellite r | vedclass

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(B) The orbital angular momentum $L$ of a satellite of mass $m$ revolving in a circular orbit of radius $r$ is given by $L = mvr$.Since the orbital ve

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$2L$

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(B) The orbital angular momentum $L$ of a satellite of mass $m$ revolving in a circular orbit of radius $r$ is given by $L = mvr$.Since the orbital velocity $v = \sqrt{\frac{GM}{r}}$,we can substitute this into the expression for $L$:$L = m \sqrt{\frac{GM}{r}} \cdot r = m \sqrt{GMr}$.This shows that $L \propto \sqrt{r}$.If the new distance is $r' = 4r$,the new angular momentum $L'$ will be:$L' = L \sqrt{\frac{r'}{r}} = L \sqrt{\frac{4r}{r}} = L \sqrt{4} = 2L$.

The orbital angular momentum of a satellite revolving at a distance $r$ from the centre is $L$. If the distance is increased to $4r$,then the new angular momentum will be:

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