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 substitute this into the expression for $L$:$L = m \sqrt{\frac{GM}{r}} \cdot r = m \sqrt{GMr}$.This shows that $L \propto \sqrt{r}$.Let the initial angular momentum be $L_1 = L$ at distance $r_1 = r$.Let the new angular momentum be $L_2$ at distance $r_2 = 4r$.Using the proportionality $L \propto \sqrt{r}$,we have:$\frac{L_2}{L_1} = \sqrt{\frac{r_2}{r_1}} = \sqrt{\frac{4r}{r}} = \sqrt{4} = 2$.Therefore,$L_2 = 2L_1 = 2L$.

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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