A satellite of mass m is moving in a circular | vedclass

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(C) Let the satellite revolve in a circular orbit of radius $r$ with a linear velocity $v$.The centripetal force acting on the satellite is provided b

Vedclass · Accepted Answer

$(G M m^2 r)^{1/2}$

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(C) Let the satellite revolve in a circular orbit of radius $r$ with a linear velocity $v$.The centripetal force acting on the satellite is provided by the gravitational force due to the earth.$	herefore F_{	ext{centripetal}} = F_{	ext{gravitational}}$$\Rightarrow \frac{mv^2}{r} = \frac{GMm}{r^2}$$\Rightarrow v = \sqrt{\frac{GM}{r}}$The angular momentum $L$ of the satellite about the center of the orbit is given by $L = mvr$.Substituting the value of $v$:$L = m \left(\sqrt{\frac{GM}{r}}ight) r$$L = m \sqrt{GM} \cdot \sqrt{r} = \sqrt{GMm^2r}$$L = (GMm^2r)^{1/2}$

$A$ satellite of mass $m$ is moving in a circular orbit of radius $r$ around the earth. The angular momentum of the satellite about the center of orbit is ($M=$ mass of earth,$G=$ gravitational constant).

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