(C) The kinetic energy $E$ of a satellite of mass $m$ moving with orbital velocity $v$ is given by $E = \frac{1}{2}mv^2$.From this,we can express the

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(C) The kinetic energy $E$ of a satellite of mass $m$ moving with orbital velocity $v$ is given by $E = \frac{1}{2}mv^2$.From this,we can express the velocity as $v = \sqrt{\frac{2E}{m}}$.The angular momentum $L$ of the satellite is defined as $L = mvr$.Substituting the expression for $v$ into the formula for $L$,we get:$L = m \left( \sqrt{\frac{2E}{m}} \right) r$$L = \sqrt{m^2 \cdot \frac{2E}{m} \cdot r^2}$$L = \sqrt{2Emr^2}$.

Class 11 Physics Gravitation Energy consideration in Planetary and Satellite motion

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$A$ satellite of mass $m$ revolving in a circular orbit of radius $r$ around the Earth has kinetic energy $E$. Then its angular momentum will be

A
$\sqrt{\frac{E}{mr^2}}$
B
$\frac{E}{2mr^2}$
C
$\sqrt{2Emr^2}$
D
$\sqrt{2Emr}$

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Gravitation

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Energy consideration in Planetary and Satellite motion

$A$ satellite of mass $m$,initially at rest on the Earth,is launched into a circular orbit at a height equal to the radius of the Earth. The minimum energy required is

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Two identical satellites $A$ and $B$ are orbiting the Earth at heights of $R$ and $2R$ respectively,where $R$ is the radius of the Earth. The ratio of the kinetic energy of $A$ to that of $B$ is:

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The figure shows the variation of energy with the orbit radius of a body in circular planetary motion. Find the correct statement about the curves $A, B$ and $C$.

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What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ into a circular orbit at an altitude of $2R$?

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The total energy of a circularly orbiting satellite is

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$A$ satellite of mass $m$ revolving in a circular orbit of radius $r$ around the Earth has kinetic energy $E$. Then its angular momentum will be

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$A$ satellite of mass $m$,initially at rest on the Earth,is launched into a circular orbit at a height equal to the radius of the Earth. The minimum energy required is

Two identical satellites $A$ and $B$ are orbiting the Earth at heights of $R$ and $2R$ respectively,where $R$ is the radius of the Earth. The ratio of the kinetic energy of $A$ to that of $B$ is:

The figure shows the variation of energy with the orbit radius of a body in circular planetary motion. Find the correct statement about the curves $A, B$ and $C$.

What is the minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ into a circular orbit at an altitude of $2R$?

The total energy of a circularly orbiting satellite is

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