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A satellite has kinetic energy $K$, potential energy $V$ and total energy $E .$ Which of the following statements is true?
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Verified Answer
The correct answer is:
$K=-V / 2$
As we know that for the earth and satellite system
Kinetic energy, $\quad K=\frac{G M m}{2 a}$
Potential energy, $V=-\frac{G M m}{a}$
and total energy, $E=-\frac{G M m}{2 a}$
where, $a=$ radius of the orbit of the satellite and $m=$ mass of the satellite
On the basis of above three expressions for the energies, we have
$K=\frac{G M m}{2 a}=-\left(-\frac{G M m}{2}\right)=-\frac{V}{2}$
Kinetic energy, $\quad K=\frac{G M m}{2 a}$
Potential energy, $V=-\frac{G M m}{a}$
and total energy, $E=-\frac{G M m}{2 a}$
where, $a=$ radius of the orbit of the satellite and $m=$ mass of the satellite
On the basis of above three expressions for the energies, we have
$K=\frac{G M m}{2 a}=-\left(-\frac{G M m}{2}\right)=-\frac{V}{2}$
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