1. Tardigrade
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  3. Physics
  4. If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth, the height of the satellite above the surface of the earth is (where R= Radius of the earth)

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Q. If an artificial satellite is moving in a circular orbit around the earth with a speed equal to half the magnitude of the escape velocity from the earth, the height of the satellite above the surface of the earth is (where $R=$ Radius of the earth)

Gravitation

Solution:

Escape velocity, $v_{e}=\sqrt{\frac{2 G M}{R}}$
Orbital velocity, $v_{o}=\sqrt{\frac{G M}{R+h}}$
Given that $v_{o}=\frac{v_{e}}{2}$
$\therefore \sqrt{\frac{G M}{R+h}}=\frac{1}{2} \sqrt{\frac{2 G M}{R}}$
or $ \frac{G M}{R+h}=\frac{1}{4} \times \frac{2 G M}{R}$
On solving, we get $h=R$