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A satellite is in an orbit around the earth. If its kinetic energy is doubled, then
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it will escape out of earth’s gravitational field
Kinetic energy, $K=\frac{1}{2} m v_0^2$
or $v_0=\sqrt{\frac{2 K}{m}}$
When kinetic energy is doubled, then
$v_0^{\prime}=\sqrt{\frac{2 \times 2 K}{m}}=\sqrt{2} \sqrt{\frac{2 K}{m}}=\sqrt{2} v_0$
But $\sqrt{2} v_0=v_e$ (escape velocity)
Hence satellite will escape out of earth's gravitational field.
or $v_0=\sqrt{\frac{2 K}{m}}$
When kinetic energy is doubled, then
$v_0^{\prime}=\sqrt{\frac{2 \times 2 K}{m}}=\sqrt{2} \sqrt{\frac{2 K}{m}}=\sqrt{2} v_0$
But $\sqrt{2} v_0=v_e$ (escape velocity)
Hence satellite will escape out of earth's gravitational field.
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