The ratio of the kinetic energy required to b | vedclass

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(B) Let $m$ be the mass of the satellite and $M$ be the mass of the Earth. The radius of the Earth is $R$.$1$. Kinetic energy required for escape $(E_

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$2: 1$

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(B) Let $m$ be the mass of the satellite and $M$ be the mass of the Earth. The radius of the Earth is $R$.$1$. Kinetic energy required for escape $(E_1)$: The escape velocity is $v_e = \sqrt{\frac{2GM}{R}}$. Thus,$E_1 = \frac{1}{2} m v_e^2 = \frac{1}{2} m \left(\frac{2GM}{R}\right) = \frac{GMm}{R}$.$2$. Kinetic energy required for orbital motion just above the surface $(E_2)$: The orbital velocity is $v_0 = \sqrt{\frac{GM}{R}}$. Thus,$E_2 = \frac{1}{2} m v_0^2 = \frac{1}{2} m \left(\frac{GM}{R}\right) = \frac{GMm}{2R}$.$3$. The ratio is $\frac{E_1}{E_2} = \frac{GMm/R}{GMm/2R} = 2:1$.

The ratio of the kinetic energy required to be given to a satellite to escape from the Earth's surface to the kinetic energy required to be given to the same satellite to revolve around the Earth in an orbit just above the Earth's surface is ...........

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