A satellite moving around the Earth in a circ | vedclass

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(B) For a satellite in a circular orbit of radius '$r$',the kinetic energy is given by $K = \frac{GMm}{2r}$ and the potential energy is $U = -\frac{GM

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$E$

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(B) For a satellite in a circular orbit of radius '$r$',the kinetic energy is given by $K = \frac{GMm}{2r}$ and the potential energy is $U = -\frac{GMm}{r}$.Thus,the total mechanical energy is $E_{total} = K + U = \frac{GMm}{2r} - \frac{GMm}{r} = -\frac{GMm}{2r} = -K = -E$.To escape the Earth's gravitational field,the final total energy of the satellite must be at least $0$.Let the energy to be added be $\Delta E$.$E_{final} = E_{initial} + \Delta E = 0$.$-E + \Delta E = 0$.$\Delta E = E$.

$A$ satellite moving around the Earth in a circular orbit has kinetic energy '$E$'. What is the minimum amount of energy to be added so that it escapes from the Earth?

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