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Find the minimum velocity that must be given to a body of mass m on the surface of earth so that it reaches moon?

Find the minimum velocity that must be given to a body of mass m on the surface of earth so that it reaches moon?

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Grade:11

1 Answers

Eshan
askIITians Faculty 2095 Points
5 years ago
Dear student,

We need to give energy to the body sufficient only to make it reach at a point between Earth and Moon where the net force is zero. After that point, the body will be attracted to moon by itself.

Let the point be at a distancexfrom center of earth.

\implies \dfrac{Gm_1m}{x^2}=\dfrac{Gm_2m}{(r-x)^2}
We can find the value ofxand use it in the conservation of energy equation-

\dfrac{1}{2}mv^2-\dfrac{Gm_1m}{R_1}-\dfrac{Gm_2m}{r-R_1}=-\dfrac{Gm_1m}{x}-\dfrac{Gm_2m}{(r-x)}

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