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Grade 11General Physics

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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keerthi

8 Years agoGrade 11

1 Answer

Eshan

8 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 distance $x$ from center of earth.

$\implies \dfrac{Gm_1m}{x^2}=\dfrac{Gm_2m}{(r-x)^2}$
We can find the value of $x$ and 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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