Satellite A is following a circular path of radius a around the earth another satellite B follows an elliptical path around the earth. The two satellites have same mechanical energy and their orbits intersect. Find the speed of satellite B at the point where its path intersects with the circular orbit of A. Take mass of earth to be M.

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$\sqrt{\frac{2 G M}{a}}$

$\sqrt{\frac{\sqrt{2} G M}{a}}$

$\sqrt{\frac{G M}{a}}$

$\sqrt{\frac{G M}{2 a}}$

answer is A.

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Detailed Solution

At the point of intersection both the satellites have same PE. Since they have same mechanical energy, their KE will be same at the point of intersection.

Therefore speed of satellite B = Speed of satellite A = $\sqrt{\frac{G M}{a}}$

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