Question

A satellite is revolving round the earth in a circular orbit of radius r and velocity v₀. A particle is projected from the satellite in forward direction with relative velocity v = (√(5/4) - 1)v₀. Calculate its minimum and maximum distances from earth's centre during subsequent motion of the particle.

Answer 1

Since, v_p lies between orbital velocity and escape velocity, path of the particle would be an ellipse with r being the minimum distance.

Let r' be the maximum distance and v'_p its velocity at that moment.

Then from conservation of angular momentum and conservation of mechanical energy, we get