A satellite of mass M_s is orbiting the Earth in a circular orbit of radius R_s. Due to a critical failure in its solar panels, it starts losing power at a constant rate C. If M_e and R_e denote the mass and radius of the Earth, then find the time it takes the satellite to fall to the surface of the Earth.

A planet is moving around the sun (mass M_s) in an elliptical orbit. When it is at a distance r_o from the sun, its velocity is v_o and the angle between the radius vecor r_o and the velocity vector v_o is equal to ø. Find the maximum and the minimum distance that will separate this planet from the sun.

A meteorite of mass m collides with a satellite of mass 10 m. The satellite is orbiting a planet in a circular path of radius R. Due to the collision, the meteorite sticks to the satellite and the satellite goes into an orbit whose minimum distance from the planet is R/2. If the mass of the planet is M, what is the velocity of the meteorite before the collision?