An out-of-control satellite is approaching the Earth and currently is located at r = 15,000 km with a velocity v = 6.43 km/s. The eccentricity of the orbit is e = 0.825. (a) Calculate the flight path angle, , at this instant. (b) Find the velocity and flight path angle when it reaches the edge of the atmosphere (assume altitude of 110 km). (c) Prove that the satellite collides with the Earth, and find its velocity at collision. Assume that the atmosphere does not exist, and therefore, the satellite does not disintegrate upon reentry.