A satellite of negligible mass is launched vertically from Earth’s surface with speed v0=11.6km⋅s−1 (slightly above Earth’s escape speed of 11.2km⋅s−1). During ascent through a tenuous layer of the upper atmosphere, the satellite experiences a nearly constant upward drag force of magnitude 1.2×103N over a vertical distance of 200km. The satellite’s mass is 450kg. Ignore all other non-gravitational forces once the satellite leaves this layer.
(a) Calculate the satellite’s total mechanical energy immediately after launch from the surface.
(b) Determine the total mechanical energy after the satellite has passed through the 200km atmospheric layer, and state whether its subsequent trajectory is bound or unbound. Show your reasoning.
(c) Once beyond the atmosphere the satellite performs a brief prograde burn at perigee. Calculate the minimum change in speed (Δv) required to return the satellite to a marginal (E≈0) escape trajectory.