An astronaut is stranded in space above the earth, in the same orbit as a space station, but 200 m behind it. Both are circling 280 km above earth’s surface in a 90-min orbit. The astronaut and spacesuit together have a mass of 100 kg.

(a) In what direction, and with what speed, can the astronaut throw a one-kilogram wrench so that the recoil will allow the astronaut to reach the vehicle and safety?

(b) How long will it take the astronaut to arrive?

(c) Sketch the trajectory of the astronaut and of the wrench after the throw, in the rest frame of the Station, and then sketch the trajectory of each in the non-rotating, inertial frame in which the Station orbits the earth.