An astronaut stranded out in space wants to figure out how far she is from Earth. The only thing that she has with her is her handy dandy indestructible stopwatch that can survive the heat of re-entry and the shock of impact with Earth. She starts the stopwatch and lets it go with approximately zero velocity in the reference frame of Earth. After the watch crashes to Earth, mission control retrieves it and finds that thestopwatch was falling for 7 days. How far away from Earth is the astronaut?

Your starship, the aimless wanderer, lands on the mysterious planet mongo. as chief scientist-engineer, you make the following measurements: a 2.50-kg stone thrown upward from the ground at 14.0 m/s returns to the ground in 5.70 s ; the circumference of mongo at the equator is 2.20×10^5 km ; and there is no appreciable atmosphere on mongo. (a) the starship commander, captain confusion, asks for the following information: what is the mass of mongo? (b) if the aimless wanderer goes into a circular orbit 2.20×10^4 km above the surface of mongo, how many hours will it take the ship to complete one orbit? (c) an unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 44.0 km . to the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 23.0 m/s . if nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?