A space-craft passes by the earth with a relative velocity of 0.01 times the speed of light. Shortly after it has passed earth, it has a near miss with an asteroid that crosses directly in-front of the ships path. Its sensors detect that the asteroid was only 1000 km away when it crossed in front and the ships clock says that 61.101 seconds had elapsed since the ship passed earth. Tip: Start by defining the relevant events and the coordinate systems. (a) To an observer on earth, how much time elapsed between when the ship passed earth and when the asteroid crossed the path of the ship?
(b) How far was the asteroid from earth at that moment?
(c) If the clocks on the ship and on earth used to measure the time have an uncertainty of 1 millisecond. Do the two clocks agree on when the asteroid crossed the ships path? Why or why not?
(d) If the space-craft was instead travelling at 5.7×106 km/h with respect to earth would the two clocks agree when the asteroid crossed the ships path? Why or why not?