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Question 3 (6 marks) A spaceship sent from Earth is now observing the black hole at the centre of the Milky Way (M~ 4 million Mo) at fixed position 1.0 AU from the event horizon. The human astronauts on the spaceship spot that an alien spaceship is also observing the black hole at a fixed position 0.20 AU from the black hole. The spacecraft and black hole are colinear (i.e. both spacecraft are at the same 8 and coordinates). (a) Calculate an expression for the ratio between the magnitude of the gravitational time dilation effect for the astronauts on the human and the alien spaceship, i.e. calculate ATA/ATE where ATE is a proper time interval measured by the human astronauts and ATA is the a proper time interval measured by the aliens. You may assume that the black hole is non-rotating. (b) Suppose the alien spacecraft is sending out light pulses at intervals of 1s, as measured by a clock on that spacecraft. What is the time between pulses as measured (i) by the Earthling's spacecraft, and (ii) by a distant observer?