Question 3 (6 marks) A spaceship sent from Earth is now observing the black hole at the centre of the Milky Way (M ~ 4 m

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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 M 1 (295.61 KiB) Viewed 44 times

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 0 and 0 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 1 s, 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?