18 17 Astronomers observing stars at the centre of our galaxy have suggested that many of them are orbiting a supermassive black hole. The mass of this black hole is 9.2 × 1036 kg. (a) Calculate the orbital period for a star in a circular orbit at a distance of 1.9 × 1014 m from a black hole of this mass. (3) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... Orbital period = .................................................................... (b) The star S0-2 is in a highly elliptical orbit around the position of the black hole. At its point of closest approach, S0-2 is at a distance of 1.8 × 1013 m from the centre of the black hole. At the most distant point of its orbit, S0-2 is 2.7 × 1014 m from the black hole. (i) Show that the change in gravitational potential between the closest and most distant points in this orbit is about 3 × 1013 J kg−1. (2) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... Turn over 19 (ii) At its point of closest approach, the star is travelling at a speed of 8.1 × 106 m s−1. Calculate the speed of S0-2 at the furthest point in its orbit using the change in gravitational potential. mass of S0-2 = 2.4 × 1031 kg (3) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... Speed = .................................................................... (c) Trigonometric parallax and Hubble’s law are two methods used to determine astronomical distances. Explain whether either of these methods is suitable to determine the distance to S0-2. (3) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... (Total for Question 17 = 11 marks)