Problem 18 The stars of the Milky Way orbit about a supermassive object at the galactic centre called Sagitarius A* which appears to have a diameter of 25x106 km. Keplerian mechanics has been shown to hold for most stars close to Sagitarius A* (but not extremely close). Astronomers have observed that a star S2 orbits Sagitarius A* with a period of 15.24 years, semimajor axis of 150x109 km and eccentricity 0.876. Use orbital mechanics to determine: a) The mass of Sagitarius A* in Sun masses. b) The total energy per unit mass of the S2 orbit. c) The total angular momentum per unit mass of the S2 orbit. d) The maximum velocity and closest approach of S2 to the surface of Sagitarius A*. (3 marks) (2 marks) (2 marks) (3 marks) e) Whether Sagitarius A* is a black hole i.e., the escape velocity at its surface is greater than or equal to the speed of light. (2 marks) A probe orbiting S2 at constant radius 8x106km is designed to descend into Sagitarius A* while transmitting measured data until it is destroyed. This is achieved by using a Hohmann transfer about the galactic centre from S2's closest approach with a periapsis equal to the radius of Sagitarius A*. Use the method of patched conics to determine the following: f) The eccentricity of the Hohmann transfer. g) The required apoapsis velocity of the Hohmann transfer. h) The time it takes for the Hohmann transfer. (2 marks) (2 marks) (2 marks) i) The required hyperbolic excess velocity after S2 escape. (2 marks) j) The required velocity increment of the impulse to escape S2 and complete the mission. (3 marks) k) Comment on the feasibility of the mission and any limitations with your analysis. (2 marks) Notes: = Sun - 132712x106 km/s, s2 = 1.85 x10 km/s, Speed of light c=3 x108 m/s,