193. Answer the following: (a) Show that the escape velocity a distance R from the centre of an object of mass M is given by: 2GM Vesc = R (b) Determine the escape velocity from the Sun for an object at the Sun's surface (Ro = 7.0 x 10' km, Mo = 2.0 x 1030 kg). (c) Determine the escape velocity from the Sun for an object at the average distance of the Earth (do = 1.5 x 108 km). Compare this with the average orbital speed of the Earth around the Sun (assume a circular orbit to determine the Earth's orbital speed). Answer: (a) N/A (b) 6.2 x 105 m/s (c) Vest = 4.2 x 104 m/s. The escape velocity is deer = v2 ~ 1.4 times bigger than the average orbital speed of the Earth around the Sun, so the Earth is going to stay in orbit around the Sun for the time being