1. The escape velocity is the minimum speed needed to project a particle of mass m upward from the surface of another mass M (such as a planet, an asteroid, or a star) so that the particle never returns. It is given by Vesc = 2GM R where R is the radius of the surface from the center of M. (a) Calculate the escape velocity vesc from the surface of the Sun. Use Mo = 1.99 × 1030 kg and Ro = 6.96 × 108 m where is the astrological symbol for the Sun. 1 (b) Suppose the Sun mysteriously begins contracting. What would be the radius for which vesc from the surface equals the speed of light c? C = 2GM Rs or Rs = 2GM c2 This radius, R., is known as the Schwarzschild radius. Anything thrown from that surface will eventually fall back on the surface. [Interestingly Newton's universal gravitation and Einstein's general relativity predict the same value of the Schwarzschild radius.] (c) Find the Schwarzschild radius for Earth's mass M = 5.97 x 1024 kg where is the astrological symbol for the Earth. (d) Find the Schwarzschild radius for your own mass. [It doesn't mean that there exists a black hole inside you. What it means is that if you are compressed to such a small size, then the escape velocity from your surface exceeds the speed of light.]

1. The escape velocity is the minimum speed needed to project a particle of mass m upward from the surface of another mass M (such as a planet, an asteroid, or a star) so that the particle never returns. It is given by Vesc = 2GM R where R is the radius of the surface from the center of M. (a) Calculate the escape velocity vesc from the surface of the Sun. Use Mo = 1.99 × 1030 kg and Ro = 6.96 × 108 m where is the astrological symbol for the Sun. 1 (b) Suppose the Sun mysteriously begins contracting. What would be the radius for which vesc from the surface equals the speed of light c? C = 2GM Rs or Rs = 2GM c2 This radius, R., is known as the Schwarzschild radius. Anything thrown from that surface will eventually fall back on the surface. [Interestingly Newton's universal gravitation and Einstein's general relativity predict the same value of the Schwarzschild radius.] (c) Find the Schwarzschild radius for Earth's mass M = 5.97 x 1024 kg where is the astrological symbol for the Earth. (d) Find the Schwarzschild radius for your own mass. [It doesn't mean that there exists a black hole inside you. What it means is that if you are compressed to such a small size, then the escape velocity from your surface exceeds the speed of light.]