Question

1. The escape speed Vis the minimum speed needed to project a mass m upward from thesurface of another
mass M (such as a planet, asteroid, or star). It is given byusing:

M = 1.99 × 10³⁰ kg ,

G= gravitational constant 6.67 x10^-11 N*m2/kg2

R = 6.96 × 10⁸m. is the radius of thesurface from the center of M

v=√2GM ====>>>>>> v= 6.1758 x10⁵ m/s

R
a) Suppose the Sun mysteriously begins to contract. What would bethe radius for which v escape fromthesurface equals the speed of light c? [This radius is known as theSchwarzschild radius. Anything thrown from that surface willeventually fall back on the surface. Interestingly Newton’suniversal gravitation and Einstein’s general relativity predict thesame value fo the Schwarzschild radius.]

b) Find the Schwarzschild radius for Earth’s mass 5.97 ×1024 kg.