1. The Schwarzschild radius (Rs) is the distance from the center of an object of

Question

1. The Schwarzschild radius (Rs) is the distance from the center of an object of mass M such that, if all the mass of the object were compressed within a sphere of radius Rs, the escape speed from the sphere surface would equal the speed of light. In useful units, Rs=[(M/MSun) x 3 km], where MSun=2e+33 g.
Calculate the Schwarzschild radius for the following objects (in km):

a. A tennis ball of mass Mtennis=60 g

b. A star of 10 solar masses, i.e. Mstar=2e+34 g

c. A galaxy of mass Mgal=2e+13 MSun

d. A cluster of galaxies of mass Mcl=3e+14 MSun

Explanation / Answer

Rs=[(M/MSun) x 3 ] km a) Rs = (0.06/2*10^33)*3 = 9*10^-35 km b) Rs = (2*10^34/2*10^33)*3 = 30 km c) Rs = (2*10^13*2*10^33/2*10^33)*3 = 6*10^13 km d) Rs = (3*10^14*2*10^33/2*10^33)*3 = 9*10^14 km

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