Calculate the Schwarzschild radius rs 2GMc2 of a spherical

Calculate the Schwarzschild radius r_s = 2GM/c^2 of a spherical object with the mass M of a person (e.g. you). Is r_s larger or smaller than the radius of a proton (you will need to look up that number, e.g. in the textbook in chapter 3)?

Solution

the radius is directly proportional to mass.

mass of the person is approximately 65 kg

mass of the proton is 1.67x10^-27 kg

from the above data, it is clear that the mass of the person is greater than the

mass of the proton, So the value r_s is greater for the person compared to proton.

for proton:

rs, _proton = 2GM/c^2

= 2*6.67*10^-11*1.67x10^-27 kg / 3x10^8*3x10^8

= 2.47e-54 m

for person:

rs,_person = 2*6.67*10^-11*65 / 3x10^8*3*10^8

= 9.63e-26 m

so,    rs,_person > rs, _proton.