Question

The mass and radius of a neutron star is 2MΘ and 15 km, respectively. Calculate the
value of gravitational red shift for light of wavelength 6000
oA
at a distance of 2 m
from its surface.

Answer 1

Gravitational redshift is given by the following approximate equation

$$\frac {\lambda} { \lambda_0}=1-\frac {GM} {r c^2} (1)$$

where λ is the is the shifted wavelength, λ₀ is the rest wavelength, G is the gravitational constant, and r is the distance from the gravitating body with mass M, c is the speed of light

Using (1) we got:

$$\lambda=\lambda_0 (1-\frac {GM} {r c^2}) (2)$$

In our case, 2MΘ=2×1.98892×10³⁰ kg, r=2 m

We got: λ=881.4×10^-6 m

Answer:

881.4×10^-6 m