Question

Find the fractional shift in frequency, as measured on Earth, for light from a star of mass 1030 kg, assuming that the photons come from just above the star's atmosphere where rb 1000 km. -

Answer 1

The fractional shift between the two locations can be found using this.

f/f0~(1- GM / r0 c²); where

f0 is frequency emitted and G is 6.674*10^-11, c is speed of light.

Here r0 = r​​​​​_{​​​​​​B} =1000km  and M=10^30 kg

f/f_{​​​​​​0} = 1- (6.674*10^-11*10^30 /1000000* 9*10^16)

f/f_{​​​​​​0}​​​_{​​​​​} = 0.999258

Now there the fractional shift represent

( f₀ -f)/f_{​​​​​​0} = GM/r_{​​​​​​B} c² =0.0007415 .​​​​_​