Answer to Question #206546 in Mechanics | Relativity for Safi Ullah

Question

 The Sun has a radius of 7:0  108 m, approximately, and a period of rotation

about its axis equal to 24.7 days. What is the Doppler shift of a spectral line with

laboratory wavelength 500 nm, in the light emitted (a) from the center of the Sun

and (b) from the edges of the Sun’s disk at its equator?

Ans.: (a) Dk ¼ 1:8  10
8 nm, (b) Dk ¼ 

0:00344 nm

Answer 1

$\lambda= \lambda_0 \frac{1+ \beta cos \theta}{\sqrt{1- \beta^2}} \approx \lambda_0(1+ \beta cos \theta+ \frac{1}2 \beta^2)$

$\nabla \lambda=\lambda- \lambda _0 \approx \lambda_0 (\frac{V}c) cos \theta+ \frac {\lambda _0}2(\frac{V}c)^2$

$\nabla \lambda \approx \frac{\lambda_0}{2}(\frac{V}c)^2$

$\nabla \lambda_0 \approx \lambda_0(\frac{V}c)+ \frac {\lambda _0}2 (\frac{V}{c})^2$ and $\nabla \lambda_{180} \approx-\lambda_0(\frac{V}c)+\frac{\lambda_0}2(\frac{V}c)^2$

$\nabla \lambda=\frac{\nabla \lambda_0+ \nabla \lambda{180}}{2} \approx\frac{\lambda_0}2(\frac{V}c)^2$