Question

A certain line in the spectrum of the light from a nebula has a wavelength of

656 nm instead of the 434 nm measured in the laboratory. If the nebula is moving

radially, what is its speed relative to the Earth? Ans.: It is moving away from the

Earth with a speed of V ¼ 0:391

Answer 1

As we know, since the nebula has a wavelength greater than the laboratory measurements, it is receding from us. Calculate the redshift based on the wavelengths:

$$z=\frac{\lambda_\text{real}-\lambda_\text{lab}}{\lambda_\text{lab}}=0.512.\\\space\\ 1+z=\sqrt{\frac{1+v/c}{1-v/c}},\\\space\\ v=0.391c.$$