Question

A spectral line of $\lambda =400nm$ from a distant star is observed to have a wavelength of $400.1nm$, speed of light is $3\times {10}^{8}m/s$. The speed of the star in the line of sight is:

• A. $40km/s$ towards earth
• B. $40km/s$ away from the earth
• C. $75km/s$ towards earth
• D. $75km/s$ away from the earth

Answer 1

The correct option is D $75km/s$ away from the earth

The correct answer is option(D).

The following formula is then used to derive the radial velocity of the star

$\frac{\Delta \lambda }{{\lambda }_0}=\frac{v_{radial}}{c}$

$\frac{(400.1-400)nm}{400nm}=\frac{v_{radial}}{3\times {10}^8}$

$v_{radial}=75km/s$

Since the sign of the velocity is positive, this means that the star is moving at 75 km/sec away from the earth.