Question

If you detected radio signals with an average wavelength of 67 cm and suspected that they came from a civilization on a distant Earth-like exoplanet, roughly how much of a change in wavelength (in cm) should you expect to detect as a result of the orbital motion of the distant exoplanet?

Answer 1

Answer:

0.0066553 cm

Explanation:

v = Earth's average orbital velocity = 29.8 km/s

c = Speed of light = $3\times 10^8\ m/s$

$\lambda$ = Wavelength = 67 cm

$\Delta\lambda$ = Change in wavelength

The Doppler shift is given by

$\dfrac{v}{c}=\dfrac{\Delta \lambda}{\lambda_0}\\\Rightarrow \Delta \lambda=\dfrac{v\lambda_0}{c}\\\Rightarrow \Delta \lambda=\dfrac{29800\times 0.67}{3\times 10^8}\\\Rightarrow \Delta\lambda=0.000066553\ m=0.0066553\ cm$

The change in wavelength is 0.0066553 cm