Suppose an astronomer living on a planet in a galaxy of the Perseus cluster (distance = 300 Mpc)looked back at our Milky Way galaxy.If she measured the hydrogen line H alpha (rest wavelength 6500 A),what wavelength would she actually measure? (H = 70 km/s/Mpc)

Question

Quizplus · Accepted Answer

The observed wavelength can be calculated using the formula for redshift, $z = \frac{\Delta \lambda}{\lambda_0} = \frac{v}{c}$, where $\Delta \lambda = \lambda_{observed} - \lambda_{rest}$, $v$ is the velocity of the galaxy relative to us, and $c$ is the speed of light. Given $H = 70 \, \text{km/s/Mpc}$ and distance $= 300 \, \text{Mpc}$, the velocity $v = H \times \text{distance} = 70 \times 300 = 21000 \, \text{km/s}$. Substituting $v$ and $\lambda_{rest} = 6500 \, \text{A}$ into the redshift formula and solving for $\lambda_{observed}$ gives an observed wavelength longer than the rest wavelength, indicating a redshift. The correct calculation leads to an observed wavelength of approximately 6955 A, taking into account the expansion of the universe which causes the light to stretch as it travels towards us, making the observed wavelength longer than the rest wavelength.

Suppose an Astronomer Living on a Planet in a Galaxy