Question

Recall the raisin cake model of the universe. Our universe is expanding between the galaxies. You measure the recession velocity of Galaxy A to be 2,000 km/sec and the recession velocity of Galaxy B to be 6,000 km/sec. What can you say about the distances to these galaxies?

Answer 1

Explanation:

Recession velocity of a galaxy is related to the distance at which the galaxy is located. This relationship is given by the hubble constant, as follows:

$v_r=HD$

Hubble constant is aproximate $70\frac{km/s}{Mpc}$ and 1 megaparsec (Mpc) is 3.26*10^6 light years. Rewriting for D:

$D=\frac{v_r}{H}$

For galaxy A:

$D=\frac{2000\frac{km}{s}}{70\frac{km/s}{Mpc}}\\\\D=28.57Mpc\\\\D=28.57Mpc*\frac{3.26*10^6ly}{1Mpc}=9.31*10^7ly$

For galaxy B:

$D=\frac{6000\frac{km}{s}}{70\frac{km/s}{Mpc}}\\\\D=85.71Mpc\\\\D=85.71Mpc*\frac{3.26*10^6ly}{1Mpc}=2.79*10^8ly$