Q13CQ - College Physics (Urone)

Question

All galaxies farther away than about \({\rm{50 \times 1}}{{\rm{0}}^{\rm{6}}}{\rm{ ly}}\) exhibit a red shift in their emitted light that is proportional to distance, with those farther and farther away having progressively greater red shifts. What does this imply, assuming that the only source of red shift is relative motion? (Hint: At these large distances, it is space itself that is expanding, but the effect on light is the same.)

Step-by-Step Solution

Answer

The expansion rate of the cosmos accelerates as we move further away from the planet.

Step 1: Define Special Relativity

The special theory of relativity, sometimes known as special relativity, is a physical theory that describes how space and time interact. Theoretically, this is known as STR theory.

Step 2: Explanation

 The expansion of the cosmos causes the red shift. And, because the red shift is related to distance, it's proportional to relative velocity, according to the Doppler effect law: \({{\rm{f}}_{{\rm{obs}}}}{\rm{ = }}\sqrt {\frac{{{\rm{1 - v/c}}}}{{{\rm{1 + v/c}}}}} {{\rm{f}}_{{\rm{source}}}}\).

 

The relative velocity (expansion velocity) is proportional to distance.

 

Therefore, the expansion rate of the universe increases as we go far away from the earth.