To find the relative velocity of one galaxy as observed from the other, we use the relativistic velocity addition formula, which states:
\[ v_{relative} = \frac{v_1 + v_2}{1 + \frac{v_1 v_2}{c^2}} \]
where:
- \(v_1\) is the velocity of the first galaxy relative to Earth (200,000 km/s),
- \(v_2\) is the velocity of the second galaxy relative to Earth (200,000 km/s),
- \(c\) is the speed of light (~300,000 km/s).
Plugging in the values:
\[ v_{relative} = \frac{200,000 + 200,000}{1 + \frac{200,000 \times 200,000}{(300,000)^2}} \]
Calculating the denominator:
\[ \frac{200,000 \times 200,000}{(300,000)^2} = \frac{40,000,000,000}{90,000,000,000} \approx 0.4444 \]
So the equation becomes:
\[ v_{relative} = \frac{400,000}{1 + 0.4444} = \frac{400,000}{1.4444} \approx 276,000 \text{ km/s} \]
Thus, the speed at which an observer in one galaxy would see the other galaxy moving away is approximately 276,000 km/s.
The correct response is:
between 200,000 and 300,000 km/s.
1 answer