Two galaxies on opposite ends of the universe are moving away from the Earth. Each has a velocity of 200,000 km/s relative to the Earth. How fast would an observer in one of those galaxies see the other galaxy moving away? (1 point)

Question

Responses

between 200,000 and 300,000 km/s
between 200,000 and 300,000 km/s

200,000 km/s
200,000 km/s

400,000 km/s
400,000 km/s

between 300,000 and 400,000 km/s

Answer 1

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.