Question

Galaxy B moves away from galaxy A at 0.577 times the speed of light. Galaxy C moves away from galaxy B in the same direction at 0.731 times the speed of light. How fast does galaxy C recede from galaxy A?

Answer 1

The value is
`p = 0.7556 c`

Step-by-step explanation:

From the question we are told that

The speed at which galaxy B moves away from galaxy A is
`v = 0.577c`

Here c is the speed of light with value
`c = 3.0 *10^(8) \ m/s`

The speed at which galaxy C moves away from galaxy B is
`u = 0.731 c`

Generally from the equation of relative speed we have that

`u = (p - v)/( 1 - ( p * v)/(c^2) )`

Here p is the velocity at which galaxy C recede from galaxy A so

`0.731c = (p - 0.577c )/( 1 - ( p * 0.577c)/(c^2) )`

=>
`0.731c [1 - ( p * 0.577)/(c)] = p - 0.577c`

=>
`0.731c - 0.4218 p = p - 0.577c`

=>
`0.731c + 0.577c = p + 0.4218 p`

=>
`1.308 c = 1.731 p`

=>
`p = 0.7556 c`