Question

Galaxy A is moving away from us with a speed of 0.85c relative to the earth. Galaxy B is moving away from us in the opposite direction with a relative speed of 0.55c. Assume that the earth and the galaxies are inertial reference frames. How fast is galaxy A moving according to an observer in galaxy B?

Answer 1

The speed of the galaxy A moving according to an observer in galaxy B is 0.95c.

Step-by-step explanation:

Given that,

Speed = 0.85c

Let
`v_(AB)` is the velocity of galaxy A relative to galaxy B,
`v_(AE)` is velocity of galaxy A relative to Earth and
`v_(EB)` velocity of Earth relative to galaxy B.

Let’s assume that galaxy A is moving to the right,along the +x direction, so its velocity relative to earth is
`v_(AE)=0.85c`

Galaxy B is moving along the–x axis with a speed of 0.55c relative to earth, so its velocity is
`v_(BE)=0.55c`

Using velocity additional formula

`v_(EB)=-(-0.55c)`

We need to calculate the velocity of the galaxy A relative to galaxy B

Using formula of relative velocity

`v_(AB)=(v_(AE)+v_(EB))/(1+(V_(AE)V_(EB))/(c^2))`

`v_(AB)=(0.85+0.55)/(1+(0.75c*0.55c)/(c^2))`

`v_(AB)=c(0.85+0.55)/(1+0.4675)`

`v_(AB)=0.95c`

Hence, The speed of the galaxy A moving according to an observer in galaxy B is 0.95c.