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

Answer:

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

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

$v_{AB}=\dfrac{v_{AE}+v_{EB}}{1+\dfrac{V_{AE}V_{EB}}{c^2}}$

$v_{AB}=\dfrac{0.85+0.55}{1+\dfrac{0.75c\times0.55c}{c^2}}$

$v_{AB}=c\dfrac{0.85+0.55}{1+0.4675}$

$v_{AB}=0.95c$

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