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Chapter 36: Q. 30 (page 1060)

A distant quasar is found to be moving away from the earth at 0.80c. A galaxy closer to the earth and along the same line of sight is moving away from us at 0.20c. What is the recessional speed of the quasar, as a fraction of c, as measured by astronomers in the other galaxy?

Short Answer

Expert verified

The quasar's recessional speed, as estimated by scientists in another galaxy, is 0.71c.

Step by step solution

01

Given Information

We have given that a distant quasar is found to be moving away from the earth at 0.80c.

A galaxy that is closer to the earth and follows the same line of sight is travelling away from us at 0.20c.

We have to find the recessional speed of the quasar, as a fraction of c, as measured by astronomers in the other galaxy.

02

Simplify

Assemble the frames as follows:

The S– Frame is the Earth.

The galaxy is the S'– Frame, which is moving at 0.20cperpendicular to the S– Frame.

The moving quasar as measured in the S– Frame. According to the S– Frame, the velocity is 0.80c.

Calculate the quasar's speed in relation to the galaxy:

ux'=ux-v1-uxvc2=(0.80c)-(0.20c)1-(0.80c)(0.20c)c2=0.71c

The quasar's speed in relation to the galaxy is0.71c.

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