Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

Galaxy A is reported to be receding from us with a speed of 0.35c. Galaxy B, located in precisely the opposite direction, is also found to be receding from us at this same speed. What multiple of c gives the recessional speed an observer on Galaxy A would find for (a) our galaxy and (b) Galaxy B?

The multiple of c is 0.35.
The multiple of c is 0.62.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Describe the expression for the relativistic velocity of the particle

The relativistic velocity of the particle is given by,

$u = \frac{u^{'} + v}{1 + \frac{u^{'} v}{c^{2}}}$

Here, u is the velocity of the particle as measured in S, u^' is the velocity of the particle as measured in S^', v is the velocity of the S^' relative to S, and c is the velocity of the light.

Step 2: Determine the multiple of c for our galaxy(a)

If a person P is moving with speed v eastward from the person Q, then person P should observe that the person Q moving v away from person P.

In the similar way, if the Galaxy A is moving from our Galaxy with a speed of 0.35c then the observer in Galaxy A must see our Galaxy with the same speed of 0.35c or 0.35 multiple of c away from him.

Therefore the speed of an observer on Galaxy A from our galaxy is 0.35 multiples of c.

Step 3: Determine the multiple of c for our galaxy B(b)

Rearrange the equation (1) as follows.

$\begin{array}{rcl} u (1 + \frac{u^{'} v}{c^{2}}) & = & u^{'} + v \\ u - v & = & u^{'} (1 - \frac{uv}{c^{2}}) \\ \frac{u'}{c} & = & \frac{\frac{u}{c} - \frac{v}{c}}{1 - \frac{uv}{c^{2}}} . . . . . . . (2) \end{array}$

Substitute -0.35c for u and 0.35c for v in equation (2).

$\begin{array}{rcl} \frac{u^{'}}{c} & = & \frac{\frac{- 0.35 c}{c} - \frac{0.35}{c}}{1 - \frac{(- 0.35 c) (0.35 c)}{c^{2}}} \\ \frac{u^{'}}{c} & = & \frac{- 2 (0.35)}{1 + {(0.35)}^{2}} \\ \frac{u^{'}}{c} & = & - 0.62 \\ u^{'} & = & - 0.62 c \end{array}$

Here, the negative sign indicates the direction of the galaxy B with respect to the observer in galaxy A.

Therefore, the multiple of c is 0.62.

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Galaxy A is reported to be receding from us with a speed of 0.35c. Galaxy B, located in precisely the opposite direction, is also found to be receding from us at this same speed. What multiple of c gives the recessional speed an observer on Galaxy A would find for (a) our galaxy and (b) Galaxy B?

Step by Step Solution

Step 1: Describe the expression for the relativistic velocity of the particle

Step 2: Determine the multiple of c for our galaxy(a)

Step 3: Determine the multiple of c for our galaxy B(b)

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Galaxy A is reported to be receding from us with a speed of 0.35c. Galaxy B, located in precisely the opposite direction, is also found to be receding from us at this same speed. What multiple of c gives the recessional speed an observer on Galaxy A would find for (a) our galaxy and (b) Galaxy B?

Step by Step Solution

Step 1: Describe the expression for the relativistic velocity of the particle

Step 2: Determine the multiple of c for our galaxy(a)

Step 3: Determine the multiple of c for our galaxy B(b)

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Famous Physicists

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics