Universe: Stars And Galaxies
Universe: Stars And Galaxies
6th Edition
ISBN: 9781319115098
Author: Roger Freedman, Robert Geller, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 24, Problem 26Q
To determine

(a)

The speed at which the blazar is moving away from the Earth.

Expert Solution
Check Mark

Answer to Problem 26Q

The speed at which the blazar is moving away from the Earth is 1.80×105km/s.

Explanation of Solution

Given:

The red shift of the given blazar is, z=1.00.

Formula used:

The expression for the ratio of the speed of the object moving away from the earth and speed of the light is given by,

vc=( z+1)21( z+1)2+1

Here, v is velocity of the object moving away, c is the speed of the light and z is the amount of the red shift.

Calculation:

The speed of the blazar in moving away from the Earth is calculated as,

vc= ( z+1 )21 ( z+1 )2+1vc= ( 1+1 )21 ( 1+1 )2+1vc=0.6v3× 105km/s=0.6

Solve further,

v3× 105km/s=0.6v=1.8×105km/s

Conclusion:

The speed at which the blazar is moving away from the earth is 1.80×105km/s.

To determine

(b)

The time for which the fluctuation lasted for an astronomers within the blazar’s host galaxy.

Expert Solution
Check Mark

Answer to Problem 26Q

The time for which the fluctuation lasted for an astronomer within the blazar’s host galaxy is 134h.

Explanation of Solution

Given:

The time span for which the fluctuation was seen on the earth is Δt=168h.

Formula used:

The expression for the time dilation as per theory of relativity is given by,

Δt=Δt01 ( v c )2

Here, Δt is the time of the observer and Δt0 is the estimated time of the receiver.

Calculation:

The time for which the fluctuation lasted for an astronomer within the blazar’s host galaxy is calculated as,

Δt=Δt0 1 ( v c ) 2 168h=Δt0 1 ( 1.8× 10 5 km/s 3× 10 5 km/s ) 2 Δt0=168h×1 ( 1.8× 10 5 km/s 3× 10 5 km/s )2Δt0=134h

Conclusion:

Therefore, the time for which the fluctuation lasted for an astronomer within the blazar’s host galaxy is 134h.

To determine

(c)

The maximum size of the region for emitting energy by the blazar.

Expert Solution
Check Mark

Answer to Problem 26Q

The maximum size of the region for emitting energy by the blazar is 995.3au.

Explanation of Solution

Given:

The time for which the fluctuation lasted for an astronomer within the blazar’s host galaxy is 134h.

Formula used:

The size of the blazar is given by,

size of the blazar=(t)(c)

Here, t is the time for which the fluctuation lasted.

Calculation:

The maximum size of energy emitting region of the blazar is calculated as,

size of the blazar=(t)(c)=(138h)(3× 108m/s)=(138h)(3× 108m/s× 10 3 km 1m× 3600s 1h)

Solve further,

size of the blazar=(1.49× 10 11km× 6.68× 10 9 au 1km)=995.32au

Conclusion:

The maximum size of the region for emitting energy by the blazar is 995.3au.

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