Universe
Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 23, Problem 7Q

(a)

To determine

The distance to M51 in megaparsecs (Mpc), if the distance modulus of galaxy M51 is mM=29.2, as may be judged from the figure which is presented below.

Universe, Chapter 23, Problem 7Q , additional homework tip  1

(a)

Expert Solution
Check Mark

Answer to Problem 7Q

Solution:

6.9 Mpc

Explanation of Solution

Given data:

The difference between the apparent magnitude and absolute magnitude is given by the folloing expression.

mM=29.2

Formula used:

Apparent magnitude (m) is related to absolute magnitude (M) and the distance to the galaxy (d) in parsecs, by the following equation.

mM=5logd5

Explanation:

Now recall the formula of apparent magnitude and absolute magnitude.

mM=5logd5 …… (1)

Use the following equation.

mM = 29.2 …… (2)

Compairing equation (1) and (2),

5logd5=29.25logd=34.2logd= 34.25=6.84

Solve further.

d=106.84=6.9×106 pc(1 Mpc106 pc)=6.9 Mpc

Conclusion:

The distance to M51 is 6.9 Mpc.

(b)

To determine

The the distance to M51 in megaparsecs (Mpc), if the distance modulus of galaxy M51 is mM=29.6, as may be judged from the figure which is given below.

Universe, Chapter 23, Problem 7Q , additional homework tip  2

(b)

Expert Solution
Check Mark

Answer to Problem 7Q

Solution:

8.3Mpc

Explanation of Solution

Given data:

The difference between the apparent magnitude and absolute magnitude is 29.6.

Formula used:

Apparent magnitude (m) is related to absolute magnitude (M) and the distance to the galaxy (d) in parsecs by the following relation.

mM=5logd5

Explanation:

Recall the formula of apparent magnitude and absolute magnitude.

mM=5logd5 …… (3)

It is given that,

mM=29.6 …… (4)

Comparing equation (3) and (4),

5logd5=29.65logd=34.6logd= 34.65=6.92

Solve further.

d=106.92=8.3×106 pc(1 Mpc106 pc)=8.3 Mpc

Conclusion:

The distance to M51 is 8.3Mpc.

(c)

To determine

The difference between the distances to M51, when the different values of mM are taken (29.2and29.6) and compare this difference with the 750 kpc distance from Earth to M31, the Andromeda galaxy.

(c)

Expert Solution
Check Mark

Answer to Problem 7Q

Solution:

The difference is 1.4Mpc, which is greater than the distance to M31.

Explanation of Solution

Introduction:

Andromeda Galaxy: This is the spiral galaxy of the distance 2.5 million ly from the Earth and it is a major galaxy, nearest to the milky way. It is also known as Messier 32 or M31.

Explanation:

Obtain the values of distance to galaxies from the above parts with respect to the two different values of m - M(29.2 and29.6).

Therefore, the distance value for 29.2 is 6.9Mpc and for 29.6 is 8.3Mpc.

The difference is given blow.

Difference=8.3 Mpc6.9 Mpc=1.4 Mpc

Conclusion:

From the calculation, it is observed that the difference is 1.4 Mpc, which is larger than the distance to M31 (750 kpc).

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