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 23, Problem 7Q
To determine

(a)

The distance to M51 in Megaparsecs (Mpc) when the brightness of the supernova 19941 in M51was measured and the distance modulus was determined to be 29.2

Expert Solution
Check Mark

Answer to Problem 7Q

Distance in Megaparsecs (Mpc) when distance modulus is 29.2 = 6.92 Mpc

Explanation of Solution

Given data Distance modulus of the supernova 19941 in M51 = 29.2

Distance modulus of the planetary nebulae in M51 = 29.6

Distance to Andromeda Galaxy from Earth = 750 kpc

Formula used

Distance modulus = mMmM=5log10(d)5 Here, d is measured in parsecs

Calculation

mM=5log10(d)5 5log10(d)=(mM)+5log10(d)=( mM)+55d=10 ( mM )+55When (mM)=29.2d=10 ( 29.2 )+55d=10 34.25d=106.84d=6918309.71 pcd=6.91830971 MpcRounding off to the second decimal place, d=6.92 Mpc

Conclusion Distance in Megaparsecs (Mpc) when distance modulus is 29.2 = 6.92 Mpc.

To determine

(b)

The distance in Megaparsecs (Mpc) when a separate distance measurement involving the planetary nebulae in M51 gave a distance modulus of 29.6.

Expert Solution
Check Mark

Answer to Problem 7Q

Distance in Megaparsecs (Mpc) when distance modulus is 29.6 = 8.32 Mpc.

Explanation of Solution

Given data Distance modulus of the supernova 19941 in M51 = 29.2

Distance modulus of the planetary nebulae in M51 = 29.6

Distance to Andromeda Galaxy from Earth = 750 kpc

Formula used

Distance modulus = mMmM=5log10(d)5 Here, d is measured in parsecs

Calculation

mM=5log10(d)5 5log10(d)=(mM)+5log10(d)=( mM)+55d=10 ( mM )+55When (mM)=29.6d=10 ( 29.6 )+55d=10 34.65d=106.92d=8317637.711 pcd=8.317637711 MpcRounding off to the second decimal place, d=8.32 Mpc

Conclusion

Distance in Megaparsecs (Mpc) when distance modulus is 29.2 = 8.32 Mpc.

To determine

(c)

The difference between the calculated distances in part (a) and part (b).

Expert Solution
Check Mark

Answer to Problem 7Q

Difference between the 2 calculated values = 1.4 Mpc

Explanation of Solution

Given data Distance modulus of the supernova 19941 in M51 = 29.2

Distance modulus of the planetary nebulae in M51 = 29.6

Distance to Andromeda Galaxy from Earth = 750 kpc

Calculation

Difference between the 2 calculated values =(8.326.92)MpcDifference between the 2 calculated values =1.4 Mpc

Conclusion

Difference between the 2 calculated values =1.4 Mpc

To determine

(d)

Compares differencecalculated value in part c, with the 750 kpc distance from Earth to Andromeda Galaxy.

Expert Solution
Check Mark

Answer to Problem 7Q

Difference of calculated values to M51 galaxy<Distance to Andromeda Galaxy from Earth

Explanation of Solution

Given data Distance modulus of the supernova 19941 in M51 = 29.2

Distance modulus of the planetary nebulae in M51 = 29.6

Distance to Andromeda Galaxy from Earth = 750 kpc

Calculation

Distance to Andromeda Galaxy from Earth = 750 kpcDistance to Andromeda Galaxy from Earth = 750 ×103 MpcDistance to Andromeda Galaxy from Earth = 0.75 MpcDifference of calculated values to M51 galaxy = 1.4 MpcAs 1.4 Mpc <  0.75 MpcDifference of calculated values to M51 galaxy<Distance to Andromeda Galaxy from Earth

Conclusion

Difference of calculated values to M51 galaxy<Distance to Andromeda Galaxy from Earth

It shows that when the distance increase, the error associated with the reading increases as well.

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