Answer:
Explanation:
The apparent magnitude of a star is related to the distance modulus as follows
[tex]m_{\lambda}= M_{\lambda}+5log_{10}d-5+A_{\lambda}[/tex]
[tex]m_{\lambda}= \text {absolute visual magnitude}[/tex]
d = distance in parsec
[tex]A_{\lambda}=\text {interstellar extinction}[/tex]
Substitute
absolute visual magnitude = -1.1
distance =700pc
interstellar extinction = 0
to determine the apparent visual magnitude of the star lying in front of nebula
[tex]m_{\lambda}= M_{\lambda}+5log_{10}d-5+A_{\lambda}[/tex]
[tex]=-1.1+5\log_{10}(700)-5+0\\\\=8.12[/tex]
Thus, the apparent visual magnitude of the star lying in front of nebula is 8.12
b) Substitute
absolute visual magnitude = -1.1
distance =700pc
interstellar extinction = 1.1
to determine the apparent visual magnitude of the star lying behind nebula
[tex]m_{\lambda}= M_{\lambda}+5log_{10}d-5+A_{\lambda}[/tex]
[tex]=-1.1+5\log_{10}(700)-5+1-1\\\\=9.22[/tex]
the apparent visual magnitude of the star lying behind nebula is 9.22
c)
without taking extinction i.e 0, the distance of the star lying just behind nebula is calculated as follows
[tex]m_{\lambda}= M_{\lambda}+5log_{10}d-5[/tex]
[tex]d=10^{(m_\lambda-M_{\lambda_5)/5}[/tex]
[tex]d=10^{(9.22+1.1+5)/5}\\\\=158.79pc[/tex]
Thus, without taking extinction , the distance of the star lying just behind nebula is 158.79pc
Compare the distance of nebula measured from earth with consideration of extinction to the distance of nebula without consideration of extinction
[tex]\frac{d_e}{d} =\frac{700pc}{1158.8pc}[/tex]
= 60.4%
thus, the percentage error in determining the distance if the interstellar extinction neglected is 60.4%
