Answer:
Option D
The star is at a distance of 100 parsecs.
Explanation:
The distance can be determined by means of the distance modulus:
[tex]M - m = 5log(d) - 5[/tex] (1)
Where M is the absolute magnitude, m is the apparent magnitude and d is the distance in units of parsec.
Therefore, d can be isolated from equation 1
[tex]log(d) = (M - m + 5)/5[/tex]
Then, Applying logarithmic properties it is gotten:
[tex]d = 10^{(M - m + 5)/5}[/tex] (2)
The absolute magnitude is the intrinsic brightness of a star, while the apparent magnitude is the apparent brightness that a star will appear to have as is seen from the Earth.
Since both have the same spectral type is absolute magnitude will be the same.
Finally, equation 2 can be used:
[tex]d = 10^{(4.8 - (-0.2)+ 5)/5}[/tex]
[tex]d = 100 pc[/tex]
Hence, the star is at a distance of 100 parsecs.
Key term:
Parsec: Parallax of arc seconds