2) Vega is a star that is about 25.05 ly away from Earth. The star has an apparent magnitude (m) of 0.0305. Calculate Vega's absolute magnitude.



Answer :

msm555

Answer:

0.61

Explanation:

To calculate Vega's absolute magnitude [tex]\bold{( M )}[/tex], we use the distance modulus formula, which relates apparent magnitude [tex]\bold{( m )}[/tex], absolute magnitude [tex]\bold{( M )}[/tex], and distance in parsecs [tex]\bold{( d )}[/tex]:

[tex] \large\boxed{\boxed{\sf m - M = 5 \log_{10}(d) - 5 }}[/tex]

First, we need to convert the distance from light years to parsecs.

Given that 1 parsec (pc) is approximately 3.262 light years (ly), we calculate:

[tex] \sf d = \dfrac{25.05 \, \textsf{ly}}{3.262 \, \textsf{ly/pc}} \approx 7.68 \, \textsf{pc} [/tex]

Nextsf, we use the distance modulus formula:

[tex] \sf m - M = 5 \log_{10}(d) - 5 [/tex]

Substitute [tex] \bold{ m = 0.0305 }[/tex] and [tex] \bold{ d = 7.68 }[/tex]:

[tex] \sf 0.0305 - M = 5 \log_{10}(7.68) - 5 [/tex]

[tex] \sf 0.0305 - M = 5 \times 0.88536 - 5 [/tex]

[tex] \sf 0.0305 - M = 4.4268 - 5 [/tex]

[tex] \sf 0.0305 - M = -0.5732 [/tex]

Solving for [tex] \bold{ M }[/tex]:

[tex] \sf M = 0.0305 + 0.5732 [/tex]

[tex] \sf M = 0.6037 [/tex]

[tex] \sf M = 0.61 \textsf{(in 2 d.p.)} [/tex]

Thus, the absolute magnitude of Vega is approximately:

[tex] \sf M \approx 0.61 [/tex]