Answer:
0.61
Explanation:
To calculate Vega's absolute magnitude \(\bold{( M )}\), we use the distance modulus formula, which relates apparent magnitude \(\bold{( m )}\), absolute magnitude \(\bold{( M )}\), and distance in parsecs \(\bold{( d )}\):
\(\large\boxed{\boxed{\sf m - M = 5 \log_{10}(d) - 5 }}\)
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:
\(\sf d = \dfrac{25.05 \, \textsf{ly}}{3.262 \, \textsf{ly/pc}} \approx 7.68 \, \textsf{pc}\)
Nextsf, we use the distance modulus formula:
\(\sf m - M = 5 \log_{10}(d) - 5\)
Substitute \(\bold{ m = 0.0305 }\) and \(\bold{ d = 7.68 }\):
\(\sf 0.0305 - M = 5 \log_{10}(7.68) - 5\)
\(\sf 0.0305 - M = 5 \times 0.88536 - 5\)
\(\sf 0.0305 - M = 4.4268 - 5\)
\(\sf 0.0305 - M = -0.5732\)
Solving for \(\bold{ M }\):
\(\sf M = 0.0305 + 0.5732\)
\(\sf M = 0.6037\)
\(\sf M = 0.61 \textsf{(in 2 d.p.)}\)
Thus, the absolute magnitude of Vega is approximately:
\(\sf M \approx 0.61\)
