The absolute magnitude of the Sun is +4.8 and its luminosity is 3.9 × 10²⁶ watts. The absolute magnitude of the star $v$ (Nu) Hydrae is -0.2. What is the luminosity of $v$ Hydrae?

Question

Quizplus · Accepted Answer

Using the formula for absolute magnitude:
M = -2.5 log(L/Lsun) + 4.8
Solving for L/Lsun:
L/Lsun = 10^((M - 4.8)/-2.5)
For the Sun:
L/Lsun = 1
For $v$ Hydrae:
L/Lsun = 10^((-0.2 - 4.8)/-2.5) = 158.49
Multiplying by the luminosity of the Sun:
Luminosity of $v$ Hydrae = 3.9 × 10^31 W x 158.49 = 6.18 × 10^33 W, which is closest to option C.

The Absolute Magnitude of the Sun Is +4 vvv (Nu) Hydrae Is -0

The Absolute Magnitude of the Sun Is +4 $v$ (Nu) Hydrae Is -0