Epsilon Indi is a main sequence star. Show that the mass of Epsilon Indi is 0.64 M

The mass of a star can be determined using the Mass-Luminosity Relation, which states that the luminosity of a star is directly proportional to the mass of the star to the power of 3.5.

The formula is: L = M^3.5

Where: L is the luminosity of the star M is the mass of the star

Epsilon Indi is a main sequence star with a luminosity of about 0.22 times that of the Sun.

So, if we set L_sun = 1 (since we're comparing to the Sun's luminosity), we have:

0.22 = M^3.5

To solve for M, we take the 3.5 root of both sides:

M = 0.22^(1/3.5)

Calculating this gives M ≈ 0.64

So, the mass of Epsilon Indi is approximately 0.64 times the mass of the Sun, or 0.64 M_sun.