How many 0.75 -M main sequence stars would it take to equal the luminosity of one 15 -M star?

Thanks but I can't find anything ... I tried that already

The next place to look (gasp!) is in your text materials.

A 15-Mag star is 14.25 Mag higher than a 0.75-Mag star. The power ratio is

2.512^14.25 = 501,500. That is how many of the less bright stars you would need.

To determine the number of 0.75-M main sequence stars required to equal the luminosity of one 15-M star, we need to compare their luminosities.

The luminosity of a star is given by the Stefan-Boltzmann law, which states that the luminosity is proportional to the fourth power of the star's surface temperature and radius.

First, let's assume that these stars have the same surface temperature, as we are only comparing their masses. This means we can ignore the temperature term in the equation.

Next, we need to use the mass-luminosity relation for main sequence stars to compare their luminosities. The relationship is given by the power-law:

L ∝ M^a

where L is the luminosity, M is the mass, and a is the exponent.

For main sequence stars, the mass-luminosity exponent is approximately 3.5.

Let's calculate the ratio of luminosities between a 0.75-M star and a 15-M star:

(L_0.75 / L_15) = (M_0.75^a / M_15^a)

Plugging in the known exponent a = 3.5, we get:

(L_0.75 / L_15) = (0.75^3.5 / 15^3.5)

Calculating this using a calculator, we find:

(L_0.75 / L_15) ≈ 0.027

This means that the luminosity of a 0.75-M star is roughly 2.7% of the luminosity of a 15-M star.

To determine the number of 0.75-M main sequence stars needed to equal the luminosity of one 15-M star, we can divide the luminosity of the 15-M star by the luminosity of a single 0.75-M star:

(1 / 0.027) ≈ 37

Therefore, it would take approximately 37 0.75-M main sequence stars to equal the luminosity of one 15-M star.