Solution to Exercise 1

1. From the mass-luminosity relation for main sequence stars, the luminosity is proportional to the mass raised to the power 3.5. Therefore a 20 solar mass main sequence star would be approximately (20)3.5 ~ 35,777 times more luminous than the Sun.

2. From the mass luminosity relation, L / L (Sun) ~ (0.1 / 1.0)3.5 ~ 0.0003 times as luminous as the Sun. These low mass stars are very common but are difficult to see at any distance because they are so faint.