Astronomy luminosity question -

Question

The luminiosity (in terms of the Sun’s luminosity) of a 0.2 M star and a 5 M star is about 0.005 and about 400. How is this calculated. Please show/explain so a math moron can follow. Thanks!

Answer 1

A rough formula is mass raised to the 3.5th power.  So a 5-solar-mass star should have a luminosity of about 5^3.5 or 280 solar luminosities; a 1/5-solar-mass star should have a luminosity of about (1/5)^3.5 or 0.0036 solar luminosities.  The age and composition of the star can have substantial effects on top of this (for instance, the Sun is about 30 to 40 percent brighter now than it was when it first formed), so without knowing more about those parameters, it's not possible to say anything more specific about the luminosities.