Chapter 5.3, Problem 7E

Mass-Luminosity Relation Roughly $90\%$ of all stars are main-sequence stars. Exceptions include supergiants, giants, and dwarfs. For main-sequence stars (including the sun), there is an important relationship called the mass-luminosity relation between the relative luminosity $L$ and the mass $M$ in terms of solar masses. Relative masses and luminosities of several main-sequence stars are reported in the accompanying table.

Star	Solar mass $M$	Luminosity $L$
Spica	7.3	1050
Vega	3.1	55
Altair	1	1.1
The Sun	1	1
61 Cygni A	0.17	0.002

a	Find a power model for the data in this table. (Round the power and the coefficient to one decimal place.) The function you find is known to astronomers as the mass-luminosity relation.
b	Kruger 60 is a main sequence star that is about $0.11$ solar mass. Use functional notation to express the relative luminosity of Kruger 60, and then calculate that value.
c	Wolf 359 has a relative luminosity of about $0.0001$. How massive is Wolf 359?
d	If one star is 3 times as massive as another, how do their luminosities compare?