# Mass Luminosity Relation : Daniel Hsu And Michael Shu Essay

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Mass-Luminosity Relation

Daniel Hsu & Michael Shu

Ever since the early days of human civilization, people gazed up into the sky into the beyond, wondering what secrets the stars held from them. The mass of stars compared to our sun is a frequented question by many astronomers. The answer lies within the luminosity and mass of the star. There are 2 different ways humans can calculate the mass of stars, both using luminosity. One way is to calculate luminosity with radius and temperature of the star being observed. Another much simpler way is to convert apparent magnitude, the brightness of the star observed from earth, to absolute magnitude, the brightness of stars when they are all lined up at the same distance, then convert into luminosity. Once luminosity is calculated, the mass — luminosity relation can be used to find mass.
Luminosity, the total amount of energy emitted by a star, is higher in stars with higher mass. The relationship between luminosity and mass is not the same for all stars. The general form of the mass-luminosity equation is given by LLsun=a(MMsun)b, where L is the luminosity of the star being observed, Lsun is the luminosity of the sun, M is the mass of the star being observed, Msun is the mass of the sun and a and b are constants for different masses of the stars. From this formula, the mass of the star star being observed can easily be found by solving an exponential equation.
For stars less than 0.43 solar masses, the mass — luminosity equation is given by LLsun=0.23(MMsun)2.3. For stars more than 0.43 solar mass but less than 20 solar masses, the equation is LLsun=(MMsun)3.9. Beyond 20 solar masses the equation flattens out into a linear relationship of LLsun=3200MMsun. All of the equations listed are ...

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...nced out by the pressure. If mass increases then gravity will increase. When gravity increases pressure will increase, thus increasing the temperature inside the star. Since luminosity is the amount of energy output per unit time, faster fusion rate means higher energy, which is why even though some stars do not differ much in mass but the more massive star is much brighter.
The mass — luminosity relation is very important in astrophysics because it can be used to calculate mass or brightness of stars. In a binary star system, the radius and mass of stars can be found with Kepler’s laws. The luminosity of the stars can then be mapped by using these values. Similarly, the mass of the star can be found easily when the luminosity of the star is known. To weigh a star, it is very easy to simply plug in the luminosity and solve an exponential function with only 1 unknown.

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