# Announcements Homework: Supplemental Problems Make your selection from the Second Project

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Announcements ãHomework: Supplemental Problems ãMake your selection from the Second Project List. The project is due at the final exam: Monday May 2 @…
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Announcements ãHomework: Supplemental Problems ãMake your selection from the Second Project List. The project is due at the final exam: Monday May 2 @ 4:00pm The HR Diagram shows that stars group together by type Most stars are on the Main Sequence Stars on the Main Sequence are fusing hydrogen into helium 4 H  He    1 4 Stars on the Main Sequence are in equilibrium: outward pressure of the energy produced balances the inward pressure of gravity The luminosity of a star on the main sequence depends on its mass A log(luminosity) versus log(mass) plot shows a straight line for main sequence stars above about 0.5 MSun A straight line on a log-log plot means there is a power relationship between the two quantities. The slope of the line gives the power. The mass-luminosity relationship is a simple power law LM 3.5 If the mass is given in Msun then the luminosity is in LSun Examples The star Sirius has a luminosity 23 times that of the Sun. What is its mass? What is the luminosity of a star with a mass of 0.75 Msun? Example Solution Solve the Mass-Luminosity relationship for mass and plug in the numbers L  M 3.5  M  3.5 L  3.5 23LSun  2.45M Sun Given the mass, just plug in the value to get the luminosity   0.75M Sun  3.5 LM 3.5  0.365LSun How long a star lives on the Main Sequence also depends on the mass fusion rate  T or T 4 pp 17 CNO As with mass-luminosity, mass-lifetime is also a power relationship 2.5  M   MS  10 years   10   M Sun  Examples How long will a 3.5 solar mass star live on the main sequence? How long will a 0.5 solar mass star live on the main sequence? Example Solution Just plug in the numbers and grind away on the calculator 2.5 2.5  M   3.5M Sun   MS  1010 years     1010 years     0.044 1010 years  Sun  M  M Sun   440 million years 2.5 2.5  M   0.5M Sun   MS  1010 years     1010 years     5.7 1010 years  Sun  M  M Sun   57 billion years
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