Announcements•Homework: Supplemental Problems

•Exam 2 will be pushed back one week to April 9 (next class meeting). Will cover telescope and lenses, distance-luminosity-brightness relationship and whatever we cover today.

•Solutions to all homework assignments, including today’s, will be posted by next Tuesday.

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

1 44 H He

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 massA 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

3.5L MIf the mass is given in Msun then the luminosity is in LSun

ExamplesThe 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

3.5 3.5 3.5 23 2.45Sun SunL M M L L M

Solve the Mass-Luminosity relationship for mass and plug in the numbers

3.53.5 0.75 0.365Sun SunL M M L

Given the mass, just plug in the value to get the luminosity

How long a star lives

on the Main Sequence

also depends on the mass

4 17fusion rate pp CNOT or T

As with mass-luminosity, mass-lifetime is also a

power relationship2.5

1010MSSun

Myears

M

ExamplesHow 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

2.5 2.5

10 10 103.510 10 0.044 10

440

SunMS

Sun Sun

MMyears years years

M M

million years

2.5 2.5

10 10 100.510 10 5.7 10

57

SunMS

Sun Sun

MMyears years years

M M

billion years

Just plug in the numbers and grind away on the calculator