To help understand the HR Diagram  More Equations To help understand the HR Diagram 

Temperature - Wein’s Law SURFACE Temperature Based on color Measures spectrum of a star Strongest wavelength tells you the surface temperature using Wein’s Law T= 3 x 106 wavelength

Temperature example A star radiates most strongly at 600 nm. How hot is the star’s surface? T = 3,000,000/wavelength T = 3,000,000/600 T = 5000 K

Luminosity Luminosity: how bright is a star Given by Inverse Square Law Magnitude Scale

Luminosity Depends on 2 factors Temperature Radius Hotter = brighter Bigger = brighter Distance can make bright stars seem dim and dim stars appear brighter

Luminosity Inverse Square Law The farther away a star is, the dimmer it is. Proportional to 1/distance2

= 1/25th as bright as the closer star Luminosity Example: Two identical stars. One is 5 times further from the earth than the other. How much dimmer does the more distant star appear to be? = 1/distance2 = 1/52 = 1/25th as bright as the closer star

Magnitude About 150 B.C., the Greek astronomer Hipparchus measured apparent brightness of stars using units called magnitudes Brightest stars had magnitude 1 and dimmest had magnitude 6 The system is still used today and units of measurement are called apparent magnitudes to emphasize how bright a star looks to an observer

Magnitude A star’s apparent magnitude depends on the star’s luminosity and distance – a star may appear dim because it is very far away or it does not emit much energy The apparent magnitude can be confusing Scale runs “backward”: high magnitude = low brightness Modern calibrations of the scale create negative magnitudes Magnitude differences equate to brightness ratios: A difference of 5 magnitudes = a brightness ratio of 100 1 magnitude difference = brightness ratio of 1001/5=2.512

Magnitude Astronomers use absolute magnitude to measure a star’s luminosity The absolute magnitude of a star is the apparent magnitude that same star would have at 10 parsecs (32.6 light years) A comparison of absolute magnitudes is now a comparison of luminosities, no distance dependence An absolute magnitude of 0 approximately equates to a luminosity of 100 x The Sun

Spectral Classes Spectra of Stars Can Tell Us: Temperature Motion Composition Rotation Speed Luminosity

Parallax Parallax is a way of measuring distance to the stars. Only accurate to 100 parsecs How? (fingers and eyes) So, each of your eyes is like when the earth is on each side of the earth (we must wait until January and June) and the star we are looking at seems to change positions Then, we can measure the parallax angle and solve for the distance using the formula: Distance = 1/parallax angle Distance (parsecs) Parallax angle (arc seconds)

Parallax Problem Solve: Distance = 1.26 parsecs Solve: Parallax = .758 arc seconds

Only Boys and Fearless Girls Kill Mice Spectral Classes Only Boys and Fearless Girls Kill Mice