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The Stars How far away are they? How bright and hot are they? How are they similar to the sun? How are they different from the sun? Distances in Solar System A beam of radar (or a laser) traveling at the speed of light takes 2.58 seconds to go from the Earth to the Moon and back. That’s 1.29 seconds one way. 1.29 x 186,000 mps = 240,000 miles. Determining Distances Beyond the Solar System • The astronomic unit works well for the Solar System, but not beyond. • It takes too long for radar to make the round trip, so… • To determine distances in space, we use the concept of Parallax. The Parsec (parallax second) • As the earth revolves around the sun, objects in space shift due to parallax. • A star is 1 parsec from earth if the shift is one arcsecond (1/3600 degree). D= 1 p Suppose a star shifts 0.1 seconds of arc during the earth’s revolution around the sun. Then… The star is 1/0.1 = 10 parsecs from Earth. Distant stars 0.1 sec Accuracy of parallax method Such very small parallax shifts tell us that stars are very far away from us. Therefore, we cannot accurately measure the distance of stars more than 50 parsecs away, which is a shift of only 0.02 arcseconds or 0.0000055 degrees. Magnitude Revisited • The brightness of the star is measured by its magnitude. • The brighter the star, the lower its magnitude. • The star Sirius has a magnitude of -1 and Polaris is +2. So Sirius is the brighter star as we see it. • This is called apparent magnitude. Absolute Magnitude • A star can be bright as we see it for two reasons: it actually is bright, or it is close to us. • Absolute magnitude compares star brightness as if they were 10 parsecs away. A B Star A appears brighter because it is closer. When we “move” them both to 10 parsecs, then B is actually brighter. It has the higher absolute magnitude. Are the stars moving? • Stars appear to be standing still (“fixed”), but they are actually moving fast. • The great distances make this proper motion difficult to detect. • Barnard’s Star has the greatest proper (sideways) motion. Big Dipper Animation Are they getting closer or farther away? • Motion toward or away from us is detected by the Doppler Effect. • If the shift is toward the red, it is receding from us. • If the shift is toward the blue, it is approaching us. The larger the shift, the faster the motion of the star! LUMINOSITY: the energy radiated in a unit of time • Luminosity can be measured in watts (i.e. a light bulb). With stars, we usually rate luminosity with Sun = 1. • Stars are very luminous if their absolute magnitudes are low, and not luminous if the absolute magnitudes are high. • Star luminosity is dependent on the star’s temperature and size (Stefan-Boltzman Law). Stefan-Boltzman Law R = 2 suns R = 1 sun T = 4000 °K L = 4πR2σT4 • If the radius is doubled, luminosity is quadrupled. • If the temperature is doubled, luminosity increases 16 fold. T = 8000 °K The spectra of stars changes with temperature HOT star: peak is in ultra violet L= 100 COOL star: peak is in far red L = 0.1 SPECTRAL CLASSES Temperature O 30,000 - 60,000 K B 10,000 - 30,000 K A 7,500 - 10,000 K F 6,000 - 7,500 K G 5,000 - 6,000 K K 3,500 - 5,000K M < 3,500 K Blue stars Blue-white stars White stars Yellow-white stars Yellow stars (like the Sun) Yellow-orange stars Red stars The commonly used mnemonic for the sequence of these classifications is "Oh Be A Fine Girl, Kiss Me". Variety in Stars: size and color For most stars, the hotter the star is the more massive it is. Why is Capella an exception? Variety in Luminosity Due to Size The Hertzsprung - Russell Diagram In the early 1900s, two astronomers independently plotted the temperatures of stars vs. their luminosities. They found most stars fell along a diagonal in the middle. The Main Sequence • This band is called the main sequence. • Generally, the hotter the star, the more luminous it will be. • The main sequence is not a straight line but a band. Why is the main sequence curved? • If all stars were the same size as the sun, the main sequence would be this red line. • However, hot stars are larger, and cool stars are smaller than the Sun. LARGE SMALL The Red Giants A minority of stars are off the main sequence. Above the main sequence on the HR Diagram are the red giants. They are cool stars but large, so they are luminous. The Supergiants! • On the very top of the HR Diagram are cool but extremely bright stars. • These are the supergiants, stars that some day will supernova. • They eventually might become black holes. White Dwarf Stars • In the opposite corner of the HR Diagram are small hot stars, the white dwarves. • Their low luminosity is due to their small size, often less than the Earth. Mass-Luminosity Relationship • By studying binary star systems, we can determine the mass of stars. • For main sequence stars, the greater the mass the more luminous they are. • In fact, the mass of a star is its most important property, determining its temperature and the length of its life. For most stars, you can determine the luminosity by this formula: Mass = 36 suns L = 363 • √36 L = M3 • √M L = 46656 • 6 = 279,936 suns Quick Quiz! • What is a parsec and how is it determined? • What is the difference between apparent and absolute magnitude? • What two factors cause luminosity to increase? • What are the spectral classes? • Why is a blue star more luminous than a yellow star of the same size? • What does the H-R diagram show us about most stars (main sequence stars)? • What are red giants and white dwarf stars? • What is the mass-luminosity relationship?