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ISU ENVI 360 - The Family of Stars

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Next Week The Vernal EquinoxThe Family of StarsTriangulationTrigonometric ParallaxCalculating Distance Using ParallaxCalculating Distance Using ParallaxExample: Distance to SiriusThe “Standard Candle” MethodLight, the Astronomer’s ToolTemperatureLuminosityLuminosityThe Inverse-Square LawThe Inverse-Square LawThe Inverse-Square LawThe Inverse-Square LawRadiusKnowing L “In Advance”Tying It All TogetherTying It All TogetherTying It All TogetherExample: Measuring the Radius of SiriusThe Magnitude ScaleSlide 24The Magnitude ScaleSlide 26The Magnitude ScaleThe Spectra of StarsMeasuring a Star’s CompositionMeasuring a Star’s CompositionMeasuring a Star’s CompositionTemperature’s Effect on SpectraTemperature’s Effect on SpectraEarly Classification of StarsModern Classification of StarsModern Classification of StarsModern Classification of StarsSpectral ClassificationSpectral ClassificationMeasuring a Star’s MotionMeasuring a Star’s MotionMeasuring a Star’s MotionBinary StarsVisual Binary StarsSpectroscopic BinariesStellar MassesStellar MassesEclipsing BinariesEclipsing BinariesSummary of Stellar PropertiesSummary of Stellar PropertiesPutting it all together – The Hertzsprung-Russell DiagramThe HR DiagramThe HR DiagramThe HR DiagramAnalyzing the HR DiagramAnalyzing the HR DiagramGiants and DwarfsGiants and DwarfsThe Mass-Luminosity RelationLuminosity ClassesLuminosity ClassesLuminosity ClassesSlide 64Summary of the HR DiagramVariable StarsMira and Cepheid VariablesThe Instability StripSlide 69Method of Standard CandlesSummarySlide 72Slide 73Slide 74Slide 75Now on to Chapter 12: Measuring the Properties of StarsNext Week The Vernal EquinoxWhen does the Spring Equinox Occur?The Family of Stars•Those tiny glints of light in the night sky are in reality huge, dazzling balls of gas, many of which are vastly larger and brighter than the Sun•They look dim because of their vast distances•Astronomers cannot probe stars directly, and consequently must devise indirect methods to ascertain their intrinsic properties•Measuring distances to stars and galaxies is not easy•Distance is very important for determining the intrinsic properties of astronomical objectsTriangulation•Fundamental method for measuring distances to nearby stars is triangulation:–Measure length of a triangle’s “baseline” and the angles from the ends of this baseline to a distant object–Use trigonometry or a scaled drawing to determine distance to objectTrigonometric ParallaxCalculating Distance Using Parallax•A method of triangulation used by astronomers is called parallax:–Baseline is the Earth’s orbit radius (1 AU)–Angles measured with respect to very distant starsCalculating Distance Using Parallax•The shift of nearby stars is small, so angles are measured in arc seconds•The parallax angle, p, is half the angular shift of the nearby star, and its distance in parsecs is given by:dpc = 1/parc seconds•A parsec is 3.26 light-years (3.09 × 1013 km)•Useful only to distances of about 250 parsecsExample: Distance to Sirius•Measured parallax angle for Sirius is 0.377 arc second•From the formula, dpc = 1/0.377 = 2.65 parsecs = 8.6 light-yearsThe “Standard Candle” Method•If an object’s intrinsic brightness is known, its distance can be determined from its observed brightness•Astronomers call this method of distance determination the method of standard candles•This method is the principle manner in which astronomers determine distances in the universeIntrinsic here refers to the properties of the star itselfDefinition insertedLight, the Astronomer’s Tool•Astronomers want to know the motions, sizes, colors, and structures of stars•This information helps to understand the nature of stars as well as their life cycle•The light from stars received at Earth is all that is available for this analysisTemperature•The color of a star indicates its relative temperature – blue stars are hotter than red stars•More precisely, a star’s surface temperature (in Kelvin) is given by the wavelength in nanometers (nm) at which the star radiates most stronglyLuminosity•The amount of energy a star emits each second is its luminosity (usually abbreviated as L)•A typical unit of measurement for luminosity is the watt•Compare a 100-watt bulb to the Sun’s luminosity, 4 × 1026 wattsLuminosity•Luminosity is a measure of a star’s energy production (or hydrogen fuel consumption)•Knowing a star’s luminosity will allow a determination of a star’s distance and radiusThe Inverse-Square Law•The inverse-square law relates an object’s luminosity to its distance and its apparent brightness (how bright it appears to us)The Inverse-Square Law•This law can be thought of as the result of a fixed number of photons, spreading out evenly in all directions as they leave the source•The photons have to cross larger and larger concentric spherical shells.•For a given shell, the number of photons crossing it decreases per unit area•The inverse-square law (IS) is:•B is the brightness at a distance d from a source of luminosity L•This relationship is called the inverse-square law because the distance appears in the denominator as a squareThe Inverse-Square Law24LBdp=•The inverse-square law is one of the most important mathematical tools available to astronomers:–Given d from parallax measurements, a star’s L can be found (A star’s B can easily be measured by an electronic device, called a photometer, connected to a telescope.)–Or if L is known in advance, a star’s distance can be found The Inverse-Square Law24LBdp=•Common sense: Two objects of the same temperature but different sizes, the larger one radiates more energy than the smaller one•In stellar terms: a star of larger radius will have a higher luminosity than a smaller star at the same temperatureRadiusKnowing L “In Advance”•We first need to know how much energy is emitted per unit area of a surface held at a certain temperature•The Stefan-Boltzmann (SB) Law gives this: •Here s is the Stefan-Boltzmann constant (5.67 × 10-8 watts m-2K-4)4B Ts=Tying It All Together•The Stefan-Boltzmann law only applies to stars, but not hot, low-density gases•We can combine SB and IS to get:•R is the radius of the star •Given L and T, we can then find a star’s radius!2 44L R Tp s=Tying It All TogetherTying It All Together•The methods using the Stefan-Boltzmann law and


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ISU ENVI 360 - The Family of Stars

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