ASTRONOMY

• Luminosity L


  The total power output of radiation emitted by a star, measured in Watts (W)
• Radiant flux intensity F


  The observed amount of intensity, or the radiant power transmitted normally through a surface per unit of area, of radiation measured on Earth

  
• The luminosity is the total radiation that leaves the star


  The radiant flux intensity is the amount of radiation measured on Earth

  
• By the time the radiation reaches the Earth


  It will have spread out a great deal, therefore, it will only be a fraction of the value of the luminosity
• Inverse square law of flux

  Light sources which are further away appear fainter because the light it emits is spread out over a greater area

  
• Inverse square law of flux


  • The power from the star radiates uniformly through space
  • No radiation is absorbed between the star and the Earth

  
• For a given star, the luminosity is constant

  
• The radiant flux follows an inverse square law
• The greater the radiant flux (larger F) measured, the closer the star is to the Earth (smaller d)

  
• Worked example: Calculating distance from luminosity and radiant flux


  1. Write down known quantities

  2. Write down inverse square law of flux

  3. Rearrange for distance d, and calculate

  
• Standard candle


  An astronomical object which has a known luminosity due to a characteristic quality possessed by that class of object
• Examples of standard candles


  • Cepheid variable stars
  • Type 1a supernovae
• Using standard candles as a distance indicator


  If the luminosity of a source is known, then the distance can be estimated based on how bright it appears from Earth

  
• Astronomers measure the radiant flux intensity of the electromagnetic radiation arriving at the Earth
• Since the luminosity is known (as the object is a standard candle), the distance can be calculated using the inverse square law of flux

  
• Collating the data and measurements from each standard candle method allows astronomers to build up a larger picture of the scale of the universe, known as the cosmic distance ladder

  
• Wien's displacement law


  The black body radiation curve for different temperatures peaks at a wavelength which is inversely proportional to the temperature

  
• The higher the temperature of a body, the shorter the wavelength at the peak intensity, so hotter stars tend to be white or blue and cooler stars tend to be red or yellow

  
• The higher the temperature of a body, the greater the intensity of the radiation at each wavelength
• Worked example: Comparing surface temperatures of stars using Wien's law


  1. Write down Wien's displacement law

  2. Rearrange for temperature T

  3. Calculate the surface temperature of each star

  4. Conclude which star is cooler

  
• Stefan-Boltzmann law


  The total energy emitted by a black body per unit area per second is proportional to the fourth power of the absolute temperature of the body
• Estimating the radius of stars


  1. Use Wien's displacement law to find the surface temperature

  2. Use the inverse square law of flux to find the luminosity

  3. Use the Stefan-Boltzmann law to obtain the stellar radius

  
• Estimating the radius of stars


  1. Using Wien's displacement law to find the surface temperature of the star

  2. Using the inverse square law of flux equation to find the luminosity of the star (if given the radiant flux and stellar distance)

  3. Using the Stefan-Boltzmann law to obtain the stellar radius

  
• Wien's displacement law


  λ_max * T = 2.9 × 10^-3 m K
• Calculating the surface temperature of Betelgeuse


  Rearrange Wien's displacement law to find the surface temperature
• Stefan-Boltzmann law


  L = 4πr^2 σT^4
• Calculating the stellar radius of Betelgeuse


  Rearrange the Stefan-Boltzmann law to solve for r

  
• The radius of Betelgeuse is about 1000 times larger than the Sun's radius
• Astronomers are very limited in how they can investigate objects in space
• All techniques used involve analysing the light emitted from the star or galaxy

  
• One technique involves analysing the emission and absorption spectra of stars

  
• Elements in the star, predominantly hydrogen and helium, absorb some of the emitted wavelengths
• Characteristic lines are present when the spectrum is analysed
• The top emission spectra shows spectral lines of hydrogen measured on Earth
• The bottom emission spectra shows the shifted spectral lines of hydrogen measured from a distant galaxy

  
• When astronomers observe light from distant galaxies, they observe differences in the spectral lines to the light from the Sun

  
• The lines have the same characteristic pattern, meaning the element can still be easily identified, they just appear to be shifted slightly
• The lines in the spectra from distant galaxies show an increase in wavelength

  
• The lines are moved, or shifted, towards the red end of the spectrum
• Doppler effect


  The apparent change in wavelength or frequency of the radiation from a source due to its relative motion away from or toward the observer