How do we know about it (Chapter 3 (Part 1)

• How do we know distances of the Moon, Sun and planets?

  
• Measuring the distances in the Sun-Earth-Moon system

  1. Aristarchus made the first attempt

  2. Aristarchus figured the Moon is not at right angles to the Sun at First Quarter

  3. Aristarchus tried to measure the Sun-Earth-Moon angle at First Quarter

  4. Aristarchus detected an average time difference of about an hour in the two halves of the lunar month

  5. Aristarchus calculated the various distances and sizes

  
• Aristarchus' calculated values


  Moon's Distance: 25 Earth Diameters

  Moon's Diameter: 0.25 Earth Diameter

  Sun's Distance: 500 Earth Diameters

  Sun's Diameter: 5 Earth Diameters

  
• Correct values


  Moon's Distance: 30 Earth Diameters

  Moon's Diameter: 0.272 Earth Diameter

  Sun's Distance: 11,700 Earth Diameters

  Sun's Diameter: 109 Earth Diameters

  
• Measuring the diameter of the Earth

  1. Eratosthenes noticed the Sun shone directly down a well at Syene but was 7.2° south of the zenith at Alexandria

  2. Eratosthenes calculated the circumference of the Earth as 250,000 stadia

  3. Eratosthenes calculated the diameter of the Earth as 80,000 stadia

  
• 1 stadium = 160 m, therefore the diameter of the Earth is 80,000 x 160 m
• Finding the distance to the Moon by parallax

  1. Two observers simultaneously observe the Moon against the starry background from positions 10,000 km apart

  2. The Moon's position against the stars differs by 1.4°

  3. Calculating the Earth-Moon distance using trigonometry

  
• The actual Earth-Moon distance is 400,000 km

  
• The Scale Model of the Solar System

  1. Copernicus calculated and tabulated the distances of the planets from the Sun in terms of the Earth-Sun distance (1 au)

  2. Copernicus used a geometric approach to determine the distance of Venus and Mercury from the Sun

  
• Astronomical unit (au)


  The distance between the Earth and the Sun

  
• Copernicus' calculated planetary distances from the Sun compared to modern values

  
• Using parallax to calculate Sun-Earth distance in kilometers

  1. Cassini and Richer measured the position of Mars among stars from two different points on Earth during Mars opposition

  2. They found the Earth-Mars distance was 70 million km, so the Earth-Sun distance is 140 million km

  
• The modern value for the Earth-Sun distance (1 au) is 150 million km

  
• Measuring Distances to Stars by the Parallax Method

  1. The baseline must be the diameter of the Earth's orbit (300 million km)

  2. The parallax is generally less than 1 arc-second

  3. Observations are made 6 months apart to provide a 2 au baseline

  4. The distance to a star with 1" parallax is 1 parsec (3.3 light-years)

  
• Sirius exhibits annual parallax of 0.385", so its distance is 2.60 parsecs or 8.5 light-years

  
• In 1838, Bessel, Struve and Henderson made the first measurements of stellar parallaxes and distances

  
• John Herschel: 'The barrier to our excursions into the sidereal Universe has been overleaped at three different points. It is the greatest and most glorious triumph which practical astronomy has ever witnessed.'
• In 1848, after the examination of most of the bright stars. α Centauri was deemed the closest

  
• By the early 1850s new parallax measurements and the ascertaining of the seven orbital elements changed Henderson's original result to 0.74 arcsec giving the often familiar 4.2 or 4.3 light-years

  
• The literature now gives the distance as 4.396 light years, rounded to 4.4 1ight-years
• Although in 1838 Bessel and others used visual observations to measure the parallaxes, it is preferable to use photographic methods now that they are available
• From the ground, it is possible to measure stellar distances up to about 100 pc with about 20% accuracy using the parallax method

  
• Computer measurements of images taken by the Hipparcos Space Telescope have extended the reach of the parallax method up to 500 pc
• Determining star distance using parallax

  1. Measure star's parallax

  2. Use parallax to calculate distance in parsecs

  
• Hertzsprung-Russell diagram


  Used to provide a good estimate of a star's luminosity, L, if its spectral class (or color, or surface temperature) is known

  
• Determining a star's distance using the Hertzsprung-Russell diagram


  1. Measure star's apparent brightness, B

  2. Use luminosity, L, and apparent brightness, B, to calculate distance, R, using the formula L = 4πR^2B

  
• Luminosity


  The astronomical term for power
• Apparent brightness


  Something that can be measured with light measuring devices
• For most stars, luminosity (power of radiation), L, depends on temperature, T

  
• Spectral types


  O B A F G K M N
• To determine a star's spectral type, one needs to get the spectrum of the star

  
• Spectral lines


  Different sets of spectral lines are seen in stars of different surface temperatures

  
• The brightest (most luminous) stars are supergiants. They have about the same luminosity (power). It makes them universal candles for determining extragalactic distances

  
• Determining extragalactic distances using supergiants

  1. Find the brightest stars in the galaxy

  2. Measure their apparent brightness

  3. Use their known luminosity to calculate distance

  
• Cepheids


  Very powerful (luminous) variable stars, where luminosity, L, is a function of period, P

  
• Using Cepheids to measure distances


  1. Find a variable Cepheid star in a galaxy

  2. Observe it to determine its period, P

  3. Use the period-luminosity relation to find the star's luminosity, L

  4. Calculate distance using the formula L = 4πR^2B

  
• Hubble's Law


  V = Ho D, where V is velocity, D is distance, and Ho is the Hubble's constant
• Hubble's Law sets up a dependence between a galaxy's distance (from us) and its recession velocity (with respect to us)

  
• Doppler shift


  The change in frequency/wavelength of light or sound waves due to the relative motion of the source and the observer
• We take distances from observations of Cepheids and velocities from measurements of the Doppler shift of spectral lines in a galaxy's spectrum