Lecture 12
The Distances of Stars
Key Concepts:
  1. How do astronomers measure distances to stars?
  2. What is parallax?
  3. What is inverse square law? luminosity? and standard candle?
  4. What is the magnitude system?

Measuring Distance through Stellar Parallax

  • Perspective and parallax


  • Triangulation: measuring distances using geometry
  • Astronomical Parallax:

    • a method of triangulation for measuring distance to nearby stars
    • arcsec = 1/60 of arcmin, which is 1/60 of a degree of arc
    • if A = 1 AU, B (distance) is inversely proportional to angle p if the angle in radian is much smaller than 1.
    • parsec (pc) = distance corresponding to a parallax of 1 arcsec. 1 pc is about 3.3 light year or 3 x 1013 km.
    • Quiz 12a


Inverse Square Law and Luminosity

  • luminosity = total amount of power radiated into space per unit time
  • inverse square law = a relationship between luminosity, distance, and apparent brightness
  • "a light appears brighter as you approach the light"
    • the same number of photons leave the star
    • a spherical shell surrounding the star increases its area as distance squared
    • apparent brightness (number of photons per unit area) decreases as distance squared

Quiz 12b


The Magnitude System

  • a logarithmic system of describing stellar brightness
  • 1 magnitude = (100)1/5 = a factor of 2.512
  • the brightest stars are 1st magnitude, the next brightest stars are 2nd magnitude, and so on. A larger magnitude means fainter -- see an example below of Ursa Major
  • apparent magnitude: how bright different stars appear in the sky
  • absolute magnitude: a measure of stellar luminosity (a star's apparent magnitude if it were at a distance of 10 parsecs away)


Quiz 12c


Measuring Distances using Standard Candle

  • seeing how bright the light is, you can figure out how far the house is
  • if you know L, you can measure B and determine distance, d
  • "standard candle" = any object of known luminosity that can be used to determine distances (e.g. stars of known mass and luminosity)

Other methods for determining distances in astrophysics



Reading assignment for next lecture: Chapter 16 (p.522-p.540)