Department of History
University of California, Irvine
 Instructor:    Dr. Barbara J. Becker

Lecture 16.  Measuring Cosmic Distances.

Are the fuzzy objects seen in the sky distant clusters of stars?  Or are they nearby clouds of luminous matter in the process of condensing into stellar systems like our own?  Before answers could be given to questions like these, it was necessary to find trustworthy ways to learn the true distances to these luminous bodies.

Celestial Yardsticks:  Measuring the Distance to the Sun

Distance to the Sun = 1 Astronomical Unit (AU)
Distance to the Moon = 60 Earth Radii (ER)
1 AU =
3rd c BCE Aristarchos
1,200 ER
2nd c CE Ptolemy
"     "
1,160 ER


"     "
1,142 ER
1600 Tycho
picked value halfway between Copernicus and Ptolemy
1,150 ER
1620 Kepler
chose value

1,800 ER

1672 Richer & Cassini
measured parallax of Mars
21,000 ER, or
140 million km
Transit of Venus
~124-154 million km
1771 Lalande
Transit of Venus
~153 million km
Transit of Venus
~149.1 million km
1877 Gill
parallax of Mars
~149.7 million km
1891 Newcomb
Transit of Venus
~149.6 million km
Triangulating the Distance to Mars

By the seventeeth century, improved instruments made it possible for astronomers to detect and measure very small differences in the positions of celestial bodies.

In 1672, when Mars was in opposition, Giovanni Domenico Cassini (1625-1712) and Jean Richer (1630?-1696) calculated a value for the distance to the Sun based on their observations of Mars from Paris and Cayenne in French Guiana.

Triangulating the Distance to Venus

Edmond Halley (1656?-1743) didn't trust the accuracy of the results from the Mars observations.  He suggested using a transit of the Sun by Venus as a superior method of determining the Earth's distance to the Sun.

In 1761, twenty years after Halley's death, groups of observers viewed a transit of Venus from widely separated locations (Paris and the island of Rodrigues, near Madagascar).  Because of their very different vantage points, the two groups saw Venus appear to move across the Sun along different paths.  The angular separation of these two paths gave astronomers a measure they could use to calculate the value of the astronomical unit.


Photograph of the transit of Venus, 8 June 2004 by Johannes Schedler as seen from Wildon, Austria. 

The next transit of Venus will take place on 6 June 2012.  Check the map below to find out where to go to see it.  The best locations are in the center of the map marked with a "V" for "visible".  Areas bounded by the curving red lines will see only part of the transit.  For observers on North America's Atlantic Coast, the transit will begin a few hours before sunset.

If you miss the transit in 2012, you'll have to wait until 2117 for another chance!

Measuring the Distances to Stars and other Celestial Objects

Convenient celestial measuring units:

  • light-year -- the distance that light travels in a year.  It is equivalent to approximately 1013 kilometers, or about 6 trillion miles.
    • The Sun is approximately 8 light-minutes away from earth.
    • The entire solar system is approximately 11 light-hours across.
    • The nearest star, Alpha Centauri, is somewhat more than 4 light-years from the sun.
    • The nearest galaxy, the Andromeda Galaxy, is about 2 million light-years away.
  • parsec -- short for "parallax second"; the distance to an object that exhibits a parallax shift of one second of arc (one arcsecond = 1/3600 of a degree).  This shift was originally measured using the heliocentric parallax method described below.  Today, the parsec is used as a convenient measurement unit to refer to distances to celestial objects regardless of the method used to determine that distance.
      • One parsec is equivalent to 3.26 light-years.
    Measuring methods:
    • heliocentric parallax ---> 100 parsecs
      As the Earth revolves around the Sun, relatively nearby stars (those less than 100 pc away) will appear to shift slightly in position as seen against the far more distant background stars.  By using the diameter of the Earth's orbit (300 million kilometers) as a baseline, astronomers can determine the distance to these nearby stars.  Heliocentric parallax works reasonably well as a method for determining stellar distances out to a distance of about 100 parsecs.

    Tycho Brahe's unsuccessful search for some sign of stellar parallax convinced him that Copernicus was wrong to suggest that the Earth moved around the Sun.  Nearly 250 years later, the Earth's motion was no longer in doubt.  In 1838, working with more precise instruments, Friedrich Wilhelm Bessel (1784-1846) measured the distance to a nearby star, 61 Cygni (distance ~ 11 ly).

    Can you detect the nearby star in these two images?  The photograph on the left was taken in January.  The photograph on the right was taken in July.


    Now, move your cursor over the image below.  Can you find the nearby star more easily now?  The amount of shift shown by this star has enabled astronomers to calculate that it is about 4.4 light years or 1.3 parsecs away.

    • statistical parallax ---> 500 parsecs
      Using the heliocentric parallax method, astronomers determined the distance to about 100 stars.

    By 1900, Dutch astronomer Jacobus Kapteyn (1851-1922) perfected a method of measuring the distance to stars that involved the collective motion of nearby clusters of stars -- groups of 100-200 stars that appear to be physically associated.
    # of stars
    Ursa Major group
    20 pc
    Hyades (Taurus)
    45 pc
    M45 (Pleiades, Taurus)
    125 pc
    M44 (Beehive, Cancer)
    160 pc
    M7 (Scorpio)
    240 pc

    The stars in the nearby Hyades cluster move together as a group in space along roughly parallel paths.

    Because of our vantage point, we see the Hyades stars appear to move toward a point of convergence.  Identifying that point gives astronomers enough information to translate each star's apparent motion into a real space velocity. 

    The distance to a star in the cluster can be deduced by comparing its actual speed with how fast it appears to be moving towards the convergent point.

    Because this method of measuring distance relied on observations of motion exhibited by a group of related stars, it is referred to as a "statistical" method.

    Kapteyn could check the validity of this new method because a few clusters (the Hyades and the Beehive cluster, for example) contain stars located close enough to be measured using heliocentric parallax.

    Statistical parallax is a method that is reliable out to a distance of about 500 parsecs.

    • spectroscopic parallax --->10,000 parsecs
      While some astronomers were measuring distances to stars, others were photographing them and searching for patterns in their spectra.  In the first decade of the twentieth century, the spectra and distances to hundreds of stars were determined.  Astronomers hoped this wealth of information would reveal something about stars' intrinsic physical and chemical structure.

    Photographic plates like this one captured the spectra of many stars at once.

    Annie Jump Cannon (1863-1941), Henry Norris Russell (1877-1922), and Ejnar Hertzsprung (1873-1967) worked on the colorful puzzle of sorting stellar spectra.

    Stars Representative of Different Spectral Classes



    The monument to spectral classification's success in 1905 was a two-dimensional chart, known today as the Hertzsprung-Russell (or H-R) diagram.

    As soon as astronomers classify a star's spectrum, they can place the star the H-R diagram.  When astronomers know a star's location on the H-R diagram, astronomers can infer much about that star's physical characteristics, including its intrinsic brightness. 

    Comparing the star's intrinsic brightness with its apparent brightness as seen from Earth makes it possible to estimate of the star's actual distance.

    Even though this method of estimating a star's distance is not based on the measurement of any observed shift in position, it is still referred to as a "parallax" method -- spectroscopic parallax.

    Spectroscopic parallax can be used reliably to measure the distance to stars as far away as 10,000 parsecs.

    Cepheid Variables--13 million (!!) parsecs
    Not all stars burn steadily.  Some vary in their brightness and some even do this in a periodic way.  The fourth brightest star in the constellation Cepheus (delta Cephei) is one such star.  All stars that show the same characteristic periodicity as delta Cephei are called "cepheid" variables.

    Cepheids exhibit a characteristic pattern of variation in their luminosity.  This enables astronomers to distinguish cepheids from other kinds of variable stars.

    The North Star, or Polaris, is a cepheid variable.  At 300 light-years, it's one of the closest of the cepheids to the Earth.  Unfortunately, very few cepheids are close enough to have their distances measured by any of the methods mentioned so far.

    The star in the center of this series of images from the Hubble Space Telescope is a cepheid variable in M100, a spiral galaxy in the constellation Coma Berenices.

    Henrietta Swan Leavitt (1868-1921) spent several years photographing the Large and Small Magellanic Clouds, massive aggregates of stars visible only in the Southern Hemisphere.  She found 1,777 variable stars, a small fraction of which were cepheids.

    We now know that the Large (left) and Small (right) Magellanic Clouds are companion galaxies to our own Milky Way located at distances of 53,000 pc (LMC) and 60,000 pc (SMC).

    Leavitt did not know the absolute distance to either of the two Magellanic clouds, but just as you would feel confident comparing and drawing conclusions about the relative heights of individuals in two distant groups of people, she was sure it was reasonable to compare characteristics of the cepheids she found in both the LMC and SMC. 

    She plotted each cepheid on a graph according to the length of its period and its average apparent brightness.  She concluded that cepheids with long periods are intrinsically brighter than those with short periods.

    "In Figure 2 ... a straight line can readily be drawn ... showing that there is a simple relation between the brightness of the variables and their periods....  Since the variables are probably at nearly the same distance from the Earth, their periods are apparently associated with their actual emission of light, as determined by their mass, density, and surface brightness."
    --Leavitt (1912)

    ["Magnitude" is the measure of a star's brightness.  The brighter the star, the lower its magnitude number -- a magnitude 12 star is brighter than one of magnitude 14.]

    Astronomers refer to cepheid variables as "standard candles" -- objects that can be used to infer the distance to other bodies.  Cepheids are extremely useful in their role as celestial yardsticks.

    Go to:
    • Natural History:  General and Particular, vol I (1749), by Georges Louis Leclerc, Comte de Buffon (1707-1788)
    • Universal Natural History and Theory of Heaven (1755), by Immanuel Kant (1724-1804)
    • The System of the World (1796), by Pierre-Simon de Laplace (1749-1827)
    Weekly Readings
    Lecture Notes