April 21, 2018

How Far? Measuring Astronomical Distances.

You hear it at every star party. It’s probably the next biggest question right behind “is there life out there,” and “can you really see the flag the astronauts left on the moon with that thing?” Just how do we know how far away things are in the universe? After all, men have never ventured beyond the Moon; and it has only been in the past half century that we have sent embassaries on trajectories that will escape our solar system… just how do we measure these enormous distances with any confidence?

The idea of cosmological distances is built like a ladder, with one proven premise stacked on top of another. This is a ladder that has taken us centuries to build, and becomes more refined as observational evidence becomes better. Still, most of us cannot grasp the truly stupendous distances entailed in astro-speak; to paraphrase the late great Douglas Adams, “light itself travels so fast it takes most species millennia to discover that it travels at all…”
To the Moon: Consider ourselves fortunate that we have had a nearby large moon for scientists to cut their teeth on over the millennia. Remember, to the ancient Greeks, the world consisted of the land area adjacent to the Mediterranean Sea; perhaps they had heard rumors of distant lands far to the south or of the Indian subcontinent far to the east. Eratosthenes was the first one to correctly deduce the curvature and size of the Earth by noting the position of the solstice sun and its changing angle at noon from two different locations. It must have then dawned on those ancient geographers that much of the globe lay unexplored as well! From this measurement, Hipparchus then made the first rough measurement to the Moon, noting the size of the cross-section of the Earth’s shadow at its average distance of about 240,000 miles. Sadly, most of these accurate discoveries would take about two millennia to re-gain acceptance in Renaissance Europe.
To the Planets: A key riddle was cracked concerning the scale of the solar system in 1619 when Johannes Kepler published Harmonices Mundi, containing his three planetary laws of motion. Here was the ratio of a heliocentric solar system and the relative organization of the planets; all that was needed was one accurate measurement to cause all the other ones to fall in place. Suddenly, chasing transits of the planet Venus became the name of the game, as astronomers risked life and limb to gain accurate measurements of these brief events. What they were after was the solar parallax or the apparent shift of Venus during ingress and egress. At a distance of about 93,000,000 miles (about 1 astronomical unit, or A.U.) this shift amounts to about 8.794” arc seconds. For contrast, Venus itself is only about 66” arc seconds in apparent size during a transit!
To Nearby Stars: The next step in the ladder was much tougher to crack; the distance to the nearby stars. Again, parallax came to the rescue, and astronomers were able to extend their visual baseline to its maximum potential by making observations six months apart on opposing sides of the Earth’s orbit. Also, those astronomers of yore had to untangle any parallactic shift imparted from the diurnal and annual aberration of starlight, as well as our own 132 mile per second motion of our own solar system about the Milky Way Galaxy…it’s amazing that such a measurement ever came to pass. At a distance of 3.2615 light years, it was expected that a star would show an apparent 1” arc second shift using this method. The fact that none did clued in astronomers that the universe had to be a stupendously huge place. Still, Friedrich Bessel in 1838 managed to get the first measurements of the star 61 Cygni at 10.4 light years distant. Why such an unassuming star? Astronomers suspected that stars that exhibited a large proper motion such as 61 Cygni were nearby and proved to be good targets.
It’s worth noting that the solar versus stellar scale is a huge jump; when you look up at the nighttime sky with the naked eye, a good majority of those stars are within a 200 light year range, some bright ones such as Sirius are normal stars close up (8.6 light years) some large stars such as Rigel far away (772 light years). But remember that light travels in a vacuum at 186,282 miles per second, and one light year contains +63,210 Astronomical Units!

To the Galaxy: Another rung in the ladder had to be added to measure distances farther than a handful of parsecs. This breakthrough came in 1908 from the insight of Henrietta Swan Leavitt, whose work led to the discovery of Cepheid variable stars as a “standard candle” by which to measure galactic distances. A Cepheid is a star that has a defined period-luminosity relationship; a light source varies by the inverse square of its distance, so if a parallax measurement to a nearby Cepheid can be measured, a standard gauge for our galaxy can be known. Delta Cephei was the prototype for this class of variables, and another famous star, Polaris or the North Star is also a well known Cepheid.
To Nearby Galaxies: Few realize just how much our cosmic horizon grew in the past century. In 1900, our galaxy was deemed to be the sum of the universe, and little smudges seen in the night sky were hypothesized to be proto-stars or proto-solar nebulas. You can see how they got there. All this changed when Edwin Hubble identified the first Cepheid variable in M31, the “Andromeda Nebula” and calculated its stupendous distance of 1.5 million light years. Here was another island universe, equal to our own. If the step up in scale between the solar system and the nearby stars isn’t humiliating enough, the next step in galactic distances is downright crushing!

& finally, that big gig known as the Universe: So, just how do those modern day cosmologists extend the ladder out to the very size of the universe itself? In the measurement of cosmological distances, a key weapon is known as redshift. As the universe expands, light traversing it is stretched as well; familiar elemental markers in the observed spectrum shift towards the red as they recede from our vantage point. The most distant object measured by this method has been the galaxy UDFy-38135539 from the Hubble Ultra-Deep Field with a redshift of 8.55 making it 13.1 billion light years distant. Redshift isn’t something that cosmologists just “made up” to justify their jobs; well equipped backyard astronomers have effectively measured redshift!
A second technique is the measurement of Type 1A supernovae. Think of this as a Cepheid variable style standard candle ramped up for extra-galactic distances. These types of supernova explode and fade in a predictable fashion, and if their brightness can be gauged, the distance to their host galaxy can be known.
An even newer technique has come into vogue over the last century, namely that of measuring the surface brightness of a particular galaxy and statistically averaging it over the known extinction levels of light by the interstellar medium across the cosmos.

As you can see, these efforts are complimentary, and build up a bulwark of our understanding of our place in the cosmos. Next time you ask an astronomer “How far?” be patient, as we know the number of deductive bridges that then must be built. Our current understanding places us in a universe about 13.7 billion years old and about 40 billion light years in across and expanding. It may be somewhat humbling to consider our tiny “you are here” marker in the cosmos on a starry night, but isn’t it exhilarating just to share this tiny corner of time and space?


  1. Shannon (@Ageekmom) says:

    Fantastic write-up! Favorited and relaying it to friends & family.


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