How do scientists measure distances to stars and galaxies?

Introduction

Many of us know that the sun is approximately 150 million km or 93 million miles away, a distance that is known as the “astronomical unit” (AU). Neptune, the most distant planet, is 30 AU from the sun, or some 44.8 billion km (27.9 billion mi). The Voyager 2 spacecraft, launched in 1977, reached Jupiter just two years later, but did not reach Neptune until 1989.

The nearest stars, Alpha Centauri A-B and Proxima Centauri, are roughly 1000 times more distant, roughly 4.3 light-years away (one light-year is the distance that light travels in a Julian year of 365.25 days, namely 9.461 trillion km or 5.879 trillion mi). The Milky Way galaxy consists of some 300 billion stars in a spiral-shaped conglomerate roughly 100,000 light-years across.

The Andromeda Galaxy, which can be seen with many home telescopes, is 2.54 million light-years away. There are hundreds of billions of galaxies in the observable universe. As of the present date, the most distant observed galaxy is some 13.2 billion light-years away, so it was formed not long after the big bang, 13.75 billion years ago (plus or minus 0.011 billion). An interesting online tool, which one can use to determine first-hand the age of the universe from known data, is available at [WMAP tool].

The scope of the universe is perhaps best illustrated by an example given by Australian astrophysicist Geraint Lewis. He noted that if the entire Milky Way galaxy is represented by a small coin, roughly one cm across, then the Andromeda galaxy would be another small coin roughly 25 cm (10 in) away. The observable universe would then extend for 5 km (3 mi) in every direction, encompassing some 300 billion galaxies [Lewis2011].

How can scientists measure or calculate these enormous distances with any confidence?

Parallax

First, it is useful to keep in mind that sophisticated mathematics and technology are often not needed to obtain at least a rough estimate of astronomical distances. Eratosthenes (276-196BC) measured circumference of Earth to within 50 miles of present value by comparing the angular altitude of the Sun at midday on same day at Syene (Aswan) and Alexandria. Subsequently, the distance to the moon was determined to within 1% of our modern value by Hipparchus (160-125 B.C.), by comparing the radius of curvature of the earth’s shadow with the radius of the moon during a lunar eclipse. From the observed ratio the size of the moon could be inferred, since the size of the earth was already known from the work of Eratosthenes, and this then yielded its distance.

One technique used in modern times is known as parallax, which was first used by German astronomer Friedrich Wilhelm Bessel in 1838. Parallax is not sophisticated — in fact your eyes use parallax to produce the perception of 3-D vision. If you cover one eye and note the position of a nearby object, compared with more distant objects, the nearby object “moves” when you view it with the other eye. This is parallax.

The same principle is used in astronomy. As the earth travels around the sun in its orbit, relatively close stars are observed to move slightly, with respect to “fixed” stars that are much more distant. In most cases, this movement is very slight, only a fraction of a second of arc, but reasonably accurate distance measurements can nonetheless be made for stars up to about 1000 light-years away.

Standard candles

For more distant objects such as galaxies, parallax measurements cannot be used because the angular motion as the earth orbits the sun is much too small to be measured even with the best telescopes. Instead, astronomers rely on what are known as “standard candles.” Since, according to elementary geometry, light flux falls off as the square of the distance, by measuring the actual brightness observed on earth using a powerful telescope, astronomers can calculate the distance to the object.

One type of “standard candle,” which has been used since the 1920s, is the class of Cepheid variable stars (stars that periodically vary in brightness), for which there is a known relation between the period and its absolute luminosity. There are some difficulties with such measurements, but most of the issues have now been worked out satisfactorily, and distances determined using this scheme are believed accurate to within about 7% for more nearby galaxies, and 15-20% for the most distant galaxies.

Type Ia Supernovas

In recent years the most widely used standard candles are what are known as Type Ia supernovas. These occur in a binary star system when a white dwarf star starts to attract matter from a larger red dwarf star. As the white dwarf gains more and more matter, eventually the star becomes unstable and undergoes a runaway nuclear fusion reaction, producing an extremely bright event that may briefly outshine an entire galaxy. Because this process is well understood, and can occur only within a very narrow range of total mass, the absolute luminosity Type Ia supernovas is very predictable, varying only slightly according to the shape of the supernova’s rise-fall curve. The uncertainty in these measurements is typically 5%.

In August 2011, worldwide attention was focused on a Type Ia supernova that exploded in the Pinwheel Galaxy (known as M101), a beautiful spiral galaxy located just above the handle of the Big Dipper in the Northern Hemisphere. This is the closest supernova to the earth since the 1987 supernova, which was visible in the Southern Hemisphere.

The cosmic distance ladder

These and other techniques for astronomical measurements, collectively known as the “cosmic distance ladder,” are described in an excellent Wikipedia article [Ladder2011].

One advantage of the numerous distance-measuring schemes in use, which overlap over a range of distances from nearby to very distant, is that astronomers can calibrate and corroborate their measurements with multiple approaches. Such calibrations and corroborations thus lend an additional measure of reliability to these schemes.

Summary

In short, distances to astronomical objects have been measured with a high degree of reliability, using calculations that mostly employ only high school mathematics. Thus the overall conclusion of a universe consisting of billions of galaxies, most of them many millions or even billions of light-years away, is now considered beyond reasonable doubt.

However, these distances do cause consternation for some, since as we peer millions of light-years into space, we are also peering millions of years into the past. Some creationists, for instance, have theorized that about 4000 BCE a Creator placed quadrillions of photons in space enroute to earth, with patterns suggestive of supernova explosions and other events millions of years ago [Boardman1973, pg. 26].

Needless to say, most observers reject this “God the Great Deceiver” theology. Kenneth Miller of Brown University, for example, blasted this notion in these terms [Miller1999, pg. 80]:

Their version of God is one who has filled the universe with so much bogus evidence that the tools of science can give us nothing more than a phony version of reality. In other words, their God has negated science by rigging the universe with fiction and deception. To embrace that God, we must reject science and worship deception itself.

This article, co-authored with Jonathan Borwein, is also posted at Math Drudge blog. An abbreviated version will soon appear at The Conversation. For additional details, see Distance.

References

  1. [Boardman1973] William W. Boardman, Robert F. Koontz and Henry M. Morris, Science and Creation, Creation-Science Research Center, San Diego, CA, 1973.
  2. [Miller1999] Kenneth R. Miller, Finding Darwin’s God: A Scientist’s Search for Common Ground Between God and Evolution, Cliff Street Books, New York, 1999.

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