Monday, June 11, 2012

Astronomy is Metal: Transit of Venus

An exceedingly rare event occurred on June 5th, 2012, a transit of Venus. Los Angeles had a prime viewing position for most of the transit, as Venus passed in front of the Sun as viewed from Earth. Taking approximately seven hours, the transit began at about 3:10pm PDT, and lasted through sunset as viewed from the pristine, marine layer free skies of Los Angeles on an absolutely gorgeous late spring day.

Occurring in pairs eight years apart approximately once every 120 years or so, a transit of Venus is of historical and scientific import. In the 16th century, Nicholas Copernicus proposed the heliocentric theory of the Solar System, forever casting aside geocentrism. Besides merely hypothesizing that the Sun is the center of the Solar System and that all of the planets, including the Earth, orbit the Sun, Copernicus also mathematically worked out the basic layout of the Solar System. To a high degree of precision, Copernicus mathematically determined the length of the known planets’ sidereal periods and their relative distance from the Sun in terms of astronomical units (AU), a unit of measurement originally defined by Copernicus. One astronomical unit is defined as the distance from the Earth to the Sun.

Of note within Copernicus’ work is his method for determining the relative distance of an inferior planet, as he referred to Venus and Mercury, from the Sun. The method involves observing the planet at greatest elongation, a position when the planet is at its largest angular distance from the Sun as viewed from the Earth. In the case of Venus, this angle varies slightly from 45 to 47 degrees since the orbits of the planets are not circular, but elliptical (a fact not realized until the discovery of Kepler’sThree Laws of Planetary Motion in the early 17th century). Even so, a bit of elementary trigonometry (see below) reveals that Venus’ mean distance from the Sun is 0.72 AU.

What was lacking, however, was a precise determination of what an AU equals in terms of miles or kilometers. Only then can the true scale of the Solar System be known. A transit of Venus (or Mercury) provides a means of making this determination, a classic problem in astronomy during the 17th-19th centuries.

The first actual observation of a transit of Venus occurred in 1639 in England by the clergyman Jeremiah Horrocks. Horrocks used Kepler’s Laws to predict the transit, and made an estimate of the size of Venus with his observations. He was also able to estimate the length of an AU at about 60 million miles, by far the most accurate determination up to that time.

A Scottish mathematician named James Gregory suggested in 1663 that parallax, a well known geometrical method of determining distance, could be used during a transit of either Mercury or Venus to determine the length of an AU. A friend of Isaac Newton, Edmund Halley, also had a hand in devising the parallax method. A simplified version of the method appears below. Essentially, the transit is observed from two different points on the Earth, shown as "d" on the diagram. If the angle theta is measured, then the distance from the Earth to Venus can be determined. From there, the length of 1 AU can be found.

The first opportunities to employ Gregory’s methods occurred during the transits of Venus of 1761 and 1769. A number of fascinating historical accounts, notably the voyage of Captain James Cook to Tahiti and the unfortunate events surrounding the travails of Guillame Le Gentil, are recommended for further reading. Cook, most notably, observed the frustrating “black drop” effect, an effect which introduced uncertainties into the determination of the length of an AU.

Finally, the calculation was nailed down to a high dregree of precision with the transits that occurred during the 19th century as a number of countries mounted serious efforts to determine the length of an AU. One AU is approximately 150 million kilometers (93 million miles), a figure known to a high degree of precision today.

The reason why the determination of the length of an AU is so important is because the AU is a “fundamental yardstick” for determining distances in the Universe. The AU is the first stepping stone in understanding the distances to the nearest stars by using parallax, and, from there, determining distances to galaxies. Our understanding of the large scale structure of the Universe, and the distances involved, really begins with our understanding of the length of one AU.

The transit of Venus of 2012 is scientifically important as the transit provides astronomers an opportunity to very carefully study the passage of a planet in front of a star. By observing a transit of Venus in our own backyard, so to speak, scientists seek to understand what happens when an exoplanet transits its host star as viewed from Earth. Properties of such planets can be gleaned from the observations of such transits.

I observed the transit of Venus of June 5th, 2012 from two locations in the Los Angeles area. I observed the transit from the location of the gathering of the learners from about 3pm until 4:30pm PDT, and then I drove home to watch the transit until sunset from my deck looking out over the Pacific Ocean. I used a 7.17” Solar Filter and a 6” SkyQuest Dobsonian Telescope, both from Orion Telescopes, as well as projecting the image of the transit through my 7x50 Alderblick binoculars onto foam board. I was even able to capture the “black drop” effect in a few of my images.


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