June 8, 2004--Venus in Transit

by Eli Maor

Princeton University Press. 185 pages.

(Available from amazon.com for $18.36 plus shipping.)

The (mean) distance between the earth and the sun is known as the astronomical unit (AU), and its measurement is the topic of this book. Recall Kepler's third law: The square of the period of rotation of a planet around the sun is proportional to the cube of its mean distance therefrom. Clearly if the distance from one planet to the sun be known then the distances of all of the others follow immediately from Kepler. And obviously the AU must be the easiest planetary distance to determine if, indeed, any can be measured. Once the AU is determined the complete scale of the solar system is known. Moreover since the diameter of the earth's orbit is used as a baseline for parallax measurements of nearby stars, knowledge of the AU is essential for extra-solar-system astronomy as well.1

The only practical way to measure the AU is by parallax, using baselines on Earth. (This raises the problem of determining the baseline accurately, which involves the touchy question of measuring longitude, unsolved until the development of John Harrison's marine chronometer in 1762.) Clearly, one cannot carry out a parallax measurement on the sun, since its brightness obscures any background which might be used as a benchmark. How about measuring the distance to Venus by parallax? After all, Venus appears in the dark sky in the early evening and early morning. Unfortunately, it is also too bright, obscuring nearby stars which might be used as measuring posts. (Venus is so bright that it can actually be seen during the day if you know where to look.)2 So in 1677 Edmond Halley (after whom the comet is named) got the idea of measuring the parallax of Venus during a transit, using the sun's face as the perquisite background. The Earth-Venus distance immediately gives the AU from Kepler's law quoted above.3

These transits, when Venus comes directly between the earth and the sun--inferior conjunction--are relatively rare due to the fact that the Venereal orbit is inclined three degrees and 22 minutes to the ecliptic. Except for this inclination there would be transits every synodic period of 584 days. (The synodic period is the time between successive inferior conjunctions of Earth and Venus.) It is for a similar reason, the inclination of the moon's orbit to the ecliptic, that solar eclipses don't occur every lunar month.Transits occur only when Earth and Venus cross the so-called "line of nodes"--the intersection of the plane of Venus' orbit with the ecliptic--at the same time. The line of nodes is fixed in space, and Venus crosses it around Dec. 8 (the ascending node) and June 7 (the descending node). So transits can only occur near those dates. It also turns out that transits usually occur in pairs, separated by eight years with the next transit coming over 100 years later. The reason for the eight-year hiatus is that five synodic periods of Venus are within two days of equaling eight Earth years. This two day discrepancy means that the second time around Venus and Earth are not in perfect alignment, but because the finite angle subtended by the sun the transit may (and almost always does) occur. After another eight years the accumulated four-day discrepancy has become too large, and there is no third transit. The observer has to wait for a conjunction at the other node, and that occurs in 121.5 years (from ascending node to descending node) or 105.5 years for the opposite. The discrepancy  of 16 years between these two numbers is due to the fact that the planetary orbits are elliptical.

Halley's method, explained in detail in the book in Chapter 5 and Appendix 1, is based on the realization that angles on the sun's surface are difficult to measure. On the other hand, transit times can be measured with a good clock, and these can be converted into angles since the further from the center of the sun the transit occurs the shorter the transit time and the greater the angle. Efforts were made to make measurements of this type on June 6, 1761 and June 3, 1769, expeditions being sent to the far corners of Earth. One of the 1761 expeditions, to Sumatra,4 was commanded by Charles Mason assisted by the young surveyor Jeremiah Dixon.5 Another measurement was made in Vienna by Fr. Maximilian Hell, S.J., director of the observatory. An interested onlooker during the transit was Archduke Joseph of Austria, later to become Emperor Joseph II of Amadeus fame.

The 1761 expeditions were not too satisfactory due to difficulties in timing; in determining longitude (recall that the first marine chronometer was not built until a year later); and because the atmospheres of Venus and Earth combined to smear out the Venereal image, make times of ingress and egress difficult to pin down. The results of the various measurements gave values of the AU ranging between 77 and 96 million miles (compared to the correct value of 93.1 million miles). So other expeditions were mounted for the 1769 transit. The leader of one of these was the famous Captain James Cook, who was sent to Tahiti (then known as Otaheite). The expedition was funded jointly by the British Admiralty and the Royal Society. As a result Capt. Cook, when he discovered two new archipelagoes, named them the Society and Admiralty Islands, names they retain to this day. There was even a transit measurement in the American Colonies, led by David Rittenhouse, the father of American Astronomy and a native of Philadelphia. (Rittenhouse Square in Philadelphia, adjacent to the Curtis Institute of Music, bears his name.) And there is still a Transit Street in Providence, RI commemorating the measurements carried out there. The 1769 measurements led to a value of 95.4 million miles for the AU, still somewhat off the presently accepted value but much better than the results eight years earlier. (The chronometer was now available).

The next two transits, Dec. 9, 1874 and Dec. 6, 1882, gave better values for the AU, but by now there were better measurements, for example parallax of Mars at inferior conjunction. So the interest in transits of Venus waned considerably except for those interested in the wonders of Nature.6 If you are one of those, be advised that the next transit will occur on June 8, 2004 (hence the title of the book). A good place to view it will be in Jerusalem; ingress will occur there at 05:19 UT (01:19 EDT) and egress at 11:23 UT. So the transit will be marginally visible from the eastern US, but in Jerusalem it will begin at 08:19 local summer time. If you read this book and look at the Plate 9 you will probably not be able to stay away.

The author of this elegant little book is a mathematician, but even so it is extremely well written. Prof. Maor goes out of his way to place the eras of the various transits in historical perspective and to humanize the different observers by giving details of their lives and work. The technical material is discussed at an elementary level so that the book could be read by intelligent laypersons starting with high-school students, but even trained scientists will find it fascinating. The work of Copernicus and Kepler is discussed briefly to set the stage; readers of this journal will be able to skip those chapters (but are advised not to as there are many interesting historical tidbits therein). In a later chapter the author discusses transits of Earth as viewed from Mars, the subject of a famous story by Arthur C. Clarke called Transit of Earth. Particularly spectacular in such a transit, could we but view it, is the second dark spot which begins to cross the sun's surface when the earth is about halfway across. It is, of course, our moon. Other interesting topics include a discussion of the transits of Mercury and the non-existent planet Vulcan which observations of one of those transits was supposed to demonstrate.

The book is remarkably free of errors, but I think I did find one. On page 4 the author, describing what Jerusalem would be like on the morning of June 8, 2004, refers to the "Via Dolorosa" as the path which Jesus took on his last journey into the walled city down the slopes from Mount Scopus. Having actually made a pilgrimage to the Via Dolorosa myself, I can say with some certainty that it was rather the path which Jesus followed beginning inside the city and continuing to Golgotha, the site of the Crucifixion (which in those days was outside the city walls). Along this route one finds the original Stations of the Cross.

There are interesting references at the end of each chapter and an extensive bibliography; these should be particularly useful to those who wish to learn more about the fascinating subject of transits and the lives of the men (sorry; no women mentioned in the book) who tried to observe them. To end on a slightly negative note, however, I found the index somewhat inadequate.

  1. "Nearby" until 1989 meant within a distance from Earth of about 30 parsecs. [1 parsec=3.26 light years is the distance at which the radius of the earth's orbit (i.e. the AU) subtends an angle of one arc second.] However in 1989 the European Space Agency launched the parallax-measuring satellite Hipparcos which is capable of measuring parallax to within 0.001 arc seconds thus extending the range of parallax measurements by about a factor of 30.
  2. It is interesting, incidentally, that ancients were not aware that the evening and morning stars were the same heavenly body so they had different names for them: in Greek, "Hesperos" and "Phosphoros" respectively and in Latin "Hesperus" (occasionally "Phosphorus") and "Lucifer." "Phosphoros" and "Lucifer" both mean "light bearing." "Hesperus" comes ultimately from the Indo-European word "wesperos" meaning "western" since the evening star is always seen in the western sky. In the Roman Catholic liturgy, the sixth of the seven canonical hours--which takes place in the evening--is called Vespers, a word deriving from Hesperus. The (only) biblical reference to Lucifer: "How art thou fallen from heaven, oh Lucifer, son of the morning." Isaiah xiv. 12 (KJV). The frequent use of the name "Lucifer" for the devil is a little odd and may trace to a misinterpretation of this quotation. A better name, dating to the Old Testament, is "Satan" [cf. Job i., ii. and Psalms cix. 9 (KJV)]. However Dante, Marlowe, Shakespeare and Milton inter alia all use the name "Lucifer" to represent God's fallen angel. The Book of Common Prayer, written at about the time of Marlowe, uses "Satan" or simply "the devil" as does the King James version of the bible, published some 50 years later. Jesus: "Get thee behind me, Satan" [Matthew xii. 26 and Mark viii. 23 (to Peter) and Luke iv. 8 (to the devil).] Then phosphorus match invented in the middle 1800's (they are referred to by Huck Finn as "new-fangled") were called "lucifers" well into the 20th century. A popular World War I song had the lyrics "Pack up your troubles in your old kit bag and smile, smile, smile. While you've a lucifer to light your fag, smile boys that's the style." ("Fag" was slang for "cigarette" in those days.)
  3. In much the same way the Earth-moon distance can be measured by parallax as the moon moves across the face of the sun, i.e. during a solar eclipse. The first such measurement reported was made in 189 B.C.E. by Hipparchus of Nicaea who reported a number within about 30 per cent of the correct value.
  1. One of Sherlock Holmes' unpublished cases involved the "giant rat of Sumatra," a case "for which the world is not yet prepared" according to Holmes' Boswell, Dr. John Watson. (A. Conan Doyle, The Case of the Sussex Vampire.) Interestingly enough, Holmes' Nemesis, Dr. John Moriarty, was an expert on triangulation (he wrote his dissertation on the Pythagorean Theorem) and thus may well have been involved in measuring the 1874 and 1882 transits although there is no official record. See The Final Problem and The Valley of Fear for more on Moriarty whose name, incidentally, derives from the Latin moriar ("I shall die").
  2. Mason and Dixon became famous later for surveying the Mason-Dixon Line, the border between Maryland and Pennsylvania, traditionally accepted as the demarcation line between North and South in the United States. There was considerable internecine violence in Maryland during the American Civil War due to its being unable to secede and join the Confederacy--to which it belonged, geographically--due to the proximity of large Federal forces in the District of Columbia.
  1. "The heavens declare the glory of God: and the firmament sheweth his handywork." Psalms xix. 1 (BCP). The knowledgeable reader will recognize that this verse has been paraphrased by Joseph Haydn for a chorus-cum-trio in his oratorio The Creation: "The heavens are telling the glory of God. The wonder of his works displays the firmament." Although Haydn wrote this oratorio in Vienna (in 1798) the original text was in English, a language with which he was familiar since he had spent a couple of years in the 1790's living in London.

Paul F. Zweifel