I N S I D E T H I S I S S U E

anticipated events in astronomy will occuron 2004 June 8, namely the first transitof Venus since 1882. Think about that fora second: nobody alive today has observeda transit of Venus. What can we learnabout transits from this year’s happenings?“Superior” conjunctions of Venus arespectacularly misnamed. At its furthestpossible distance from Earth, the tiny (10arc second) full disc of the planet crawlsever so slowly nearer the Sun for severalmonths and takes equally long to finallyput enough apparent distance betweenitself and our brilliant star to make itsnext appearance in the evening sky. Bycontrast, at so-called “inferior” conjunction,Venus swoops between the Earth andSun at breakneck speed, its huge (60+arc second) but skinny crescent rapidlychanging in appearance as it catapultsfrom evening to morning sky virtuallyovernight.The reason for all this is the relativedistance of the two events. At 0.72astronomical units from the Sun, Venus’distance from Earth varies from roughly0.28 AU from Earth at inferior conjunctionto 1.72 at superior. At superior conjunctionit is therefore some six times the distance,and one-sixth the apparent size, as atclosest approach. Its apparent speed isslower still, as it is now moving “with”the Sun, whereas at inferior conjunctionit is going in the opposite direction.But some conjunctions are moresuperior than others. While this June’soccultation was unobservable in theconventional sense, in this day and agesuch events are easily available to thevirtual observer. Idle thought experimentscan actually be tested. Equipped with thesoftware program Guide 6.0, I “observed”long series of Venus conjunctions to testand confirm some conclusions I hadalready reached. And, by golly, logic winsout yet again.All Venus watchers become awareof the eight-year periodicity of itsapparitions. As noted by theMesopotamians, Mayans, and others, ittakes almost exactly eight years (actually,eight years minus about 2.3 days) forVenus to orbit the Sun thirteen times. Inthat time, Venus “laps” Earth five times(synodic revolutions), after which thetwo planets return to a very similaralignment as their “starting point” eightyears previous. There are therefore fivemorning and evening apparitions of Venusthat repeat themselves to a high degreeof similarity over the course of a humanlifetime.An even more exact periodicity of152 synodic revolutions per 243 yearscomes into play when considering longtermcycles. Why 243? In that time therehave been 30 eight-year cycles, meaningthe deficit of 2.3 days from each will nowhave amounted to roughly 69 days. Twomore 584-day synodic cycles of Venusamount to three years plus about 72 days,eliminating that deficit more efficientlythan a modern government. The “interest”of three days is attributable to Earth’sprecession, which in 243 years would havecompleted about 1% of a cycle.As an aside, my dear friend the lateFather Lucian Kemble, a self-proclaimed“Fibonacci nut” who pondered theFibonacci sequence in the relationshipbetween 5 synodic cycles to 8 Earth yearsto 13 Venus orbits, would have beenamused to note that the periods of 8 and243 years can be represented in exponentialnotation as 2 3 and 3 5 !In a 243-year cycle there are, in thecurrent era, two pairs of Venus transits,each at eight-year intervals and separatedby more than a century. One pair willoccur in June at the descending node, theother pair in December at the ascending.(Transits can also act alone, but therehasn’t been a singleton since 1396, norwill there be another until 3089. Indeed,in the long term — the 9000 years from2000 bce to 7000 ce were reviewed —single transits are almost as common aspairs. The fascinating pattern of theseevents is best left for a future article.)But shouldn’t transits andoccultations be inter-related? Given the13:8 periodicity, after four Earth yearsVenus will have completed 6.5 orbits, or2.5 synodic revolutions. As in therelationship between solar and lunareclipses, Venus should be at one node ofits orbit at the transits, and the oppositeat the midway points. This explains whyVenus was occulted in 2000, almost fouryears to the day before the transit.As I pondered all this it occurred tome that from our perspective Venus shouldalso stick about six times closer to theecliptic when at superior conjunction.Accordingly, there should be about sixtimes as many occultations of Venus bythe Sun as there are transits. (The samethought occurred independently to MichaelWatson, who posted his similar findingson the RASCals Discussion List in mid-June.) I examined every superiorconjunction of Venus between 1960 and2060 on Guide (using geocentriccoordinates), and the pattern emergedas shown in the table.Occultations of Venus:Transits of Venus:Date Midpoint Duration Date Midpoint Duration1976 June 18 01:26 UT 8.3 hours1984 June 15 19:58 28.11992 June 13 14:34 36.82000 June 11 09:14 42.0 2004 June 8 8:21 UT 6.2 hours2008 June 9 03:41 44.8 2012 June 6 1:31 UT 6.72016 June 6 21:52 45.72024 June 4 16:17 44.62032 June 2 10:32 41.42040 May 31 04:30 35.72048 May 28 22:06 25.5One can readily see the 8 year minus~ 2.3 day periodicity. The first occultationoccurs near the north limb of the Sun.The events grow in duration as they262JRASC December/ décembre 2000