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Venus Transit Cycles

Venus to cross the solar disk on June 5, 2012

Be sure to circle June 5, 2012, on your calendar. This day will present the last chance in your lifetime to witness the planet Venus swinging directly in front of the Sun. From Tupper Lake, watch Earth's sister world appear in silhouette as a small, dark spot in front of the solar disk from about 6 p.m. until sunset (8:30 p.m.) on Tuesday, June 5. This is really a special kind of eclipse, whereby a smaller celestial object, like a planet, passes directly in front of a larger celestial object, such as the Sun. Astronomers refer to this type of solar eclipse as a transit of Venus.
Proper eye protection is absolutely essential for watching the transit of Venus, else you risk blindness or permanent eye damage. Let the Adirondack Public Observatory or a public facility near you safely show you this grand astronomical attraction. Bring your family and friends.
Only planets that orbit the Sun inside of Earth's orbit can ever transit the Sun. These two worlds are Mercury, the innermost planet, and Venus, the second planet outward from the Sun. If the orbits of the Mercury, Venus and Earth were aligned on the same plane, a transit of Mercury would take place 41 times every 13 years, and a transit of Venus would happen 5 times every 8 years.
As the geometry of the solar system would have it, though, Mercury's orbital plane is inclined 7o to Earth's orbital plane and Venus orbital plane at 3.4o to the plane of our orbit. Whenever Mercury and Venus in their orbits pass in between the Earth and Sun, Mercury and Venus more often than not swing above or below the Sun - meaning no transit is visible from Earth. In the 21st century, there are only 14 transits of Mercury and two transits of Venus (June 8, 2004, and June 6, 2012).
Yet, the orbit of any solar system planet crosses the Earth's orbital plane at two points called nodes. If the planet is traveling from south to north, it's an ascending node. Or if the planet is going from north to south, it's a descending node. Luckily for us, Venus will be near its descending node as its passes between the Earth and Sun on June 5, 2012, to stage the last transit of Venus until December 11, 2117!

Why Only Two Transits of Venus in 21st Century?

Ryan asks, I have a question. Why is the next Venus transit not until 2117 when the last one was only 8 years ago? I thought it would occur on a consistent basis.
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Ryan, take a look at the graphic below, courtesy of the NASA Eclipse Site. In 8-year cycles, Venus returns to nearly (but not exactly) the same spot relative to the sun. The sun crossed the southern part of the solar disk in June 2004 and will cross the northern part of the solar disk in June 2012. Venus will 1/3 degree farther north in June 2012 of where it was in June 2004. Conversely, in June 1996, Venus was 1/3 degree south of where it was in June 2004.

In June 2020, Venus will lie 2/3 degree north of where it was in June 2004, or 1/3 degree north of where it was in June 2012. In other words, Venus will be too far north of the solar disk to transit the sun in June 2020.
In a nutshell, it's impossible to have three transits in 16 years. The sun's diameter spans 1/2 degree, but the change of Venus' position after 16 years is 2/3 degree.
As Venus returns to its fifth inferior conjunction every 8 years (more precisely: 8 years-2.4 days or 7.9936 years) Venus will get farther away from its node and farther north of the ecliptic. Venus will peak out at close to 9o north of the Sun as it reaches inferior conjunction on March 9, 2324. Inferior conjunctions taking place in March always find Venus far north of the Sun.
Yes, even though Venus' greatest heliocentric latitude is only 3.4o, it's geocentric latitude at inferior conjunction can exceed 8o 50'. The diagram below helps to illustrate.

After Venus reaches its northernmost point in the cycle, it'll start to go southward again every 8 years, until nearing its ascending node and giving a transit of Venus on December 16, 2603 and December 13, 2611. (See table below.)
This represents 75 8-year returns in 599 years rather than 600 years, because the cycle regressed one-half year, past January and into the December of the previous year. Or, if you prefer, 75 7.9936-year returns = 599.5 years
In much the same vein, this 8-year sequence goes full cycle relative to its node in a period of 1215 years, rather than 1216 years, providing descending node transits on June 20, 3219 and June 17, 3227. This represents 152 8-year returns in 1215 years, because the cycle backtracked nearly one full year. Or, if you prefer, 152 7.9936-year cycles = 1215 years.

Maximum: Two Venus' Transits Per Century

Although transits will come in pairs some 8 years apart for centuries to come, it's possible to have only one transit per century for centuries on end, if the transits are close to central.
It's possible to have no transits in a particular century, if the transits (or transit) in the century before came late in the century. This is the case for the 26th century (2501-2600) and 32nd century (3101-3200).

The 243-year Transit of Venus Cycle

Descending node transits come in June and in cycles of 243 years. Ascending node transits come in December and also come in cycles of 243 years. They generally alternate century by century as displayed in the table below.
You'd think midway between the 243-year gap in June descending node transits, you'd find a December ascending node transit 121.5 years after the former and 121.5 years before the latter. Or vice versa: you'd think midway between the 243-year gap in December ascending node transits, you should find a June descending node transit in the same 121.5-year period.
Apparently, no such symmetry exits. A December ascending node transit takes place 113.5 years (121.5 - 8 = 113.5) after the June descending node transit and 129.5 years (121.5 + 8 = 129.5) before the next June descending node transit. Or, if you will, you can say a June descending node transit takes place 129.5 years after the December ascending node transit and 113.5 years before the next December ascending node transit.
The lack of symmetry is probably due to the eccentricity of the Earth's orbit. After all, we're close to aphelion during the June transits and to perihelion during December transits.

243-Year Transit Cycle

June Descending Node TransitsDecember Ascending Node Transits
2004 Jun 82117 Dec 11
2012 Jun 62125 Dec 8

2247 Jun 112360 Dec 13
2255 Jun 92368 Dec 10

2490 Jun 122603 Dec 16
2498 Jun 102611 Dec 13

2733 Jun 152846 Dec 17
2741 Jun 132854 Dec 14

2976 Jun 163089 Dec 18
2984 Jun 14near miss

3219 Jun 203332 Dec 20
3227 Jun 17near miss

If you'd like a more comprehensive list of Venus transits for 6,000 years, click on Six Millennium Catalog of Venus Transits.


Reconciling 8-Year Inferior Conjunction Cycles With 243-Year Transit Cycles

In some respects, there are five 8-year (more accurately: five 7.9936-year) inferior conjunction cycles going on concurrently. In the table below, I give each inferior conjunction cycle its own number (1, 2, 3, 4 and 5) and the number of 8-year (7.9936-year) repetitions for each cycle before a transit recurs in another century.
Each numbered cycle goes full circle relative to a particular node in periods of 1215 years. Though five 243-year cycles make up 1215 years, it is important to note that a different numbered cycle brings about the transits every 243 years (7.9936/5 years x 152 = 243). Every 243-year transit cycle is made of 30 8-year (7.9936-year) inferior conjunction cycles consisting of 240 years (239.808 years) + 3 years.
Looking at the transit cycles on the above table, let's focus on June descending node transits. Inferior conjunction cycle 1 (see numbered inferior conjunction cycles in table below) brought June descending node transits in 2004 and 2012, followed by inferior conjunction cycle 3 in 2247 and 2255, inferior conjunction cycle 5 in 2490 and 2498, inferior conjunction cycle 2 in 2733 and 2741 (see above), inferior conjunction cycle 4 in 2976 and 2984 (see above) and inferior conjunction cycle 1 in 3219 and 3227 (see above).
Now for the December ascending node transits: inferior conjunction cycle 2 brought about the December ascending node transits in 2117 and 2125, followed by inferior conjunction cycle 4 in 2360 and 2368, inferior conjunction cycle 1 in 2603 and 2611 (see above), inferior conjunction cycle 3 in 2846 and 2854 (see above), inferior conjunction cycle 5 in 3089 (see above) and inferior conjunction cycle 2 in 3332 (see above).

Five 8-Year Cycles of Venus at Inferior Conjunction

NumberDate & HourAngular distance from eclipticDate & HourAngular distance from ecliptic
12004 Jun 8 9UT0o 11' south (transit)2012 Jun 6 1UT0o 9' north (transit)
22006 Jan 13 24UT5o 31' north2014 Jan 11 12UT5o 11' north
32007 Aug 18 4UT7o 59' south2015 Aug 15 19UT7o 50' south
42009 Mar 27 19 UT8o 10' north2017 Mar 25 10UT8o 18' north
52010 Oct 29 1UT5o 59' south2018 Oct 26 14UT6 o 15' south
Add 112 years (14 8-year returns)
NumberDate & HourAngular distance from eclipticDate & HourAngular distance from ecliptic
12116 May 7.84o 21' north2124 May 5.54o 38' north
22117 Dec 11.10o 12' north (transit)2125 Dec 8.60o 13' south (transit)
32119 Jul 17.55o 06' south2127 Jul 15.24o 50' south
42121 Feb 23.28o 41' north2129 Feb 20.88o 36' north
52122 Sep 26.18o 30' south2130 Sep 23.78 o 35' south
Add 128 years for a total of 240 years (30 8-year returns)
NumberDate & HourAngular distance from eclipticDate & HourAngular distance from ecliptic
12244 Apr 1.28o 03' north2252 Mar 29.88o 12' north
22245 Nov. 2.55o 42' south2253 Oct 31.06o 00' south
32247 Jun 11.50o 12' south (transit)2255 Jun 9.20o 09' north (transit)
42249 Jan 15.95o 29' north2257 Jan 13.55o 11' north
52250 Aug 20.27o 58' south2258 Aug 17.97 o 50' south
Add 112 years for a total of 352 years (44 8-year returns)
NumberDate & HourAngular distance from eclipticDate & HourAngular distance from ecliptic
12356 Feb 28.68o 46' north2364 Feb 26.28o 42' north
22357 Sep 30.58o 25' south2365 Sep 28.28o 50' south
32359 May 10.94o 21' north2367 May 8.64o 38' north
42360 Dec 13.10o 11' north (transit)2368 Dec 10.60o 14' south (transit)
52362 Jul 19.75o 07' south2370 Jul 17.34 o 50' south
Add 128 years for a total 480 years (60 8-year returns)
NumberDate & HourAngular distance from eclipticDate & HourAngular distance from ecliptic
12484 Jan 20.45o 48' north2492 Jan 17.95o 28' north
22485 Aug 23.78o 06' south2493 Aug 21.47o 59' south
32487 Apr 3.38o 04' north2495 Mar 31.98o 13' north
42488 Nov 3.55o 42' south2496 Nov 1.06o 00' south
52490 Jun 12.60o 11' south (transit)2498 Jul 10.30 o 08' north (transit)

copyright 2012 by Bruce McClure

Resources:
Are transits and rotation linked? by Nick Lomb
Astronomical Tables of the Sun, Moon and Planets (2nd edition) by Jean Meeus (page 22, pages 413-419)
Mathematical Astronomy Morsels III by Jean Meeus (pages 264-276)
The Sky Astronomy Software

May 2012 Feature * July 2012 Feature