## Venus-Jupiter Conjunction Series

This page provides more detail about how Venus/Jupiter conjunctions are spaced in time, and shows how the different conjunction series relate to one-another.

Venus has a synodic period (returns to same place in sky relative to the Sun) every 1.6 years. Jupiter has a synodic period of 1.09 years. Hence, every 3.2 years, Venus is in the same position as it was relative to the Sun, and Jupiter returns to the same position in 3.27 years. As a result, there are families of conjunctions that are separated by about 3 years and 3 months that occur in a similar position relative to the Sun.

Usually as Jupiter passes by the Sun it encounters Venus only once. However when the situation is such that Jupiter encounters Venus when the latter is nearly at its greatest elongation from the Sun in the evening sky, then Venus has time to turn around and catch Jupiter in what I call a 'transition conjunction' before Jupiter leaves the area. A final conjunction follows as Jupiter exits the area. This situation is shown in the diagram below, and occurs in 2015.

As you can see, the middle conjunction (named `Transition' in the figure) is typically a wide one because of the tilt of Venus's orbit relative to that of the Earth. Because the 3.27 year cadence of Jupiter is just a bit longer than that of Venus, Jupiter lags a bit each 3.2-year cycle, and the morning conjunctions gradually move closer to the Sun, while the evening ones gradually move away from the Sun. Referring to the diagram above and adding 3 years and 3 months to the dates, we see there should be a morning conjunction sometime around 1/25/2019, and in fact, a conjunction does occur on 1/23/2019. What about the one for the evening cycle, which should be around 9/30/2018? This one does not happen because Jupiter doesn't make it in far enough to intersect there with Venus before Venus turns back to the west. Hence, years where triple conjunctions occur mark the end of one series and the beginning of the next one.

The plot below summarizes the series by displaying all the conjunctions between 1990 and 2060. Only one complete series is displayed (series 3), as they each last 70 years or so. Conjunctions with negative values on the y-axis occur to the west of the Sun and are visible in the morning, while those with positive y-axis values occur to the east of the Sun and are visible in the evenings. The different symbols refer to how close the conjunction appears. The best conjunctions are those where the planets are less than a degree apart (filled symbols), and are more than 20 degrees above the horizon at sunset or sunrise (above and below the two dotted lines, respectively).

A few other things to note:

• The closer conjunctions tend to occur between the dotted lines:
This is rather unfortunate, because these are difficult to observe owing to the Sun's glare. Conjunctions between the dotted lines happen when Venus is on the opposite side of its orbit from the Earth (superior conjunction with the Sun when the y-axis value is zero), so the fact that Venus is a bit out of the plane of the Earth's orbit matters less. However, when Venus is near the Earth, any deviations from the Earth's orbital plane become magnified, and therefore it is more difficult to line up with Jupiter. Jupiter's inclination is less of an issue, because being an outer planet, it is always behind the Sun and therefore far from Earth when Jupiter and the Sun are near in the sky. Jupiter has a rather small inclination (1.3 degrees; Venus is 3.4 degrees).
• The y-axis values increase steadily for each series, but they are bumpy:
The bumpiness comes from the different times of year for the points. Recall that we are plotting elevation of the conjunction at sunset or sunrise. Elevation is related to the angular separation between the Sun and the planets, but is only equal to it if the line that connects the Sun to the planets is perpendicular to the horizon. In general, the angle between the Sun and planets depends on the season of the year. There is also a smaller effect from the fact that planetary orbits are elliptical and not circular.
• Pick any time. A vertical line intersects three series:
This must be the case, because there is a conjunction nearly every year, and after a little over three years you return to the original series.
• Transition conjunctions are the magenta cicles:
These conjunctions mark the end of one series and the beginning of a new one. The magenta lines connect the three conjunctions depicted in the first figure. When the magenta line crosses the y-axis, Venus lines up with the Sun (inferior conjunction with the Sun).

It is fun to look at these cycles and think about the connection between the past and the future. Because each cycle lasts about 70 years and a new one is born about every 24 years, they have similar life spans and intervals as human generations do. At any given time, three cycles are active, transitioning between morning conjunctions in their youth, to near the Sun in midlife, and evening conjunctions in later life. In a way, series 1 has accompanied the WWII generation, series 2 the baby boomers, and series 3 the millennials.

If you look closely, you will see that the shapes of the different series are similar. Recall that the `bumpiness' in each series is caused primarily by the conjuctions occurring at different times of the year. That the bumps line up suggests that some points between the series happen at the same time of the year. Indeed this is true. It turns out that 22 synodic periods of Jupiter equal 24.024 years, and 15 synodic periods of Venus equals 23.985 years. Hence, after 24 years a conjuction from the next series will occur at the same time of the year and have a similar separation. Looking at the plot below, three of the four best evening conjuncitons are 2/23/1999, 3/1/2023, and 3/7/2047, separated by almost exactly 24 years. They are gradually getting wider, and the next three in this group, 3/14/2071, 3/21/2095, 3/29/2119, have elevations of 36, 39, and 41 degrees, and separations of 1.4, 1.9, and 2.4 degrees, respectively. The previous ones in this sequence, 2/17/1975, 2/11/1951, and 2/4/1927 were quite nice evening conjunctions, with elevations 24, 20, and 17 degrees, and separations 0.20, 0.43, and 0.58 degrees, respectively.

How does the 24-yr cycle relate to the June 30, 2015 conjunction? In around 24 years on 7/8/2039, Venus will approach Jupiter, but doesn't quite get there because it is just beyond the end of its cycle (series 2). Hence, the 6/30/2015 conjunction is the last of its 24-year group. However there was an evening conjunction 24 years prior on 6/17/1991 with an elevation of 38 degrees and separation 1.2 degrees (part of what would be Series 0 in the above plot). Previous ones include 6/9/1967, 6/1/1943, 5/25/1919, 5/18/1895, and so on going back every 24 years all the way in the past to 865 years ago on Halloween morning in the year 1150 which began the 24-year cycle with a 0.75 degree conjunction at an elevation of 43 degrees.

Think about the history that has passed during that time. Someone in a medieval field undoubtedly looked to the sky that cool morning in 1150 and marvelled at the beautiful sight. A new 24-yr group begins in the morning of 10/25/2015, stretching to the future, with its final conjunction in the evening of May 31, 2856. Do you suppose anyone from that future date will imagine our lives today?

Finally, here's a plot of all the conjunctions between 1990 and 2060. Only a few with very large separations of more than 3 degrees, and those that line up almost exactly with the Sun are not plotted. The degrees above the horizon are for Houston, and as noted above these will shift downward a few degrees for a typical northern city, depending on the season of the year. The evening winners appear to be 6/30/2015, 3/1/2023, and 2/23/1999, and the morning standout is clearly 11/2/2039. If you manage to get an excellent horizon with clear skies, I'd say 8/27/2016 (evening) and 2/12/2056 (morning) are probably worth some special effort to see.