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. It occurred in 2015, and will again in 2036.
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:
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. The dots
occur in the evening and the open squares in the morning. 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.
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 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.
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.
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).