## Venus-Jupiter Conjunctions: A Guide Through 2040

Why are conjunctions of Venus and Jupiter worth looking at?
Venus and Jupiter are the two brightest planets in the sky (sometimes Mars argues with Jupiter for second place, but never when it is close to Venus in the sky), and so are easy to see even from the center of a big city. Observing them is a connection to the natural world no matter where you are located. When they appear close in the sky it is easy to observe night-to-night variations in their positions. Evening conjunctions occur right after dark, and so can be shown to children easily as demonstrations of what they might be learning in school.

How often do Venus and Jupiter line up?
Venus appears to follow the Sun around the sky as seen from the Earth because Venus is an inner planet. Jupiter on the other hand, is an outer planet that moves around the Sun slowly. As a result of the Earth's motion around the Sun, Jupiter appears to circle the sky relative to the Sun roughly once a year as viewed from Earth, and so will pass by Venus, which is always somewhere in the vicinity of the Sun, annually. Hence, Venus and Jupiter typically have one conjunction (lining up as seen from the Earth) each year.

Are there relationships between successive Cytherian-Jovian conjunctions?
Venus goes around the Sun once every 224.7 days, which puts it in the same place relative to the Sun every 1.60 = 8/5 Earth years. Jupiter goes around the Sun once every 11.86 Earth years, which puts it in the same place relative to the Sun every 1.09 years. Hence, if Venus and Jupiter appear together in the sky, then 3.20 years later Venus will be in the same position relative to the Sun, and in 3.27 years Jupiter will be in that position. As a result, similar conjunctions of Venus and Jupiter occur in regular intervals of about 3 years and 3 months.

What makes a conjunction a good one?
Conjunctions are `good' if the planets are far enough from the Sun to be observed easily after sunset or before sunrise. This can be a problem with Venus, because it never strays too far from the Sun. As noted above, if we have a good conjunction in the morning sky, there is another similar one in 39 months or so. Usually a good morning conjunction is followed 10 months later by a good evening one, and then the third one in the sequence occurs when Jupiter and Venus are very close to the Sun. There is some gradual drift because the cycles of 3.27 years and 3.20 years do not exactly match.

Another criterion for a `good' conjunction is that the planets are close together in the sky. This depends somewhat on your location, because if the closest approach occurs during daylight you won't see it. However, the planets appear to move slowly enough relative to one another on the sky that this factor doesn't matter too much. If you miss the night of closest approach because it was cloudy, the preceding or following night will not be too much worse. More important are the inclination of the orbits: 1.3 degrees for Jupiter and 3.4 degrees for Venus. If these line up then you have a close conjunction; if they do not, then the conjunction is a wide one. Also, as noted below, conjunctions are easier to see from locations closer to the equator than near the poles. In the US, that means that the southern states typically enjoy a few more degrees elevation, but the effect is usually not too large.

What are the best conjunctions in the recent past and future?
For the best viewing you want a close conjunction that is high in the sky. Consider the following plots for a typical southern city (Houston) and northern city (New York). The best conjunctions are the ones in the upper right quadrant. Circles are evening conjunctions, and squares are morning. As you can see, the conjunction of June 30, 2015 was the best evening one, rivalled only by the one on March 1 2023, which is not quite as close. For reference, the size of the full Moon on the sky is 0.50 degrees.

The best one in the time interval 2000-2040 appears to be the morning conjunction on Nov 2, 2039. A curious fact about the June 30, 2015 conjunction was that after only 4 months there was another good one in the morning (see plots), also well-separated from the Sun but with a somewhat wider separation between the planets. Essentially Venus has managed to loop in front of the Sun fast enough to catch Jupiter as it emerges into the dawn sky. These loops mark the end of one series of conjunctions and the beginning of another. Want to know more?

How much easier are these to see in the southern states?
There is an elevation benefit of 0 - 6 degrees between Houston and New York, depending on the time of year and if it is a morning or evening conjunction. The maximum difference occurs around February for morning conjunctions, and August for evening conjunctions, with little difference in February for evening conjunctions, and August for morning ones. If you imagine being able to tilt the horizon with respect to the sky, the optimal orientation is one where the planets are vertical relative to the horizon when the Sun is rising or setting. Changing latitude is the equivalent of rotating the horizon. As one proceeds towards the poles, the path of the planets on the sky becomes more aligned with the horizon, so it becomes harder to get any elevation even if there is a substantial angular separation between the Sun and the planets.