Venus and the Pleiades together on the sky – understanding the great Venus orbit cycle, part 1

The biggest celestial event in April 2020 was definitely the meeting between our closest planet Venus and one of the most renowned open star clusters – the Pleiades. The phenomenon was interesting due to its rarity. Throughout our life it will happen every 8 years, but what’s next? This article brings you not only the certain dates when you can expect Venus near the Pleiades cluster but also a bit of the orbiting mechanism.
Venus orbits the Sun once every 225 days, nearly one of third time quicker than Earth. As a result, the synodic period of this planet to the Earth counts around 584 days. This period of time lies in an interesting coincidence, where the 13 Venu’s “years” correspond almost to 8 Earth’s years. This coincidence plays an important role in transit predictions. Important is also the difference with the plane of the orbit. Whereas the Earth moves along the ecliptic plane, Venus doesn’t. The inclination of Venus’s orbit is about 3.4 degrees to the ecliptic plane. The presence of inclination results in 2 “places”, where the Venus orbit crosses the orbit of Earth. These “places” are called nodes. Basically, if Venus crosses the node in its orbit, then an observer on Earth can see Venus transit across the solar disk. The node means, that Venus is at the exact line between Earth and Sun. Moreover, the nodes divide the Venus orbit on “northern” and “southern” against the ecliptic. Again, if the inferior conjunction of Venus with the Sun falls near the node, the second planet passes directly between the Sun and Earth. Consequently, we can see how this planet moves across the solar disk (Pic. 1).

Pic. 1 Venus transit at the descending node (Forbes, 1874).

The transit of Venus can fall near the ascending and descending nodes. Usually, it occurs in pairs, but there are exceptions. Sometimes (in terms of the long time period) we can face one-ascending node transits, which are driven by both Earth and Venus orbit precession. Another problem refers to moving nodes (from west to east in doing so 29,8 arcsec per year)(Maor, 2004). Consequently every year it takes Earth a bit longer time to cross Venus’s nodes. Nowadays, the 243-year Venus cycle starts in early December (ascending node) and continues in early June (descending node), whereas around 1000 years ago it was accordingly mid-November and mid-May. The delay is finally about 2 days per cycle. We could see one pair of transits, where Venus just passed the descending node in June 2004 and prior to reaching the descending node in June 2012. These transits were spaced by 122,5 years from the previous pair as occurred in December 1874 and December 1882. In turn, the new transit cycle begins after 105,5 years in December 2117 (Pic. 2).

Pic. 2 The Venus cycle graph and timescale between ascending and descending node transits, where: A – ascending node transit; D – descending node transit. A complete transit cycle called the “Venus cycle” lasts 243 years (Maor, 2004).

The time between the first ascending node transit and the first descending node transit is always 129,5 years, while the time between the first descending node transit to the first ascending node transit is always  113,5 years (Borgia, 2006). For us important will be the information, that the ascending node transits belongs to one group and the descending node transits to another group. You will get to know about another group of transits in the next part of this article.

In each pair of transits, the observer can see Venus moving across the lower and upper parts of the solar disk. This is caused by the geometry of the orbits of these 2 planets. The 5 synodic periods of Venus are almost exactly equal to 8 Earth years (Maor, 2004).  Here we must stress the word “Almost” because the smallish difference causes Earth to lag behind Venus by about 2.46 days every fifth conjunction (Maor, 2004).  It’s sufficient to move Venus slightly higher or lower in its orbit against the ecliptic. If we take into account Venu’s orbital velocity combined angle of inclination to the ecliptic, then Venus will appear 22 arcmins higher or lower in its orbit roughly at the node. It explains, why the separate transits in pairs fall on the opposite parts of the solar disk. Moreover sometimes, when one transit occurs near the middle of the solar disk, another one may not be visible, as Venus passes just outside the Sun (Pic. 2). This situation is going to happen on  Christmas Day, December 25, 3818 for ascending node and July 11, 5900  for descending node, making them the longest Venus transits ever (8 hours and 9 minutes).

Pic. 3 The single Venus transit pattern (Maor, 2004).

This situation is a result of the very slow drifting of each inferior conjunction point westward around the Sun with a single cycle (Borgia, 2006) because the 13 to 8 resonance of these 2 planets is not strictly precise. A good example is the period between 2004 and 2012 transits, where the time interval was 7,997, not 8 years (Borgia, 2006). Over thousands of years, the passage points drift far away from the node, which leads to one-node transit instead pair of transits. For descending nodes, this situation occurred till the year AD 60 and will be back again in  AD3956. Another issue is the parallax, causing a slightly different track appearance and length of the transit phenomenon (Pic. 4).

Pic. 4 The transit of Venus parallax as seen from different locations on Earth (Forbes, 1874).

The parallax is important for grazing transits, like in 2611 on the northern hemisphere, where only a part of Venus’s disk will be visible on the solar edge, as well as in Antarctica 243 years later, where the second planet of our Solar System will touch the solar disk externally.
The last thing, which should draw our attention in terms of Venus’s inferior conjunction is the direction of transit itself. Because Venus orbits around the Sun quicker than Earth it will always happen from the eastern to the western edge of the Sun, unlike solar eclipses, where the Moon proceeds another way round.

Knowing the general Venus orbit mechanism, which has been well explained by the transit phenomena, we can move away from the Sun and figure out what usually happens in the other Venus’s position against Earth.  It couldn’t be described without this long and detailed Venus cycle explanation above.
Using some basic Astro software I could check the position of Venus for an exact range of dates, as it was shown for transit phenomena.  I found, that there is another giant Venus cycle above the 243-year one, commonly known. The matter applies not only to the nodes themselves but a whole orbit of Venus’s inclination to the orbit of our planet. Following the pattern of Venus’s orbit, appropriate to the current year – 2020, which was presented and described here, we must assume a different position of Venus in the sky  (Pic. 5).

Pic. 5 The Venus orbit in 2020 with inferior conjunction marked (3.06.2020), conjunction with Pleiades (3.04.2020), and maximum east elongation (blue triangle)(24.03.2020)(based on Universalworkshop.com).

I highlighted 3 major moments, that happened right now, at the time when this article was produced. The maximum east elongation occurred on March 24, and the best conjunction with the Pleiades (measured by the closest meeting with Alcyone star) on April 3. We are still before the inferior conjunction, which will happen on June 3.
Now let’s consider what the author of the aforementioned graph wanted to show all of us. If the inferior conjunction Venus with the Sun falls just before the descending node, then the maximum east elongation should fall just before the orbit inclination reaches maximum value against the ecliptic. In turn, the conjunction with the Pleiades shall fall after the orbit inclination maximum. As the “place” of inferior conjunction moves leftward on our image, the maximum elongation should consequently fall further from the peak of orbit inclination, “pushing” the conjunction with the Pleiades towards this moment, where Venus orbit reaches the biggest inclination against the ecliptic. It perfectly explains why during the cyclic presence of Venus in the Pleiades, the planet’s path in the sky is “lifted up” a bit (Pic. 6-8) As a result the conjunctions with the Pleiades are more effective for the time being. However, this situation won’t last forever.

Pic. 6 The different conjunction of Venus with the Pleiades in the 8-year timespan, as seen from Poland (Piotr Strzelczyk, Marcin Jadczyszyn). Click to enlarge.

Pic. 7 Venus passing the Pleiades in 2004, 2012, and 2020 (credits: Mariusz Swietnicki).

The basic angular difference is around 22′ when Venus crosses the node. In case, when the planet is close to the maximum inclination, this difference is much smaller and usually confined to a few arcminutes. It’s still enough to see how Venus’s track is “crossing” the Pleiades in the span of tens of years.
Our generation is fortunate to live in the time when the descending node transit pair took place in 2004 and 2012. With this pair of transit, which occurs around early June, the conjunction with the Pleiades is strongly related. On the contrary, another group of transits – ascending ones, which happen around early December is preceded by a very close conjunction with Antares – the brightest star in the Scorpius constellation. The nearest certain date, where the conjunction falls is October 19, 2117, and the angular distance between these two bodies is only between 0’39” in Antarctica and 1’01” in the Arctic region. In the case of ascending node transits, the conjunction of Venus with Antares predates the transit 8 years earlier and next occurs just before the ascending transits a few weeks earlier (Pic. 8).

Pic. 8 The nearest Venus conjunction with Antares – the brightest star in the Scorpius constellation compared to the great conjunctions preceding the ascending node transits in 2117 and 2125.  The blue line shows the angular distance between these 2 bodies in the 2021 conjunction. Simulation in Cartes du Ciel Sky Charts 4. Click to enlarge.

In this event, the Venus orbit moves downward about 5′ per 8-year cycle, as opposed to the Pleiades, where every 8 years this orbit is lifted up.
The amount of conjunctions with the Pleiades explains the angular width of this cluster, surpassing 1 arcdegree.
I would say, that the series of conjunction the Venus with the Pleiades begins 8 years after the descending node transits take place (Pic. 9-10).

Pic. 9, 10 – The Venus orbit simplified patterns throughout the Pleiades cluster between 2004 and 2060. The grey track applies to the cycles in the past. Yellow tracks are current (2020) and future (2028-2060) covering the great conjunction with the Pleiades at once. One dot – 1 hour; 9 – Cartes Du Ciel Sky Charts; 10 – Wikimedia.org image template. Click to enlarge.

In each period of conjunction, which lasts usually from 10 to around 30-35 hours, Venus meets the brightest stars of this cluster, approaching some of them very close. The best moment will happen on April 3, 2028, when Venus will be passing the Merope star in a barely 1,5′ angular distance. It means, that for naked-eye observers this star can be definitely outshined by much brighter Venus, which will be reaching its maximum brightness after the greatest eastern elongation about 10 days earlier. Due to the parallax, described above, the best location to see these 2 bodies really close to each other will be the southern hemisphere (Pic. 11, 12).

Pic. 11 The best moment of conjunction Venus with the Pleiades cluster, when Venus will approach the Meropa star (23 Tauri) in just a 1,5′ distance at 23UTC on April 3 (based on Cartes du Ciel Sky Charts 4).

Pic. 12 The smallest angular distance between Venus and Merope star (23 Tauri) at 23UTC on April 3, 2028, across the Globe – simplified sketch. The smallest angular distance falls on Antarctica and counts barely above 1′(based on the Vidiani.com world contour map).

In 2060, the Venus orbit will leave the Pleiades cluster, still heading towards the maximum of its orbit inclination. It’s worth knowing what will happen next.
I wrote earlier, that the 243-year Venus cycle is not the only one, as we can be aware of. It’s good to check how the position of this planet looks at a certain date. In our case, this date is the moment of best conjunction with the Pleiades or alternatively the closest approaching to this cluster from any part of the sky.
Standing by 2060 for a moment, we can take a look at another, but further conjunctions that take place earlier on later (Pic. 13).

Pic. 13 All conjunctions of Venus with the Pleiades cluster between 2058 and 2063 around April (Cartes du Ciel Sky Charts 4).

As we can see, there are 3 separate orbit tracks. Basically, Venus will cross the Taurus constellation 5 times within the 8-year period, but again, we are considering as many fixed moments of time as possible. Taking into account the April approaching, an observer will see Venus in this section of the sky 3 times in this 8-year cycle. To make you more convinced of this, let’s add up to 8 years to each date presented here. Finally, we are getting 2066, 2068, and 2071. Taking the 8 years down from the basic moment, we will receive accordingly 2050, 2052, and 2055. As you can see, in the 8-year period Venus meets the Taurus constellation in April 2058, next in April 2060, then in April 2063, and finally again in April 2066 after 8 years, which opens somewhat the new “period”.
Translating it into the meeting with the Pleiades, we will get essentially the repeatable conjunctions as the Venus orbit “moves” northward in the sky. Previously I wrote, that this period lasts about 50 years. Now we are interested in the timespan between the 2 periods such that. Thereby we are “observing” another 2 orbits shown in the pattern above. Knowing, that all of these lines “lift up” every 8 years by a few arcminutes, it must come the moment, when the second (middle) orbit will reach the Pleiades. It was told, that the Venus cycle lasts 243 years, being enclosed with ascending and descending node transits. Knowing it, we are aware, that the time needed for the middle orbit pattern (bright blue) to supersede the top orbit pattern (dark blue) is exactly 243 years!
For sake of clarification, we can see a few patterns below, bound together in the 40-year (8×5) timespan (Pic. 14). Remember also, that this 8 years period varies around 2,46 days, which makes certain dates a bit shifted.

Pic. 14 The comparison of Venus orbits in the single 8-year period in April as it “moves” northwards throughout the Taurus constellation. Every single orbit has been marked on a different color, whereas the blue color represents the current one, applicable for our life period. Next, the orbit reaches a maximum inclination and starts to decrease moving away from the Pleiades. Next for a long time, the maximum orbit inclination indicates simultaneously the closest approach to the cluster. Sketch made by Cartes du Ciel Sky Charts 4. Click to enlarge.

Firstly, back to the point, where I showed you the last close conjunction of Venus with the Pleiades on April 6, 2060, which is marked by the blue line, we can see that this track is “replaced” with the garish blue track around April 11, 2303 (243 years and 5 days later). Secondly, watch what is happening with the blue track, represented by the Venus orbit corresponding to the circumstances occurring at the time of our life. It reaches the maximum inclination north of the Pleiades cluster in 2092 and 2100, moving away toward the west afterward, as this inclination starts to drop. Before it happens, the Venus conjunction with the Pleiades occurs twice within a period shorter than 50 days (Pic. 15).

Pic. 15 The Venus orbit pattern near the maximum inclination near the Pleiades cluster. Finally, the planet meets the Pleiades cluster twice within a max of 50 days. The date of the lowest distance between the Sun and the Pleiades has been also marked. Simplified chart according to Cartes du Ciel Sky Charts 4. Click to enlarge.

Over the next spans of 8 years, as the Venus orbit reaches the Pleiades close to its maximum inclination, the double conjunction won’t be visible, because the second approaching falls very close to the Sun. In 2068, the second meeting Venus with the Pleiades is its inferior conjunction with the Sun at once (Pic. 15).

Following the previous pattern (Pic. 14) we can see how our current Venus orbit as well as the following text, corresponding to the next Venus cycles behaves. Everything looks pretty much the same and repeats every 243 years. The pattern is rounded off by Venus’s orbit position in the 2498 year, which corresponds exactly to 2012 when the second descending node transit occurred. This timespan is roughly 486 years and closes up perfectly with our three orbits taken into account.
So far I was considering the three single orbit patterns inching northward every 8 years. We still don’t know what is happening in a much wider period of time both earlier and later. For this reason, I used the Cartes du Ciel Sky Charts 4 to simulate earlier and later dates matching the best to the situation, where Venus is the closest to the Pleiades. I do not mean the conjunction right now, but only the moment, when for this given orbit Venus appears to have the smallest angular distance to the Pleiades cluster in the Taurus constellation. This grand period of changes, where these moments make a 360-degree rotation in the sky I called the Venus great orbit cycle, which can be treated as a saros-like period, which tends to repeat after about 3159-3160 years. In the case of the current ascending-node great Venus orbit cycle is 3152 years and 3,5 weeks (Pic. 16). This timescale is big enough to see the changes in the sky caused by the Earth’s orbit precession. This time includes exactly 394 8-year cycles, where every single one is located around 22′ from the other.

This chart appearance is intentionally upside down, because of the Venus orbit circumstances. It was told, that every 8 years the Planet crosses the Pleiades cluster higher in the sky.
Following the pattern, the Venus “travels” from the last ascending-node transit pair, as occurred on November 21-22, BC 549 and November 19, BC 541 (grazing transit) through the exterior conjunction in AD 1124, which states the ratio: 1673 years to 1479 years, next reaches the Pleiades cluster in 2012, which leaving in 2060. It finishes off very similar ascending-node transits in 2603 and 2611, where the second one is grazing! The Venus path angular difference between the 2 transits mentioned is about 1,5′ (Pic. 17). The grazing transit in 2611 can be seen in total (all 4 contacts) from Antarctica, whereas its counterpart 3152 years earlier was barely noticeable from the same region and missed elsewhere on Earth.

Pic. 16 The grand venus orbit cycle for ascending-node transits, stretched between BC 549 and AD 2603. The Pleiades has been circled with a yellow oval, a yellow thin line is an ecliptic, and another thick blue line states the “local” Venus orbit circumstances to the solar position; blue dates indicate the moment of the smallest angular distance to the Pleiades cluster west of, and next east of the Sun, which the position at the same time has been marked with yellow dates. Click to enlarge.

Understanding this simple pattern, generated by the Cartes du Ciel Sky Charts 4 is a pivot thing to grasp the behavior of Venus’s orbit in its long-term period. In many sources, we can find that the ascending or descending-node transit pairs are different from each other, You can convince, see, for instance, the transit patterns for the current and past Millenium. The transit of Venus, as well as its appearance in the Pleiades or in Antares (including also its occultation “from time to time”), has a cyclical nature! It repeats on average every 3159-3160 years. For the orbit cycle, which I am describing right now it’s 3152 years and 3,5 weeks, as shown above! The current opposite –  great Venus orbit cycle for descending-node transits counts 16 years more, about which in detail in the next writing.  The 3159-year time span gives exactly 13 of the standard Venus cycles, as we know from transit phenomena. These 13 standard cycles are expressed by the individual great orbit cycles in the sky, as shown earlier (Pic. 13, 14).

Pic. 17 The second descending-node Venus transits from the pair, which marks the beginning and the end of the great Venus orbit cycle. Both of them are grazing, which means, that an observer can see the I and IV contact only. As you can see, there are about 1.5 arcminute differences between the first one shown and its counterpart nearly 3152 years later. The simulation has been done for Antarctica, which has the best conditions for these transits. The observer in 541 BC could barely notice the short grazing transit, whereas about 3152 years later it’s fully visible from this location. Click to enlarge.

I believe, that this Venus orbit cycle is not the ultimate one, which could occur. However, we should realize the precession of our orbit, which in consequence changes the Ecliptic arrangement in the sky. This fact influences directly any conjunction circumstances not only on Venus but the other planets. In this event a consideration, what is happening in a longer timespan, that aforementioned 3159-3160 years doesn’t really make sense I think.
The other part of this article is coming, where I would like to take a look at the analog circumstances for descending-node transits, where a major role in Conjunction with Venus plays Antares.

Mariusz Krukar

References:

1. Borgia M.P., 2006, Human vision and the night sky: How to improve your observing skills, Springer Sciences, New York
2. Forbes G., 1874, The Transit of Venus, Mcmillan and Co, London & New York
3. Maor E., 2004, Venus in transit, Princeton University Press

Links:

1. https://www.universalworkshop.com/2019/10/24/venus-nodes/
2. Earthsky.com: Venus & Pleiades (Alcyone star) conjunctions in the XXI century
3. https://skyandtelescope.org/astronomy-news/observing-news/transits-of-venus-explained/
4. http://astro.ukho.gov.uk/nao/transit/periodicity/index.html
5. https://johncarlosbaez.wordpress.com/2014/01/04/the-pentagram-of-venus/
6. Synodic period
7. Synodic period of Venus
8. Venus elongation calculator
9. Venus fact sheet
10. VT 2603
11. VT 2611
12. Transit of Venus – motion

Wiki:

1. Alcyone_(star)
2. Antares
3. Ecliptic
4. Elongation_(astronomy)
5. Merope_(star)
6. Orbit_of_Venus
7. Orbital_mechanics
8. Orbital_period
9. Pleiades
10. Transit_of_Venus
11. Venus – Orbit_and_rotation

Read also:

1. Transit of Venus – have you seen this celestial event?