819 and the Mayan Calendar

I came across this article about a 819 day cycle used by the Mayan Calendar and I was prompted to delve into the matter further. I asked Gemini:

Is this article factual or fictional: https://www.ecoticias.com/en/two-researchers-had-been-stuck-on-a-mayan-number-for-years-they-changed-a-single-rule-and-a-pattern-appeared-that-was-impossible-to-ignore/26402

The article is factual.

It reports on a legitimate scientific breakthrough published in the peer-reviewed journal Ancient Mesoamerica by anthropologists John Linden and Victoria Bricker from Tulane University.

Here are the specific facts behind the story:

• The Mystery: For decades, researchers understood the Mayan 819-day calendar count but could not make it align perfectly with the movements of all visible planets. While it matched Mercury's cycle, it fell out of sync with Mars, Venus, Jupiter, and Saturn.

• The "Rule" Change: The researchers discovered that if they expanded the timeline from a single cycle (819 days) to 20 cycles (roughly 45 years), the math aligned perfectly.

• The Result: Over this 45-year period, every visible planet’s synodic period (the time it takes to return to the same spot in the sky) fits into the grid as a whole number. This proved the Maya created a much larger astronomical system than previously thought.

While the headline uses dramatic language ("stuck on a Mayan number," "impossible to ignore"), the underlying discovery is authentic and widely accepted in the archaeological community.

Can you provide the details of the synodic periods for the various planets and how they fit into this 819 * 20 cycle.

In the model proposed by Linden and Bricker, the Mayan 819-day count is not a standalone cycle but a component of a larger system spanning 20 cycles, which totals 16,380 days (approximately 45 years).

Within this 16,380-day window, every visible planet aligns with a multiple of 819 days at specific "stations." To achieve this, the researchers demonstrated that the Maya used specific integer values for the synodic periods (the time it takes for a planet to return to the same visual position relative to the Sun).

Here is the detailed mathematical breakdown of how each planet fits into this system:

1. Mercury (Syncs every 1 Cycle)

Mercury is the fastest planet and the anchor for the single 819-day count.

• Synodic Period: 117 days

• The Maths: :  $117 \text{ days} \times 7 = 819 \text{ days}$

• The Fit: Mercury synchronizes perfectly with the calendar every single cycle.

2. Venus (Syncs every 5 Cycles)

Standard Mayan astronomy often used 584 days for Venus, but for the 819-day count to work, the period aligns at 585 days.

• Synodic Period: 585 days

• The Maths: $585 \text{ days} \times 7 = 4,095 \text{ days}$

• The Fit: $4,095$ days is exactly 5 cycles of 819 ($819 \times 5 = 4,095$). This means Venus realigns with the system every 5 cycles.

3. Saturn (Syncs every 6 Cycles)

Saturn requires a longer duration to align with the 819-day count.

• Synodic Period: 378 days

• The Maths: $378 \text{ days} \times 13 = 4,914 \text{ days}$

• The Fit: $4,914$ days is exactly 6 cycles of 819 ($819 \times 6 = 4,914$). Saturn realigns with the system every 6 cycles.

4. Jupiter (Syncs every 19 Cycles)

Jupiter has one of the longest intervals before it matches the count.

• Synodic Period: 399 days

• The Maths: $399 \text{ days} \times 39 = 15,561 \text{ days}$

• The Fit: $15,561$ days is exactly 19 cycles of 819 $(819 \times 19 = 15,561)$. Jupiter realigns with the system every 19 cycles.

5. Mars (Syncs every 20 Cycles)

Mars is the defining planet for the total length of the Grand Cycle. It takes the full duration to align.

• Synodic Period: 780 days

• The Maths: $780 \text{ days} \times 21 = 16,380 \text{ days}$

• The Fit: : $16,380$ days is exactly 20 cycles of 819 $(819 \times 20 =16380)$

Summary of the Grand Cycle

By extending the calendar to 20 cycles (16,380 days), the Maya created a "least common multiple" system where:

• Mercury fits 140 times.

• Venus fits 28 times (realigning every 5 cycles).

• Mars fits 21 times (realigning at the end).

• Jupiter and Saturn have their own station points at cycles 19 and 6, respectively.

 This 20-cycle span also perfectly links to the sacred Tzolk'in calendar (260 days), as $16,380$ is exactly 63 Tzolk'in cycles. 

Explain the synodic period of a planet in the Solar System.

The synodic period is the time it takes for a planet to return to the same alignment with the Sun and Earth. It is essentially the "lap time" for a planet relative to Earth, rather than the stars.

Because Earth is constantly moving around the Sun, a planet has to travel a little more (or less) than one full orbit to "catch up" to Earth and line up again. This creates a difference between how long a planet takes to circle the Sun (Sidereal Period) and how long it takes to appear in the same phase in our sky (Synodic Period).

The "Track Runners" Analogy

Imagine a race track with the Sun in the center.

• Earth is a runner in the middle lane.

• Mars is a slower runner in the outer lane.

If they start the race lined up perfectly (at the starting line), Earth will quickly pull ahead.

• Sidereal Period: The time it takes Mars to finish one full lap.

• Synodic Period: The time it takes for Earth to run all the way around and "lap" Mars, so they are lined up again.

Inferior vs. Superior Planets

The cycle works slightly differently depending on whether the planet is closer to or further from the Sun than Earth.

1. Inferior Planets (Mercury, Venus)

These planets orbit inside Earth's path. They move faster than us.

• The Cycle: They race ahead of Earth, reach maximum distance to the left (morning star), cross behind the Sun, reach maximum distance to the right (evening star), and then pass between Earth and the Sun.

• Key Alignment: The synodic period is the time from one Inferior Conjunction (passing between us and the Sun) to the next.

2. Superior Planets (Mars, Jupiter, Saturn, etc.)

These planets orbit outside Earth's path. They move slower than us.

• The Cycle: Earth acts as the faster runner. We catch up to them, pass them (at which point they appear opposite the Sun in the sky), and leave them behind until we lap them again.

• Key Alignment: The synodic period is the time from one Opposition (when Earth is directly between the Sun and the planet) to the next.

Comparison of Periods

Notice how the Synodic period can be drastically different from the actual orbit time.

Why This Matters

The synodic period dictates observation windows.

• If you want to send a spacecraft to Mars, you cannot just launch anytime; you must wait for the synodic alignment (roughly every 26 months) when the distance is shortest.

• If you are observing Jupiter, the "best time" (Opposition) happens every 399 days.

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Relating this to real Astrology is a topic that I'll cover in my Astrology blog.