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Moon's Many Motions
How have people been predicting eclipses for so many centuries? To envision some of the moon's many motions in a paper plate activity, you can pair a Moon Finder plate with a new Regression of the Nodes plate to demonstrate the Saros cycle.
The Motions
The moon has many concurrent motions to consider when you are discerning when and where an eclipse will occur, including these:
The moon orbits earth as they collectively orbit the sun. Their respective angles determine monthly phases, yet recurring new and full moons do not yield monthly eclipses. The moon's orbit is inclined, so often the moon and earth are a little above or a little below each other's shadow. The plane of that 5 degree angle wobbles around like a fun spinning hula hoop flopping on the ground, though with the ominous name Regression of the Nodes. When the lunar orbit's plane comes back to its starting point (like the settling hula hoop doing one spin) after 18 years, 11 days, and 8 hours, you get nearly identical circumstances for another Saros cycle of eclipses. The previous 18+ year pattern of eclipses repeats. However, because of those eight hours, the earth has rotated eight hours past the original eclipse starting point, so some other longitudes of the globe enjoy it.
Phew! That's complicated. So let's make a paper plate model.
The Plates
A background plate with two slits holds earth and the moon on a stick, with a string linking earth to the sun. The plate will show how the moon's orbit is inclined, with eclipses happening at lunar nodes. But first, on top of the background plate you'll slide a simple Moon Phases plate to illustrate Orbit Around Earth
The background plate has a blue M&M candy taped to a stick at the center, with a brown M&M on the stick at the edge of the plate. Therefore, the plate represents the orbit of the moon around earth. Two slits nearly bisect the plate, leaving just enough remaining plate for a piece of tape on the backside to hold it together and to secure the string underneath that drops through a hole at the center of the plate. The string stretches outward toward the sun, which anchors the other end of the string.
Actually, the slit representing the line of nodes is a small wedge (and should be larger), for it depicts the range in which partial eclipses can occur as well. Only when the moon aligns with the slit can an eclipse occur.
I recommend Guy Ottewell's illustration (Astronomical Calendar 2024, page 90). I print and cut out the diagram and mark upcoming new moons in yellow highlighter (see banner image). Placing his image on my plate, I align the nodes correctly and label the monthly new moon positions on the plate. In early 2024 they occur on Jan. 11, Feb. 9, March 10, and, of course, April 8 (aligning with the upper slit).
For the moon phase plate, I label the positions of the four key phases and cut a slit halfway across the plate.
I slide it over the background plate, past the string in the center of the plate. My starting position is the approximate location of the new moon on January 11, 2024.
Now put it all in motion.
Orbit Around Earth
Earth at the center of the plate is viewed from above. The M&M candy at the end of the stick is the moon orbiting around M&M earth. The sun is to the right, along the string, about 193 paper plate diameters away if to scale.
Phases shown are new, first quarter, full, and last (or third) quarter. A sidereal month later it seems to be new again, with the earth-moon-sun the same as when you started.
However...
Orbit Around Sun
While the moon orbited the earth once, the earth revolved somewhat around the sun. After the moon revolved 360 degrees, the earth-moon-sun are not yet aligned.
The moon has to advance a bit further. Each successive synodic month (29.5 days) the new moon appears to move left against the background stars until it again aligns nearly with the sun.
Three months of movement show the direction toward the sun for the 2024 January, February, and March new moon positions. Then, with the April new moon, the earth-moon-sun are aligned along the axis of the slits, dubbed the lunar nodes.
It continues, shown through August.
However...
Moon's Inclined Orbit
Not so fast. We've shown the moon going around the plate that is in the same plane as the sun, as if they are are all sitting on a table.
In reality, the moon's orbit is inclined five degrees to the earth's orbit around the sun. In the opening three months of 2024, the moon is a few degrees below the string (line of sight to the sun). Spend some time studying Guy Ottewell's excellent depiction.
At the April new moon, at the slit (the node), the string is in line with the earth-moon-sun. Solar eclipse! As the earth continues around the sun past April, the string is now under the plate, under the hula hoop lunar orbit.
Six months later, on October 2 with the moon at the opposite node, the string again aligns with the earth-moon-sun. Another solar eclipse, this time an annular eclipse!
Observation: Eclipses occur in seasons, six months apart, and lunar and solar eclipses happen within half a month from each other. In 2024 the eclipse season is in April and October.
However...
Regression of Lunar Nodes
The moon's orbit is in a plane that wobbles, like a hula hoop winding down onto the ground. The slit "regresses" about 20 degrees per year (360 divided by 18), going clockwise around the sun.
After 18+ years, all the key factors--the orbit around the earth; the orbit around the sun; the inclined orbit, and regression of the nodes--come together. In the next 18-year Saros Cycle, the circumstances repeat anew.
However...
Saros Cycle Shifts
If the Saros Cycle were an even number of days, similar eclipse circumstances would happen at the same location after that number of days. However, the earth rotates another eight hours, so the eclipse touches down eight hours further west.
For example notice the similarities of the 2021 Dec. 4 and 2034 Dec. 15, shown in blue over Antarctica.
Video
For an excellent video that pulls this all together, see the Exploratorium's video How to Predict Eclipse at https://www.exploratorium.edu/eclipse/learn, with one large caveat.
While the text seems correct throughout, the illustrations in the opening sequence incorrectly show the moon moving right, or west, each successive day. In fact, the real moon appears to move left, or east, each day. At no time does the narrator say left, right, east, or west, so the narration is correct despite the visual incongruence.
Again, the rest of the video is excellent at demonstrating the Saros cycle.
Predicting Eclipses
Knowing earth's relationship with the sun and the moon, many cultures have been absorbing eclipses for thousands of years. With patterns like the Saros cycle, they have been able to anticipate alignments of the earth-moon-sun.
Around those eclipse experiences they have also grown their respective traditions. The Astronomical Society shares Ways of Knowing, Solar Eclipses Around the World, which shows there are multiple ways different cultures understand eclipses and the universe.
When predicting eclipses there are factors in the moon's orbit to consider in addition to what's conveyed on the paper plates. For starters, see both Fred Espenak's Periodicity of Solar Eclipses and his explanation of lunar months and eclipse cycles.
See more sun-related paper plate activities. For comments or corrections, contact Chuck.