Should this be under Astronomy or under Lego? The page was prompted by a question from one of our daughters. To illustrate the “problems” I built an orrery from Lego, but the subject is astronomy of course, not Lego.
The purpose of the orrery was to show the paths of the Earth and the Moon around the Sun, in an attempt to explain eclipses.
Sometimes the Sun is obscured by the Moon passing in front of it, a phenomenon known as an eclipse. Eclipses of the Sun are short (less than 7 minutes), occur rarely, and when they do they are visible only on a small part of the planet.
To understand eclipses we need to understand the motions of the Earth and Moon relative to the Sun.
If all were Perfect
The ancient Greeks thought all heavenly phenomena were perfect: the bodies were perfect spheres, they moved in perfect circles. It was a good approximation and a laudable attempt at a geometric model of the solar system.
If all were perfect, then we would have a situation like in the image below:
The Sun, Earth and Moon would be a perfect spheres, the orbits of the Earth and the Moon would be perfect circles, all axes would be perpendicular to the plane of the Earth’s orbit, and the Moon’s orbit would also be in the plane of the Earth’s orbit.
The plane of the Earth’s orbit is called the ecliptic.
In addition, all rotation would be in the same sense (green arrows; as seen from the North). In reality, all planets and moons do indeed turn in the same sense, with a few very rare exceptions such as the moons of Mars.
The Moon turns around the Earth once a month.
If the Moon and the Earth both moved in the ecliptic, as in the “perfect” case, there would be a solar eclipse and a lunar eclipse each month: the Moon would pass exactly between the Earth and the Sun and it would also pass directly behind the Earth over the course of each turn around the Earth. Twice a month the Moon would be exactly on the red line that goes from the centre of the Sun through the centre of the Earth:
There would be an eclipse of the Sun at each New Moon (position N) and a lunar eclipse at each Full Moon (position F): at N the shadow of the Moon would touch some point on the Earth’s equator and at position F the Moon would entirely be in the shadow of the Earth.
Because the shadow of the Moon on the Earth is very small, solar eclipses would only be visible at the equator and nowhere else.
Not so Perfect
Reality is somewhat different.
First, the axes around which the Sun, Earth and Moon turn are not perpendicular to the ecliptic (the plane of the Earth’s orbit). The axis of the Earth is tilted by somewhat more than 23º (which is why most commercially sold Earth globes have a tilted axis). That already makes eclipses occur also at other places than the equator.
But the plane of the Moon’s orbit around the Earth is at an angle to the ecliptic. It cuts the ecliptic along a line AB. This line is called the nodeline.
Points A and B are on the ecliptic, but they are not necessarily on the Earth-Sun line.
Part of the time the Moon is above the ecliptic (lighter shaded half of the Moon orbit disc) and part of the time it is below the ecliptic (darker shaded half disc). Thus on most months there are neither solar nor lunar eclipses.
As the Earth runs around the Sun, the disc of the Moon’s orbit follows it, but it stays roughly parallel to itself. Because of perturbations the Moon’s orbit does not stay exactly parallel to itself, it turns slowy too, but it needs more than 18 years to complete one revolution. For our purposes here we can say the Moon’s orbit stays parallel to itself.
Because the plane of the orbit of the Moon stays parallel to itself as the year progresses, the nodeline AB also stays parallel to itself during the year.
There are then only two times in the year when that line goes through the Sun, and the Moon can be directly between the Earth and the Sun (the rightmost situation in the image below). At other times the Moon is either below or above the ecliptic when it is on the Sun’s side, similarly when it is on the far side of the Earth.
Even at the two moments of the year where the nodeline is oriented through the Sun, it is unlikely that the Moon is at that exact time also at the right position to cause a solar or lunar eclipse.
Of course there may be an eclipse visible even when things are not precisely lined up because the Earth, Moon and Sun are not points, they are fairly large objects: we can have partial eclipses, or very short total ones.
In addition, when there is a solar eclipse it does mean there is a fairly accurate line-up of the orbit of the Moon, and because the Earth is much larger than the Moon, it is then likely that there is still sufficient line-up either half a month later or half a month earlier for the Earth to eclipse the Moon at least partially.
This explains why lunar and solar eclipses often occur at about two weeks from each other.
A lunar eclipse can be seen by everyone who is on the night side of the Earth, but a solar eclipse can only be seen by people living right under the shadow of the Moon when it passes over the Earth.
The Lego orrery shows these effects by presenting a lunar orbit that is inclined to the ecliptic.
To my knowledge it is the only Lego orrery with this property.