If you’re careful enough, you can learn more about the Solar System than you ever imagined.
This year, on March 20th, the full Moon will illuminate the night sky. With the Moon reaching perigee, or the point in its orbit where it comes closest to Earth, just the day before, we’ll have a supermoon: where the Moon appears substantially larger and brighter than average. Although supermoons happen a few times per year, the one occurring on March 20th is special.
That’s because it’s also the spring equinox, where the Earth’s axis is tilted perfectly perpendicular to the imaginary line connecting the Sun and Earth. While we get a spring equinox every year, the coincidence of a full Moon with the spring equinox is much rarer, as it happens only once every 19 years. This is a pretty special occurrence, and it gives us the opportunity to learn some things about our world that we rarely get to explore.
Although equinox literally means “equal night,” it isn’t exactly true that there are 12 hours of day and 12 hours of night everywhere on Earth during the equinox. Nor is the equinox defined by a specific calendar day; rather, it’s a specific moment in time that corresponds to planet Earth passing through a special point on its orbit.
If you were to draw an imaginary line through the Earth, from North Pole to South Pole, you’d find the line that represented Earth’s rotational axis. If you drew a second imaginary line, connecting the center of the Earth to the center of the Sun, you’d see that these two lines made an angle with one another. During the solstices, the Earth’s axis tilts maximally towards or away from the Sun. But during the moment of equinox, you make a right (90°) angle, which means that something very special occurs.
At the moment of equinox, all of the Sun’s rays falling on Earth are perpendicular to that imaginary line. This means that the following things are true at the two equinoxes, and not on any other day of the year:
- Exactly 50% of the Sun is visible from the North and South poles. (If the Sun were a point, instead of a disk, it would be barely visible from both locations.)
- From where the midpoint of the Sun rises over the horizon to where the midpoint of the Sun falls below the horizon takes 12 hours from everywhere on Earth’s surface.
- And if you measure the shadow cast by a perfectly vertical stick when the Sun is at its zenith (highest point in the sky), the angle you measure will reveal your precise latitude.
But it’s very rare indeed to get a full Moon that coincides with the equinox, because of a fact known for thousands of years: the lunar calendar (where you keep track of time based on the new-to-full-and-back-to-new Moon cycles) and the solar calendar (where you keep time based on the Earth’s orbit around the Sun) line up after 235 lunar months, or 19 calendar years.
This month, March of 2019, sees the full Moon and the equinox line up. It will happen again in 2038; it almost happened (it missed by a few hours) in 2000, and it happened before that in 1981. Every 19 years, we have this alignment. Similarly, the September equinox full Moons occurred in 1991, 2010, and will return in 2029.
You may remember that two months ago, in January, we received a total lunar eclipse: where the Sun, Earth, and full Moon were perfectly aligned. Now that it’s two months later, the full Moon is misaligned, because the plane that the Moon orbits the Earth in is tilted with respect to the Sun.
This is incredible for science! On any old equinox, you can measure your latitude on Earth; on any solstice, you can measure the axial tilt of the Earth. Well, on an equinox that coincides with a full Moon, you can measure how far out of the Sun-Earth plane the Moon actually is at this particular moment in time. And if you know when the last eclipse was and the next eclipse will be, you can actually determine the tilt of the Moon’s orbit. Here’s how.
The Moon orbits the Earth in an ellipse, and that ellipse is tilted with respect to the Earth-Sun orbital plane. That ellipse remains in a constant shape, however, as the Earth orbits the Sun. There are two points where the Earth-Moon plane crosses the Earth-Sun plane, known as the line of nodes. Every six months, the nodes approximately line up with the imaginary line connecting the Earth to the Sun, which enables eclipses to occur: solar eclipses if the near node is aligned, lunar eclipses if the far node is aligned.
Three months (or, more precisely, 88 days) from perfect alignment, we’ll achieve maximum misalignment. Three months after a total solar eclipse, the new Moon will be misaligned from the Earth-Sun plane by the maximal amount; three months after a total lunar eclipse, the full Moon will be misaligned from the Earth-Sun plane by the maximal amount.
The equinox is special, because if you measure the smallest shadow cast by a vertical stick during the day, you can measure a particular angle to the shadow, which tells you your latitude.
If you then performed that same exact experiment at night, by moonlight, you’d get a different particular angle that’s extremely important. If you took that measurement you got for your angle by moonlight, and subtracted your latitude (or your daytime-measured angle), you’d get your measured angular misalignment for the Moon, at present, relative to the Earth-Sun plane.
All that’s left to do, in order to know the tilt of the Moon’s orbit, is a little math.
Because it takes approximately 88 days to go from maximum alignment of the Moon’s orbit to maximum misalignment, then knowing that there was a total lunar eclipse on the evening of January 20th/morning of January 21st and that the equinox is on the evening of March 20th (or the morning of March 21st) allows you to do that key calculation.
There are 59 days between January 21st and March 21st, but it takes 88 days to go from maximum alignment to maximum misalignment. So take that measured angular misalignment, divide it by the sin((59/88)*90°) that occurred from the prior lunar eclipse until today’s full Moon, and that’s the tilt of the Moon’s orbit!
This is a case where we actually know what the answer is, and so with just a little math-in-reverse, we can predict what we ought to observe on the night of March 20th/21st. Since the Moon’s known orbital tilt with respect to the Earth-Sun plane is 5.14°, we can multiply it by the math factor we just devised: sin((59/88)*90°), which comes out to about 5.1°*0.87, or about 4.4°.
No matter where you are on Earth, so long as you can see the Sun and the Moon clearly when they’re at their highest points in the sky and there are no nearby lights ruining your shadows, you can perform this measurement for yourself. Sure, it’s rare that we get a full Moon during the equinox (about once per decade), and even rarer (about a 1-in-4 shot) that the full Moon is a supermoon, but the science you can do is the real star of the show. After all, how often do you get to figure out the Solar System for yourself?
Ethan Siegel is the author of Beyond the Galaxy and Treknology. You can pre-order his third book, currently in development: the Encyclopaedia Cosmologica.