Today's post will explain the difference between the Moon's synodic month and sidereal month. The synodic ("with the Sun") month, as already discussed, is the cycle of lunar phases (a lunation) which lasts approximately 29.53 days.
Just for kicks, I decided to look at all the New Moons from January 1, 2000 to January 1, 2025 - a 25 year span of time. I can do this easily because I have a program called Mica (Multiyear Interactive Computer Almanac) from the U.S. Naval Observatory. In that span of time, there are 310 New Moons. That gives, on average, 12.4 lunations each year (which is why traditional lunar calendars, like those used by almost all ancient cultures, always had to be fudged - there aren't an even number of lunar phases in a year).
If I look at the length in time between each adjacent New Moon, I get an average interval of 29.531314 days with a maximum lunation of 29.8242 days from December 18, 2017 to January 17, 2018 and a minimum lunation of 29.2822 days from May 25 to June 24, 2017. That's a difference of 0.542 days (around 13 hours).
It's interesting that 2017 comes up for both the maximum and minimum lunations (it's also the year of a solar eclipse visible in the U.S.). Maybe we'll see why when looking at the elliptical orbit of the Moon in a future post (I don't really know why as I write this right now).
Given that a cycle of phases lasts 29.53 days, you might think that's how long it takes the Moon to orbit the Earth, especially given the figure below we've discussed in previous posts.
Turns out that when you look up the period of the Moon's orbit around the Earth, you get a completely different number - 27.321661 days (27 days, 7 hours, 43 minutes, and 11.5 seconds). A two day difference! What's up with that?
Keep in mind that the synodic month (one lunation) is the time it takes from New Moon to New Moon - the time when the Moon is exactly lined up between the Earth and the Sun as seen above. But the image above is static. Both the Earth and the Moon are orbiting the Sun and that's where the difference comes in. Let's look at the image below:
Here we'll look at the length of time from Full Moon to Full Moon (same as New Moon to New Moon). We need some way to mark the Moon's revolution around the Earth. The easiest way to do this is to mark the Moon's position in the sky with respect to some distant star (they're all distant!). The image above uses Regulus in the constellation of Leo as an example. Why a distant star? Because they're so far away from the Earth that they don't shift visibly in the sky no matter where the Earth and Moon are in their orbits.
Let's suppose, from the perspective of us on Earth, that the perfectly full Moon lines up with Regulus. What we'll see is that in 27.32 days, the Moon will once again line up with Regulus so we know it's made one complete revolution around the Earth. This is called a sidereal month, from the Latin word sidus which means "star".
But, after this one revolution with respect to the distant stars, it's not a Full Moon yet! Why? Because the Earth-Moon system has also been moving almost 1/12 of the way around the Sun and the geometry has changed. The Moon has to travel just a little bit more in its orbit (almost 2 days) to reach the position where it's directly opposite the Sun.
Here's a nice animation.
That's why the synodic ("with the Sun") month is 29.53 days long and the sidereal ("with the stars") month is 27.32 days long. Think that's bad, there are other types of "months" we'll talk about shortly as well.
Some ancient cultures actually marked time with sidereal months instead of synodic months. Look at the image below. It shows the Full Moon after midnight on July 15 from Ulster County, NY. The Moon is in the constellation of Sagittarius.
Twenty seven days later, about one sidereal month, on August 10, the Moon will also be in Sagitarrius. But the Moon's not full yet.
The Full Moon occurs one synodic month after July 15 on August 13. But now the Moon is in the constellation of Capricornus.
What some cultures did was watch the Moon move through the zodiacal constellations and then use this to keep track of calendar time. More on this tomorrow...