Why so few eclipses?

The moon makes a full circuit around the Earth every month. In theory, this should include one point at which it’s directly between the sun and the Earth, shouldn’t it? Even if the orbit of the moon is not on the exact same plane as the orbit of the Earth around the sun, they should intersect once a month, shouldn’t they?

So why don’t we have a solar eclipse evey month? Or at least a heck of a lot more often than we do?

Chaim Mattis Keller

“Sherlock Holmes once said that once you have eliminated the
impossible, whatever remains, however improbable, must be
the answer. I, however, do not like to eliminate the impossible.
The impossible often has a kind of integrity to it that the merely improbable lacks.”
– Douglas Adams’s Dirk Gently, Holistic Detective

In short, because the Moon’s orit is inclined to the Earth, they only intersect twice during the Moon’s orbit of the Earth (technically, the Moon doesn’t orbit the Earth, but that’s another story). For a solar eclipse to happen, the moon has to be crossing the Earth’s orbit precisely durring the time of the new Moon.

Jim Petty
An oak tree is just a nut that stood it’s ground

Well, the moon’s orbit is not in the exact same plane as the Earth’s.
Picture this way: we draw a line between the Earth (simplifying by leaving out the fact that the Earth is a body of perceptible size, and that its rotating) and the Sun (simplifying by ditto). We draw the Moon’s orbit (yes, I know that the Moon cannot be said to orbit the Earth in the same way that the Earth orbits the Sun, or that Io orbits Jupiter. Go away). If the drawing is in a flat plane, the orbit always intersects that line.
But, this is all happening in a 3-dimensional space. That orbit, in 3-space, can actually intercept the line, or be above or below it. If the synodic period of the Moon (interval between moonrise and moonrise as seen from a constant point on the Earth) were an exact divisor of the orbital period, the Moon would always be in the same point in its orbit, it would always (or never) be in the same plane as the Sun-Earth line, and we would have a solar eclipse at every (or no) new moon.
Often, there are “partial” eclipses, where a portion of Sun’s disk, but not all of it, is obscured, for just this reason.
Since the Moon’s orbit is not circular, but elliptical, its apparent diameter varies somewhat. Ordinarily, we don’t even notice – but if an eclipse occurs when the Moon is near apogee, and its apparent size is distinctly smaller than the Sun’s, we get an “annular” eclipse, where a thin ring of light is visible around the obscured disk.
The orbital mechanics are such that a fair number of solar eclipses do occur – between two and five each yearr, IIRC. But a lot of them are partial (not impressive) or annular (not much more impressive). Or else, they occur out in the middle of the Pacific, where no one but a few albatrosses and maybe a passing ship can see them.
You-didn’t-ask-but-I’m-telling-you-anyway: the same thing applies to Neptune and Pluto. On a flat page, their orbits appear to intersect. Actually, Pluto’s orbit is inclined at (I think) 17° to the ecliptic (and thereby to Neptune’s orbit, to a good first approximation); the two don’t come anywhere near each other.

“Kings die, and leave their crowns to their sons. Shmuel HaKatan took all the treasures in the world, and went away.”

Not only that, but because of the relative distance between the earth and the moon, even when the two orbits intersect, the “match” between the apparent sizes of the two bodies isn’t always sufficient to produce a true total eclipse. In those instances, we get what is called an “annular” eclipse, in which the surface of the sun is visible as a ring around the moon.

Oh, I understand why there would be few total eclipses. But it seems to me that even partial eclipses are rare, and in the geometric part of my mind I can’t see why we’d have a month with not even a partial eclipse unless the moon’s orbit was around the Earth via the poles, perpendicular to the Earth’s orbit around the sun.

Chaim Mattis Keller

The moon is about 2200 miles in diameter, and 240,000 miles from the earth. Now, draw

Remember that line from the earth to the sun that Akatsukami was talking about? Imagine this: You’ve got this ball spinning cirles around you. It’s 240,000 miles away, and only 2200 miles in diameter. Once a month it will be near that line, but it could easily go above it or below it. For a partial eclipse, any part of the ball has to hit the line, and for a total eclipse, the line has to pretty much go thru the middle of the ball. Remember, this ball is 240000 miles away, and if the middle of the ball misses the line by even 2201 miles, no eclipse happens at all.

      • Not to upset you, cmkeller, but partial solar eclipses aren’t all that rare. They happen much more often than total solar eclipses, but it’s the totals that get the publicity. Much of the time the viewing area is limited in accessibility, such as remote ocean areas or rugged mountains, or in countries inhospitable to US tourist dollars. Sky and Telescope or Astronomy magazine always has articles on upcoming events, and there are home computer programs available can predict them very accurately for decades into the future (except for the local weather, of course). - I have never seen a total solar eclipse. I want to see one once, but probably wouldn’t bother twice. The total lunar eclipse I saw was kinda neat, but hardly exciting. - MC

{{{technically, the Moon doesn’t orbit the Earth, but that’s another story}}}—Jimpy

Yup, Asimov did a good job on the numbers for the lay-person. (Of Time and Space and Other Things–Isaac Asimov)

The “Moon” is actually a co-planet rather than a satellite of the earth…still makes for romantically lit nights though.

(The Original EnigmaOne)
Common ¢ for all ages.

The reason, cmkeller, that partial solar eclipses are rarer than you’d think is that the Moon’s orbit isn’t just off the ecliptic by a little - it’s off by a lot. 5°, if I remember correctly. Now, that may seem insignificant, but the angular diameter of the Moon itself, as seen from Earth, is only ½°, making the entire region of the sky which could be inhabited by the Moon a band twenty Moon-diameters wide. And so, when the Moon crosses the Sun, there’s a good chance that it won’t be right in the middle of this band. I hope this makes sense.

This isnt bery related to the topic but i must share, In 2017, there will be a total eclipse that will cross the U.S. It will make landfall around San Francisco. Lucky me, San Francisco isnt too far from here (just 100 miles), and i believe the width of the shadow in Europe where it was fully eclipsed was 70 miles wide :).

For what it’s worth, total eclipses are relatively common, about one every 18 months (about half of those are annular eclipses). That’s about a 5.5% chance of a total eclipse occurring during any new moon, just under 3% if you discount annular eclipses.

The reason they seem rare is that the moon’s umbra covers only a small portion of the Earth’s surface during an eclipse, so even when they occur only a few people see them…