Treebeard's Homepage : Stumpers

Treebeard's Stumper Answer
14 January 2000

Total Eclipse

I'm worried about the lack of rain here in central California this winter, but I suppose there's always a plus side. The clear winter nights have been great for star watching, and we'll get a special treat next week if they continue clear. There will be a total eclipse of the Moon next Thursday night! The action starts at 7:00 p.m. PST, with the full Moon in the deepest part of the Earth's shadow from 8:05 to 9:22. The Moon orbits the Earth about every 29.5 days. So why don't we have eclipses every month? And why do total eclipses of the Sun seem even less common?


Diagram (slightly modified) courtesy of Fred Espenak, NASA/GSFC.

For more info on the January 20 eclipse, check out Fred Espenak's Eclipse Home Page and Sky & Telescope magazine. Clear skies didn't happen for us in central California. We were totally socked in by clouds and had to cancel our special Eclipse Night Hike Club. An eclipse party is one school event we can't postpone for a week or two! Unfortunately, we didn't get much rain either. I'm worried about summer.


If the moon moved around the earth in the same flat plane that the earth moves around the sun, we would have eclipses every month. But the moon's orbit is tilted from the earth's by about five degrees, enough that the moon is usually above or below the line between earth and sun. Eclipses are rare because they can only happen when the moon is near one of the two slowly moving nodes where these orbits intersect. Solar eclipses are actually more common than lunar eclipses, but they're only visible along a narrow path. I've yet to see a total solar eclipse.

Notes:

The best place to view this eclipse was in an airplane above the clouds! We'll get another chance for a lunar eclipse in about 6 months on July 16, but it happens just before sunrise, and we won't see the whole eclipse here in California.

We have the wrong idea of the solar system because of apple and grape models. I have an antique Trippensee Planetarium Company model at school that I use often (mine isn't quite this old):

The model does show the tilt of the earth and the different tilt of the moon's orbit, but it doesn't matter, there would still be eclipses every month. These models are useful, but they don't even try to get the scale right, and we get the wrong idea. Here's a real scale model of the earth and moon with one pixel = 400 miles:

Of course, the sun doesn't belong in this picture. My monitor is a 17 inch NEC with a a screen size of about 12.5 x 9.5 inches to show 1024 x 768 pixels, about 80 pixels per inch. To show the whole sun at the same pixel size, I would need another 51 inch monitor running at 3200 X 2400 pixels located about 250 feet away. I want to play games on that screen! This picture shows how easy it is for the moon to be above or below the earth's shadow. The angular size of the moon (from earth) is about 1/2 degree, but the moon can be 10 times that above or below the earth's shadow. The solar system is a mostly empty place, and eclipses are something special,

I used my planetarium at school to pose the stumper: What would the eclipse look like from the moon? We figured that a lunar eclipse on earth would be an eclipse of the sun on the moon. But the earth would appear much larger than the sun (about 2 degrees vs. 1/2 degree), so it would block the sun completely with no corona. Graybear adds this thought:

It would be interesting to be on the moon's surface during the event, which I guess would be called a solar eclipse, there. The only light from the sun reaching the moon would be refracted and filtered through the earth's atmosphere and probably appears as a halo of reddish orange light around the silhouette of the earth.
An eclipse of the sun on the earth would look very different from the moon. We'd see the relatively small moon's shadow move quickly across the earth. NASA has a great movie clip that shows this as photographed by the GOES-10 satelite.

The story is told that Christopher Columbus was stranded in Jamaica on his fourth voyage in 1504. The natives were friendly at first, but the crew's rude behavior made the situation perilous. Columbus was a navigator who knew the stars and had a nautical almanac that held the accumulated wisdom of star-watchers over millenia. He consulted his almanac and invited the natives to a meeting on the night of 29 February 1504 (a leap day!), and foretold that the Almighty would remove the moon unless the natives obliged. The full lunar eclipse happened on cue, and Columbus got what he wanted. Arthur C. Clarke says "Any sufficiently advanced technology is indistinguisable from magic." Science and religion both give power.

Mark Twain uses a similar story in A Connecticut Yankee in King Arthur's Court, but maybe the Columbus story is real. (That eclipse is not listed on Fred Espenak's Eclipse Home Page, but he lists a full moon on March 1 at 00:34 UT, which would still be February 29 in Jamaica. It's possible!) The year 1504 is many years before Copernicus and Galileo, but I believe the mariner Columbus knew the patterns if not the reasons. Here's my best shot at figuring out how he could have predicted an eclipse that long ago.

Eclipses are completly predictable in principle, but the details are messy. Here's a different model (modified from Peter Duffett-Smith, Practical Astronomy with Your Calculator). I can't resist trying to understand this.

Eearth
S'sun
m'moon
iinclination of moon's orbit
N1'ascending node
N2'descending node
P'perigee
Yvernal equinox
Llongitude of sun
wlongitude of perigee (+U)
vmoon's true anomaly
U longitude of ascending node

This geocentric picture shows how things look from the earth (E) at the center. (That's a convenient fiction. Imagine you are looking down at the solar system from a long ways away, and that you are moving in such a way as to keep the earth stationary.) Both the moon (m') and the sun (S') move counter-clockwise in elliptical paths around the earth in a month and a year. The moon's orbit is inclined to the sun's by angle i. N1' and N2' are the ascending and descending nodes where the orbits intersect. P' is the moon's perigee, when it is closest to the earth. The point of perigee also moves around the orbit counter-clockwise, making one full revolution in 8.85 years. The line between the nodes N1'-N2' also moves around the earth, but it moves in a clockwise retrograde motion, making one full revolution in 18.61 years.

I have a hard enough time remembering how many days each calendar month has. These different motions of the moon make it worse because there are several different months and years that clock different aspects of the earth and moon's orbit. (Days are confusing too; these times are all 24 hour mean solar days.)

    Synodic month 29.5306 days The time from one full moon to the next.

    Draconian month
Nodical month
27.2122 days The time for the moon to move from one ascending node (N1') to the next. This is less than a synodic month because the nodes move backwards.

    Sidereal month 27.3217 days The time for the moon to return to the same place among the background stars. This is less than a synodic month because the earth moves in it's orbit around the sun.

    Anomalistic month 27.5546 days The time from perigee to perigee, when the moon is closest to the earth (P').

    Tropical year 365.2422 days This is a "normal year." Officially, it's the time the sun takes to return to the vernal equinox, the ascending node where the ecliptic crosses the celestial equator on the vernal equinox. This is also known as the first point of Aries, but it's no longer in the actual constellation of Aries because of precession of the equinoxes.

    Sidereal year 365.2564 days   How long it takes the sun to return to the same place against the background stars. It's a bit less than a tropical year because of precession.

    Anomalistic year 365.2596 days The time from perihelion to perihelion, when the earth is closest to the sun.

    Eclipse year 346.6 days How long it takes the sun to return to the moon's ascending node (N1'). This is about 18.6 days less than it would take if the nodes didn't move.

The important cycles for eclipses are:

The Least Common Multiple (LCM) of a group of integers is the smallest whole number that they all can divide. We don't usually look for the LCM of decimal numbers, but there is an interesting convergence here:

   223 Synodic months = 223 x 29.5306 days = 6585.32 days
   242 Draconian months = 242 x 27.2122 days = 6585.35 days
   239 Anomalistic months = 239 x 27.5546 days = 6585.49 days

This period of 6585 1/3 days is about 18 years and 10 or 11 days depending on leap years. This is the Saros Cycle in which very similar eclipses repeat. The moon, the nodes, and perigee are all in about the same places, so eclipses repeat in patterns. This cycle was known in ancient Babylon, and Stonehenge and Chaco Canyon suggest that it was known elsewhere as well.

Eclipses can only happen when both the sun and the moon are within about 18.6 degrees of either of the nodes. It will be a solar eclipse when they're at the same node, and a lunar eclipse when they're at opposite nodes. The sun passes each node once a year, which results in a 37.5 day (2 x 18.6) eclipse season when eclipses can happen if the moon is also near a node. Since the speedy moon goes around in just 29.5 days, eclipses are inevitable during every eclipse season, at least twice a year. In fact, eclipse always come in pairs or triples because the eclipse season is longer than the moon's rotation, so the moon must enter the eclipse window at least twice while the sun is also there. For example, there will be a partial eclipse of the sun in about two weeks on Feb. 5, 2000. (But it's only visible from Anarctica!)

The nodes themselves move slowly backwards towards the sun, so the sun gets to each node about 20 days earlier each year, and the pattern of eclipses seems to cycle backwards through the calendar a bit less than 6 full moons apart. We missed the January 20 lunar eclipse because of clouds, but there will be another on July 16, a bit less than 6 months away when the sun, moon, and node again coincide.

Let's see if we can figure that next lunar eclipse more precisely. The moon was full on January 20, so it will be full again in 6 synodic months, 6 x 29.5306 = 177.18 days. The moon was close to the node on January 20. (How close?) It will be equally close to the node in 6 draconian months, or 6 x 27.2122 = 163.27 days. That's about 14 days from the full moon, within the +- 18.6 day eclipse season, so we should have another lunar eclipse in 177 days from January 20. That's July 16. The extra 0.18 days is about 0.18 x 24 = 4.5 hours. The last eclipse peaked at about 4:44 UT (8:44 PST), so the next eclipse should peak about 4.5 hours later at 8:44 UT on July 16. The official prediction for that eclipse is July 16 at 13:55 UT, about 5 hours later. Even this rough estimate is close enough to show it's possible to predict an eclipse without a computer!

There's so much free astronomy software and info on the Web! Here are a few links that helped me understand and appreciate eclipses:

Back to Stumper


Last modified .

Copyright © 2000 by Marc Kummel / mkummel@rain.org