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The Webfooted Astronomer - October 1999

 

Minutes: The Wonder of Eclipses

by Leslie Irizarry

The September SAS meeting was held September 15 in the Physics-Astronomy Building on the University of Washington campus.

Announcements
Calendars and Observing Handbook forms are available. See Bruce Kelley at the September, October, and November meetings. [Also see page 10 in this issue—Editor.] Peter Hirtle announced that there will be a Telescope Makers meeting Saturday October 6 at his house. Pat Lewis announced that there will be a Vive la Lune meeting Friday, September 17 if there is a Moon! There is an Imaging the Sky conference in Salem, Oregon, Keith Allred announced. See the link on the SAS Web page or September Webfooted Astronomer for more information.

Jerry West announced that the annual banquet will be held at the Yankee Diner on January 29, 1999. There will be no regular meeting in January. A vote was taken on the price levels and cuisine: the majority voted on Prime Rib or Salmon at approximately $25.00 per person. [See page 8 in this issue for more information—Editor.]

The Wonder of Eclipses
According to Guillermo Gonzales, our speaker for the evening, eclipses are very special. There are several factors necessary in order to have a total eclipse. Three bodies in a straight line. The sun, moon, and Earth have to be in a straight line, which happens infrequently. Looking at the apparent movement of the sun and moon around the Earth, there are nodes in which the sun’s apparent orbit and the moon’s ap parent orbit intersect. (The line of nodes.) It is only at the line of nodes that the moon, with an orbital inclination of 5 degrees, intersects the ecliptic. The moon will thus not produce an eclipse during most new moons. These nodes are 180 degrees opp osite each other. This line of nodes rotates relative to the stars every 18.6 years. There is a cycle of repeatability of eclipses. If you wait 54 years, the sequence of eclipse will nearly repeat itself. (There is some eccentricity making it less than ex act.) During an eclipse, the moon casts a shadow on the Earth. The shadow is divided into two sections: the penumbra and the umbra.

The apparent size of the moon must be larger than the apparent size of the sun. In the case of the sun and the moon, the sun is 400 times larger than the moon, but the sun is also 400 times further away than the sun, so it is nearly a perfect match. Th e moon has to be near perigee. If the moon is not near perigee, an annular eclipse will occur.

Guillermo then presented a slide show of the eclipse seen in India. The chromosphere was pink, which is due to hydrogen-alpha emissions. When the moon’s apparent size is such that it is just big enough to cover the sun, you can see deeper into the chro mosphere and see smaller prominences. There is a range of relative apparent sizes of the moon vs. the sun. If it were a longer eclipse, the apparent size of the moon would be longer, less pink, and less small. Guillermo defines "perfect" eclipses as those in which you can see both the chromosphere and the corona.

How do eclipses on Earth compare with others in the solar system? As you get closer to the sun, the apparent size of the sun increases, but the moons do not. Of Saturn’s 44 satellites, only two have an eclipse that just covers the sun. The apparent si ze of Pluto’s satellite (compared to the apparent size of the sun) is so big, it casts a huge shadow on the planet.

On the subject of roundness Guillermo noted that there are a lot of potato-shaped objects in the solar system that do not produce elegant eclipses! The moon is one of the roundest bodies in the solar system. It is oblate by 0.06 percent. The sun is obl ate by 0.009 percent. The shapes of the Galilean moons become rounder as they move away from Jupiter. This is because there is a higher percentage of ice. Callisto is the roundest of the Jovian Moons.

On the subject of temporal domain of eclipses as seen from the Earth, Guillermo said the elements of the moon are changing. You can examine growth layers of coral (bivalves, stromatolytes, or tidalytes) and organisms that live the shallow sea, and look for patterns. This gives us information on the daily and monthly cycles of the tides, and the growth layer (high and low tides). By studying the growth layer and variations of thickness, you can determine the number of days in a year and the number of da ys in a month at a given time, although you cannot determine the absolute length of the year. The length of year has been shown not to change. The earth's orbital eccentricity, however, has changed over long periods of time.

The rate at which the moon is moving away from the Earth can be determined by lunar lasering. You can measure the distance to the moon to within a couple of centimeters because of retro reflectors on moon. The mean rate at which the moon is moving awa y is 3.82 centimeters per year. This is called the secular rate of the increase of the moon's orbit.

The moon is moving away because of the tides. The angular momentum of the Earth decreases as tidal friction slows its rotation. The energy lost by the Earth's slowing rotation is transferred to the moon’s orbital motion. The moon experiences a slightly faster orbital speed, which causes the moon to move further and further away from the Earth over time. This is the most important factor in calculating how long Earth will experience solar eclipses. The diameter of the sun is increasing at 6 centimeters per year. The variation in eccentricity of Earth's orbit also plays a role. There is a slow decrease in eccentricity of the moon's orbit, which is slowly becoming more circular. The moon’s orbit is exceedingly complicated. There are thousands of terms, al l with different amplitudes in the equations, describing elliptical orbital motion. When considering all these factors, calculations show that we will see uninterrupted total eclipses for another 250 million years.

Guillermo mentioned practical uses for eclipses, such as observing the faint outer corona of the sun; measuring the rate at which Earth's rotation is slowing down; studying documentation regarding ancient eclipses and providing the best estimate of lon g-term changes of Earth's rotation.

The moon is quite large compared to the Earth. There is a close connection between habitability and eclipses because a satellite the size of the moon has a stabilizing affect on the orbital and rotational dynamics of a planet. The moon was probably cre ated by a large collision of a Mars-sized body colliding in a glancing blow with the proto-Earth. This explains the lack of a large core and the size of moon.

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