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    Managing Multiple Moons, Part 2!

    copyright 1998 by Linda "Sweetwind" Tam

    Several more issues arise on a planet with two moons, beside the configurations of the phases discussed earlier in this space. Today I'll address the question of the moons' relative proximity to the planet, potential for eclipses, and the lengths of the phase cycles. The effect of two moons on the planet's tides is a subject for an entire essay in itself, so I'll leave that for another time!

    Skywise the Dreamer by Wendy Pini First off, which moon is closer? A glance at the diagram of Abode's planetary system in The Wolfrider's Guide to the World of Elfquest (Robeson, Plate 14) shows the smaller satellite, Daughter Moon, closer to Abode than the larger satellite, Mother Moon. This arrangement is very conveniently confirmed elsewhere the Guide (Robeson, p. 241), in a delightful Wendy sketch of Skywise under two crescent moons. Daughter Moon's crescent clearly appears in front of Mother Moon. (Scavenger Hunt time! Is there anywhere else in canonical sources that one moon is plainly in front of the other? Write to me in care of Sendings, and the first person to provide each reference will receive a nice prize.) The orbits of the two moons are not given in the planetary system diagram, however. The simplest thing to assume is that the orbit of Daughter Moon is completely within the orbit of Mother Moon. That is, Daughter Moon is always closer to Abode. Using our own solar system as a guide, it's the safest assumption that the two moons both have nearly circular orbits around Abode - this is the same arrangement of the two satellites of Mars, and all of the multiple satellites of Jupiter, Saturn, Uranus, and Neptune. Indeed, that is also the arrangement of all the planets around our sun - with the exception of Pluto, whose orbit crosses over the orbit of Neptune. Pluto is usually the most distant planet, but sometimes it is closer to the Sun than Neptune is. Is it possible that the two satellites of Abode have orbits which cross? In other words, can Mother Moon ever be closer to Abode than Daughter Moon? Taking our own solar system as the guide, my opinion is that it's highly unlikely, since no known satellites have crossing orbits. Until I see some more definitive data from the Elfquest canon, I'll assume that the orbit of Daughter Moon remains safely inside the orbit of Mother Moon, and that both orbits are well-behaved near-circles.

    Assuming that Mother Moon remains further away than Daughter Moon, unfortunately, removes the possibility for an eclipse of Daughter Moon by Mother Moon. By this I mean the smaller moon disappearing behind the larger, which would have been quite a sight to watch. However, the inhabitants of Abode do get treated to the sight of Daughter Moon moving across the face of the larger moon, as in the Skywise picture from the Wolfrider's Guide. The astronomical term for this event is a transit. There are lunar eclipses as well, just as on Earth, when the moon moves into the shadow of the planet - in fact, I would guess that lunar eclipses would be twice as common as here on Earth, since there are twice as many moons to stumble into Abode's shadow. There could also be a double lunar eclipse - when both moons are eclipsed simultaneously.

    Leetah Witnesses Solar Eclipse Solar eclipses also exist on the World of Two Moons. During the original Quest, Leetah describes them: "Twice in my life I have seen the sun turn into a black disc, haloed all around with rainbow streamers of light." (Pini, p. 70) These "rainbow streamers" are the corona of the Daystar, the tenuous outermost part of the Daystar's glowing atmosphere. In the illustration accompanying Leetah's words, the corona of the Daystar is clearly shown around the face of the eclipsing moon. The corona is only visible when the eclipsing body and the eclipsed star are a very close match in apparent size. Since Mother Moon eclipses the Daystar so nicely, smaller Daughter Moon must be too little to do a true eclipse by itself. When Daughter Moon passes across the face of the Daystar (technically, a transit rather than an eclipse), folks on the planet's surface would notice a reduction in the Daystar's brightness. They might look up to see the sun with a bite or a disc cut out its normal shape (and thus risk going blind, like Suntoucher!). But only Mother Moon can produce the darkness of a total solar eclipse, so total eclipses are as rare on Abode as on Earth.

    The term "month" in Elfquest refers to a cycle of the Mother Moon (Robeson, p. 159), but just how many days make a month has been left ambiguous. There are a few things we can deduce, however. The smaller moon must complete its cycle in less time than the greater moon. This follows from Kepler's third law, which requires the square of the cycle time to be proportional to the cube of the distance from the planet. For example, if the greater moon were four (2²) times as far from Abode as Daughter Moon, its cycle would take eight (2³) times as long as Daughter Moon's. Imagine the lesser moon zipping from full to new and back again eight times while the greater moon did it only once! I'm betting that their cycles are not that different. Another thing we can say with confidence about the two moons' cycle times is that they are unlikely to be a simple ratio like 1:2, 1:3 or 2:3 (or even 1:8, as in the example above) (Peterson, p. 265). This is a consequence of orbital dynamics. Suppose the two satellites had a 1:2 ratio of cycle times, that is, Mother Moon took twice as long to circle Abode as Daughter Moon did. Then the two moons come closest to each other in the same point in their orbits over and over again (see figures 1 through 3). As Peterson says, "over time, these coincidences accumulate into perceptible gravitational effects" (Peterson, p. 165) which can perturb the orbits and make them unstable. The stable moons and planets in our solar system generally do not exhibit such so-called resonances.

    Figure 1. Begin Time Figure 2. One-Half Month Later Figure 3. One Month Later

    So, what might be a reasonable guess as to the number of days each moon takes to complete a cycle of phases? Suppose that Mother Moon was twice as far from the planet as Daughter Moon. This is roughly the case for the two moons of Mars in our own solar system (actually, Mars' further moon is about 2.5 times more distant than the closer moon). By Kepler's third law, Mother Moon's month would be (square root of 2) × 3, or 2.8 times as long as the smaller moon's. If we give Mother Moon a month of about 28 days, similar to our own Moon, then Daughter Moon would go through a full cycle of phases in about 10 days. This is sheer speculation on my part, of course, using lots of assumptions, but I hope it and my other musings gives you an idea of what is involved in the dynamics of a two-mooned system.

    References:

    Scavenger Hunt Results!

    I cancelled the Scavenger Hunt. I hadn't received a single entry through May 2000. So rather than awarding prizes, I'll just write up the results of my own searching, and subject you all to it in a future article.

    Elfquest art copyright 2000 Warp Graphics, Inc. Elfquest, its logos, characters, situations, all related indicia, and their distinctive likenesses are trademarks of Warp Graphics, Inc. All rights reserved.

    © 2000 linda_tam@alumni.hmc.edu

    Last updated on July 1, 2000

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