Roche limit at 106,000 miles. A few thousand miles in ward and Jupiter would have rings. I would like to make the suggestion therefore that once we reach outward to explore other stellar systems we will discover (probably to our initial amazement) that about half the large planets we find will be equipped with rings after the fashion of Saturn.
Next we can try to do the same thing for the inner planets. Since the inner planets are, one and all, much less massive than the outer ones and much closer to the com peting Sun, we might guess that the range of distances open to true satellite formation would be more limited, and we would be right. Here are the actual figures as I have calculated them.
Distance of True Satellite Planet maximum minimum
(miles from the center (tug-of-war = 30)
of the primary) (Roche limit)
Mars 15,000 5150
Earth 29,000 9600
Venus 19,000 9200
Mercury 1300 3800
Thus, you see, where each of the outer planets has a range of two million miles or more within which true satel lites could form, the situation is far more restricted for the inner planets. Mars and Venus have a permissible range of but 10,000 miles. Earth does a little better, with 20,000 miles.
Mercury is the most interesting case. The maximum dis tance at which it can expect to form a natural satellite against the overwhelming competition of the nearby Sun is well within the Roche limit. It follows from that, if my reasomng is correct, that Mercury cannot have a true satel lite, and that anything more than a possible spattering of gravel is not to be expected.
In actual truth, no satellite has been located for Mercury but, as far as I know, nobody has endeavored to present a reason for, this or treat it as anything other than an empirical fact. If any Gentle Reader, with a greater knowl edge of astronomic detail than myself, will write to tell me that I have been anticipated in this, and by whom, I Will try to take the news philosophically. At the very least, I will confine my kicking and screaming to the privacy of my study.
Venus, Earth, 'and Mars are better off than Mercury and do have a little room for true satellites beyond the Roche limit. It is not much room, however, and the chances of gathering enough material over so small a volume of space to make anything but a very tiny satellite is minute.
And, as it happens, neither Venus nor Earth has any satellite at all (barring possible minute chunks of gravel) within the indicated limits, and Mars has two small satel.Iites, one perhaps 12 miles across and the other 6, which scarcely deserve the name.
It is amazing, and very gratifying to me, to note how all this makes such delightful sense, and how well I can reason out the details of the satellite systems of the various planets. It is such a shame that one small thing remains unaccounted for; one trifling thing I have ignored so far, but WHAT IN BLAZES IS OUR OWN MOON DOING WAY OUT THERE?
It's too far out to be a true satellite of the Earth, if we go by my beautiful chain of reasoning-which is too beau tiful for me to abandon. It's too big to have been cap tured by the Earth. The chances of such a capture having been effected and the Moon then having taken up a nearly circular orbit about the Earth are too small to make such an eventuality credible.
There are theories, of course, to the effect that the
Moon was once much closer to the Earth (within my per mitted limits for a true satellite) and then gradually moved away as a result of tidal action. Well, I have an objection to that. If the Moon were a true satellite that originally had circled Earth at a distance of, say, 20,000 miles, it would almost certainly be orbiting in the plane of Earth's equator and it isn't.
But, then, if the Moon is neither a true satellite of the
Earth nor a captured one, what is it? This may surprise you, but I have an answer; and to explain what that an swer is, let's get back to my tug-of-war determinations.
There is, after all, one satellite for which I have not cal culated it, and that is our Moon. We'll do that now.
The average distance of the Moon from the Earth is 237,000 miles, and the average distance of the Moon from the Sun is 93,000,000 miles. The ratio of the Moon-Sun distance to the Moon-Earth distance is 392. Squaring that gives us 154,000. The ratio of the mass of the Earth to that of the Sun was given earlier in the chapter and is 0.0000030. Multiplying this figure by 154,000 gives us the tug-of-war value, which comes out to: Moon 0.46
The Moon, in other words, is unique among the satel lites of the Solar System in that its primary (us) loses the tug of war with the Sun. The Sun attracts the Moon twice as strongly as the Earth does.
We might look upon the Moon, then, as neither a true satellite of the Earth nor a captured one, but as a planet in its own right, moving about the Sun in careful step with the Earth. To be sure, from within the Earth-Moon sys tem, the simplest way of picturing the situation is to have the Moon revolve about the Earth; but if you were to draw a picture of the orbits of the Earth and Moon about the Sun exactly to scale, you would see that the Moon's orbit is everywhere concave toward the Sun. It is always
"falling" toward the Sun. All the other satellites, without exception, "fall" away from the Sun through part of their orbits, caught as they are by the superior puR of their pri.rnary-but not the Moon.
And consider this-the Moon does not revolve about the Earth in the plane of Earth's equator, as would be ex pected of a true satellite. Rather it revolves about the Earth in a plane quite close to that of the ecliptic; that is, to the plane in which the planets, generally, rotate about the Sun. This is just what would be expected of a planet!
Is it possible then, that there is an intermediate point between the situation of a massive planet far distant from the Sun, which, develops about a single core, with numer ous satellites formed, and that of a small planet near the Sun which develops about a single core with no satellites?
Can there be a boundary condition, so to speak, in which there is condensation about two major cores so that a double planet is formed?
Maybe Earth just hit the edge of the permissible mass and distance; a little too small, a little too close. Perhaps if it were better situated the two halves of the double planct would have been more of a size. Perhaps both might have bad atmospheres and oceans and-life. Perhaps in other stellar systems with a double planet, a greater equal ity is more usual.
What a shame if we have missed that
Or, maybe (who knows), what luck!
8. First And Rearmost
When I was in junior high school I used to amuse myself by swinging on the rings in gym. (I was lighter then, and more foolhardy.) On one occasion I grew weary of the exercise, so at the end of one swing I let go.
It was my feeling at the time, as I distinctly remember, that I would continue my semicircular path and go swoop ing upward until gravity took hold; and that I would then come down light as gossamer, landing on my toes after a perfect entrechat.
That is not the way it happened. My path followed nearly a straight line, tangent to the semicircle of swing at the point at which I let go. I landed good and hard on one side..
After my head cleared, I stood up* and to this day that is the hardest fall I have ever taken.
I might have drawn a great deal of intellectual good out of this incident. I might have pondered on the effects of inertia; puzzled out methods of sumn-ting vectors; or de duced some facts about differential calculus.
However, I will be frank with you. What really im pressed itself upon me was the fact that the force of gravity was both mighty and dangerous and that if you weren't watching every minute, it would clobber you.
Presumably, I had learned that, somewhat less dras tically, early in life; and presumably, every human being who ever got onto his hind legs at the age of a year or less and promptly toppled, learned the same fact.