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!

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.

People react oddly. After I stood up, I completely ignored my badly sprained (and possibly broken, though it later turned out not to be) right wrist imd lifted my untouched left wrist to my ear.

What worried me was whether my wristwatch were still running.

In fact, I have been told that infants have an instinctive fear of falling, and that this arose out of the survival value of having such an instinctive fear during the tree-living aeons of our simian ancestry.

We can say, then, that gravitational force is the first force with which each individual human being comes in contact. Nor can we ever manage to forget its existenc6, since it must be battled at every step, breath, and heart beat. Never for one moment must we cease exerting a counterforce.

It is also comforting that this mighty and overwhelming force protects us at all times. It holds us to our planet and doesn't allow us to shoot off into space. It holds our air and water to the planet too, for our perpetual use. And it holds the Earth itself in its orbit about the Sun, so that we always get the light and warmth we need.

What with all this, it generally comes as a rather sur prising shock to many people to learn that gravitation is not the strongest force in the universe. Suppose, for in stance, we compare it with the electromagnetic force that allows a magnet to attract iron or a proton to attract an electron. (The electromagnetic force also exhibits repul sion, which gravitational force does not, but that is a detail that need not distress us at this moment.)

How can we go about comparing the relative strengths of the electromagnetic force and the gravitational force? . Let's begin by considering two objects alone in the uni verse. The gravitational force between them, as was dis covered by Newton, can be expressed by the following equation (see also Chapter 7):

Gmr amp;

Fg = (Equation 1) d2 where F, is the gravitational force between the objects; m is the mass of one object; the mass of the other; d the distance between them; and G a universal "gravitational constant."

We must be careful about our units of measurement. If we measure mass in grams, distance in centimeters, and G in somewhat more complicated units, we will end up by determining the gravitational force in something called "dynes." (Before I'm through this chapter, the dynes will cancel out, so we need not, for present purposes, consider the dyne anything more than a one-syllable noise. It will be explained, however, in Chapter 13.)

Now let's get to work. The value of G is fixed (as far ,as we know) everywhere in the universe. Its value in the units I am using is 6.67 x 10-8. If you prefer long zero riddled decimals to exponential figures, you can express

G as 0.0000000667.

Let's suppose, next, that we are considering two objects of identical mass. This means that m = m'. so that mm' becomes mm, or M2. Furthermore, let's suppose the parti cles to be exactly I centimeter apart, center to center. In that case d = 1, and d2 = 1 also. Therefore, Equation 1 simplifies to the following:

F, = 0.0000000667 m2 (Equation 2)

We can now proceed to the electromagnetic force, which we can symbolize as F,.

Exactly one hundred years after Newton worked out the equation for gravitational forces, the French physicist Charles Augustin de Coulomb (1736-1806) was able'to show that a very similar equation could be used to deter mine the electromagnetic force between two electrically charged objects.

— Let us suppose, then, that the two objects for which we have been trying to calculate gravitational forces also carry electric charges, so that they also experience an electro magnetic force. In order to make sure that the electromag netic force is an attracting one and is therefore directly comparable to the gravitational force, let us suppose that one object carries a positive electric charge and the other a negative one. (The principle would remain even if we used like electric charges and measured the force of clec tromagnetic repulsion, but why introduce distractions?)

According to Coulomb, the electromagnetic force be 102 tween the two objects would be expressed by the foflo ' wmg equation:

F. (Equation 3) d2 where q is the charge on one object, q' on the other, and d is the distance between them.

If we let distance be measured in centimeters and elec tric charge in units called "electrostatic units" (usually abbreviated "esu7'), it is not necessary to insert a term analogous to the gravitational constant, provided the ob jects are separated by a vacuum. And, of course, since I started by assuming the objects were alone in the universe, there is necessarily a vacuunf between them.

Furthermore, if we use the units just mentioned, the value of the electromagnetic force will come out in dynes.

But lefs simplify matters by supposing that the positive electric charge on one object is exactly equal to the nega tive electric charge on the other, so that q = q,* which means that the objects . qq = qq = q2. Again, we can allow to be separated by just one centimeter, center to center, so that d2 = 1. Consequently, Equation 3 becomes:

Fe = q2 (Equation 4)

Let's summarize. We have two objects separated by one centimeter, center to center, each object possessing identi cal charge (positive in one case and negative in the other) and identical mass (no qualifications). There is both a gravitational and an electromagnetic attraction, between them.

The next problem is to determine how much stronger the electromagnetic force is than the gravitational force (or how much weaker, if that is how it turns out). To do * We could make one of them negative to allow for the fact that one object carries a negative electric charge. Then we could say that a negative value for- the electromagnetic force implies an attraction and a positive value a repulsion. However, for our pur poses, none of this folderol is needed. Since electromagnetic at traction and repulsion are but opposite manifestations of the same phenomenon, we shall ignore signs.

this we must determine the ratio of the forces by dividing

(let us say) Equation 4 by Equation 2. The result is:

F, q2 (Equation 5) 

F, 0.0000000667 M2

A decimal is an inconvenient thing to have in a denomi nator, but we can move it up into the numerator by taking its reciprocal (that is, by dividing it into 1). Since 1 di vided by 0.0000000667 is equal to 1.5 x 101, or 15,000, 000, we can rewrite Equation 5 as:

F, _ 15,000,000 q2 (Equation 6)

Fg m2 or, still more simply, as:

F,. = 15,000,000 (VM)2 (Equat;on 7)

Since both F, and F, are measured in dynes, then in taking the ratio we find we are dividing dynes by dynes.

The units, therefore, cancel out, and we are left with a "pure number." We are going to find, in other words, that one force is stronger than the other by a fixed amount; an amount that will be the same whatever units we use or whatever units an intelligent entity on the fifth planet of the star Fomalhaut wants to use. We will have, therefore, a universal constant.

In order to determine the ratio 0 the two es, we see from Equation 7 that we must first determine the value of qlm; that is, the charge of an object divided by its mass. Let's consider charge first.