But the superior planets are not in fact at rest, as we have supposed, but are all the while moving eastward, though with a slower motion than the earth. Indeed, with respect to the remotest planets, as Saturn and Uranus, the forward motion is so exceedingly slow, that the above representation is nearly true for a single year. Still, the effect of the real motions of all the superior planets, eastward, is to increase the direct apparent motion communicated by the earth, and to diminish the retrograde motion. This will be evident from inspecting the figure; for if the planet actually moves eastward while it is apparently carried eastward by the earth's motion, the whole motion eastward will be equal to the sum of the two; and if, while it is really moving eastward, it is apparently carried westward still more by the earth's motion, the retrograde movement will equal the difference of the two.
If Mars stood still while the earth went round the sun, then a second opposition, as at A, would occur at the end of one year from the first; but, while the earth is performing this circuit, Mars is also moving the same way, more than half as fast; so that, when the earth returns to A, the planet has already performed more than half the same circuit, and will have completed its whole revolution before the earth comes up with it. Indeed Mars, after having been seen once in opposition, does not come into opposition again until after two years and fifty days. And since the planet is then comparatively near to us, as at M, while the earth is at A, and appears very large and bright, rising unexpectedly about the time the sun sets, he surprises the world as though it were some new celestial body. But on account of the slow progress of Saturn and Uranus, we find, after having performed one circuit around the sun, that they are but little advanced beyond where we left them at the last opposition. The time between one opposition of Saturn and another is only a year and thirteen days.
It appears, therefore, that the superior planets steadily pursue their course around the sun, but that their apparent retrograde motion, when in opposition, is occasioned by our passing by them with a swifter motion, of which we are unconscious, like the apparent backward motion of a vessel, when we overtake it and pass by it rapidly in a steam-boat.
Such are the real and the apparent motions of the planets. Let us now turn our attention to the laws of the planetary orbits.
There are three great principles, according to which the motions of the earth and all the planets around the sun are regulated, called Kepler's Laws, having been first discovered by the astronomer whose name they bear. They may appear to you, at first, dry and obscure; yet they will be easily understood from the explanations which follow; and so important have they proved in astronomical inquiries, that they have acquired for their renowned discoverer the appellation of the 'Legislator of the Skies.' We will consider each of these laws separately; and, for the sake of rendering the explanation clear and intelligible, I shall perhaps repeat some things that have been briefly mentioned before.
Fig. 63. Fig. 64.
First Law.—The orbits of the earth and all the planets are ellipses, having the sun in the common focus. In a circle, all the diameters are equal to one another; but if we take a metallic wire or hoop, and draw it out on opposite sides, we elongate it into an ellipse, of which the different diameters are very unequal. That which connects the points most distant from each other is called the transverse, and that which is at right angles to this is called the conjugate, axis. Thus, A B, Fig. 63, is the transverse axis, and C D, the conjugate of the ellipse A B C. By such a process of elongating the circle into an ellipse, the centre of the circle may be conceived of as drawn opposite ways to E and F, each of which becomes a focus, and both together are called the foci of the ellipse. The distance G E, or G F, of the focus from the centre is called the eccentricity of the ellipse; and the ellipse is said to be more or less eccentric, as the distance of the focus from the centre is greater or less. Figure 64 represents such a collection of ellipses around the common focus F, the innermost, A G D, having a small eccentricity, or varying little from a circle, while the outermost, A C B, is an eccentric ellipse. The orbits of all the bodies that revolve about the sun, both planets and comets, have, in like manner, a common focus, in which the sun is situated, but they differ in eccentricity. Most of the planets have orbits of very little eccentricity, differing little from circles, but comets move in very eccentric ellipses. The earth's path around the sun varies so little from a circle, that a diagram representing it truly would scarcely be distinguished from a perfect circle; yet, when the comparative distances of the sun from the earth are taken at different seasons of the year, we find that the difference between their greatest and least distances is no less than three millions of miles.
Second Law.—The radius vector of the earth, or of any planet, describes equal areas in equal times. You will recollect that the radius vector is a line drawn from the centre of the sun to a planet revolving about the sun. This definition I have somewhere given you before, and perhaps it may appear to you like needless repetition to state it again. In a book designed for systematic instruction, where all the articles are distinctly numbered, it is commonly sufficient to make a reference back to the article where the point in question is explained; but I think, in Letters like these, you will bear with a little repetition, rather than be at the trouble of turning to the Index and hunting up a definition long since given.
