Astronomy for Everybody/Part 4/Chapter 1

The orbits in which the planets revolve around their central luminary are in strictness ellipses, or slightly flattened circles. But the flattening is so slight that the eye would not notice it without measurement. The sun is not in the centre of the ellipse but in a focus, which in some cases is displaced from the centre by an amount that the eye can readily perceive. This displacement measures the eccentricity of the ellipse, which is much greater than the flattening. For example, in the case of Mercury, which moves in a very eccentric orbit, the flattening is only one fiftieth; that is, if we represent the greatest diameter of the orbit by fifty, the least diameter will be forty-nine. But the distance of the sun from the centre of the orbit is ten on the same scale.

To show this we give a diagram of the orbits of the inner group of planets showing quite nearly their forms and respective locations. A simple glance will show that the orbits are much nearer together at some points than at others.

In explaining the various aspects and motions, real and apparent, of the planets a number of technical expressions are used which we shall explain.

Inferior planets are those whose orbits lie within the ​orbit of the earth. This class comprises only Mercury and Venus.

Superior planets are those whose orbits lie without that of the earth. These comprise Mars, the minor planets or asteroids, and all four of the outer group of major planets.

When a planet seems to us to pass by the sun, and so is seen as if alongside of it, it is said to be in conjunction with the sun.

An inferior conjunction is one in which the planet is between us and the sun.

A superior conjunction is one in which the planet is beyond the sun.

​A little consideration will show that a superior planet can never be in inferior conjuction, but an inferior planet has both kinds of conjunction.

A planet is said to be in opposition when it is in the opposite direction from the sun. It then rises at sunset, and vice versa. Of course, an inferior planet can never be in opposition.

The perihelion of an orbit is that point of it which is nearest the sun; the aphelion its most distant point from the sun.

As the inferior planets, Mercury and Venus, perform their revolutions they seem to us to swing from one side of the sun to the other. Their apparent distance from the sun at any time is called their elongation.

The greatest elongation of Mercury is generally about twenty-five degrees, being sometimes more and sometimes less, owing to the great eccentricity of the orbit of this planet. The greatest elongation of Venus is almost forty-five degrees.

When the elongation of one of these planets is east from the sun we may see it in the west after sunset; when west we may see it in the east in the morning sky. As neither of them ever wanders from the sun farther than the distances we have stated, it follows that a planet seen in the east in the evening, or in the west in the morning, cannot be either Mercury or Venus.

No two orbits of the planets lie exactly in the same plane. That is, if we regard any one orbit as horizontal, all the others will be tipped by small amounts toward one side or the other. Astronomers find it convenient to take ​the orbit of the earth, or the ecliptic, as the horizontal or standard one. As each orbit is centred on the sun it will have two opposite points which lie on the same horizontal plane as the earth's orbit. More exactly, these are the points at which the orbit intersects the plane of the ecliptic. They are called nodes.

The angle by which an orbit is tipped from the plane of the ecliptic is called its inclination. The orbit of Mercury has the greatest inclination, more than 6°. The orbit of Venus is inclined 3° 24′; those of all the superior planets less, ranging from 0° 46′ in the case of Uranus to 2° 30′ in the case of Saturn.

Leaving out Neptune, the distances of the planets follow very closely a rule known as Bode's Law, after the astronomer who first pointed it out. It is this: Take the numbers 0, 3, 6, 12, etc., doubling each as we go along. Then add 4 to each number, and we shall hit very nearly on the scale of distances of all the planets except Neptune, thus:

On these actual distances we remark that astronomers do ​not use miles or other terrestrial measures to express distances between the heavenly bodies, for two reasons. In the first place, they are too short; to use them would be like stating the distance between two cities in centimetres. In the next place, distances in the heavens cannot be fixed with the necessary exactness in our measures, whereas, if we take the sun's distance from the earth as the unit of measure, we can determine other distances between the planets with great precision in terms of this measure. So, to get the distances of the planets from the sun in astronomical measure, we have to divide the last numbers of the preceding table by ten, or insert a decimal point before the last figure of each.

We have not in this table distracted the attention of the reader by using unnecessary decimals. Actually, the distance of Mercury is 0.387, etc.; we have simply called it 0.4 and multiplied it by 10 to get the proportion for comparing with Bode's Law.

The motions of the planets in their orbits take place in accordance with certain laws laid down by Kepler, and therefore known as Kepler's laws. The first of these has already been mentioned; the orbits of the planets are ellipses, of which the sun is in one focus.

The second law is that the nearer the planet is to the sun the faster it moves. With more mathematical exactness, the areas swept over by the line joining the planet and sun in equal times are all equal.

The third law is that the cubes of the mean distances ​of the planets from the sun are proportional to the squares of their times of revolution. This law requires some illustration. Suppose one planet to be four times as far from the sun as another. It will then be eight times as long going around it. This number is reached by taking the cube of four, which is sixty-four, and then extracting the square root, which is eight.

The unit of measure which the astronomer uses to express distances in the solar system being the mean distance of the earth from the sun, it follows that the mean distances of the inferior planets will be decimal fractions, as we have just shown, while those of the outer ones will vary from 1.5 in the case of Mars to 30 in the case of Neptune. If we take the cubes of all these distances and extract their square roots we shall have the times of the revolution of the planets, expressed in years.

It will be seen that the outer planets are longer in getting around their orbits, not only because they have farther to go, but because they actually move more slowly. If, as in the case first supposed, the outer planet is four times as far from the sun, it will move only half as fast. This is why it takes eight times as long to get around. The speed of the earth in its orbit is about 18.6 miles per second. But that of Neptune is only about 3.5 miles per second, although it has thirty times as far to go. This is why it takes more than one hundred and sixty years to complete a revolution.