The Story of the Heavens

by Robert S. Ball

It is comparatively easy to learn the proportions of this system, to measure the relative distances of the planets from the sun, and even the relative sizes of the planets themselves. Peculiar difficulties are, however, experienced when we seek to ascertain the actual size of the system as well as its shape. It is this latter question which the transit of Venus offers us a method of solving.

Look, for instance, at an ordinary map of Europe. We see the various countries laid down with precision; we can tell the courses of the rivers; we can say that France is larger than England, and Russia larger than France; but no matter how perfectly the map be constructed, something else is necessary before we can have a complete conception of the dimensions of the country. We must know the scale on which the map is drawn. The map contains a reference line with certain marks upon it. This line is to give the scale of the map. Its duty is to tell us that an inch on the map corresponds with so many miles on the actual surface. Unless it be supplemented by the scale, the map would be quite useless for many purposes. Suppose that we consulted it in order to choose a route from London to Vienna, we can see at once the direction to be taken and the various towns and countries to be traversed; but unless we refer to the little scale in the corner, the map will not tell how many miles long the journey is to be.

A map of the solar system can be readily constructed. We can draw on it the orbits of some of the planets and of their satellites, and we can include many of the comets. We can assign to the planets and to the orbits their proper proportions. But to render the map quite efficient something more is necessary. We must have the scale which is to tell us how many millions of miles on the heavens correspond to one inch of the map. It is at this point we encounter a difficulty. There are, however, several ways of solving the problem, though they are all difficult and laborious. The most celebrated method (though far from the best) is that presented on an occasion of the transit of Venus. Herein, then, lies the importance of this rare event. It is one of the best-known means of finding the actual scale on which our system is constructed. Observe the full importance of the problem. Once the scale has been determined, then all is known. We know the size of the sun; we know his distance; we know the bulk of Jupiter, and the distances at which his satellites revolve; we know the dimensions of the comets, and the number of miles to which they recede in their wanderings; we know the velocity of the shooting stars; and we learn the important lesson that our earth is but one of the minor members of the sun's family.

As the path of Venus lies inside that of the earth, and as Venus moves more quickly than the earth, it follows that the earth is frequently passed by the planet, and just at the critical moment it will sometimes happen that the earth, the planet, and the sun lie in the same straight line. We can then see Venus on the face of the sun, and this is the phenomenon which we call the transit of Venus. It is, indeed, quite plain that if the three bodies were exactly in a line, an observer on the earth, looking at the planet, would see it brought out vividly against the brilliant background of the sun.

Considering that the earth is overtaken by Venus once every nineteen months, it might seem that the transits of the planet should occur with corresponding frequency. This is not the case; the transit of Venus is an exceedingly rare occurrence, and a hundred years or more will often elapse without a single one taking place. The rarity of these phenomena arises from the fact that the path of the planet is inclined to the plane of the earth's orbit; so that for half of its path Venus is above the plane of the earth's orbit, and in the other half it is below. When Venus overtakes the earth, the line from the earth to Venus will therefore usually pass over or under the sun. If, however, it should happen that Venus overtakes the earth at or near either of the points in which the plane of the orbit of Venus passes through that of the earth, then the three bodies will be in line, and a transit of Venus will be the consequence. The rarity of the occurrence of a transit need no longer be a mystery. The earth passes through one of the critical parts every December, and through the other every June. If it happens that the conjunction of Venus occurs on, or close to, June 6th or December 7th, then a transit of Venus will occur at that conjunction, but in no other circumstances.

The most remarkable law with reference to the repetition of the phenomenon is the well-known eight-year interval. The transits may be all grouped together into pairs, the two transits of any single pair being separated by an interval of eight years. For instance, a transit of Venus took place in 1761, and again in 1769. No further transits occurred until those witnessed in 1874 and in 1882. Then, again, comes a long interval, for another transit will not occur until 2004, but it will be followed by another in 2012.

This arrangement of the transits in pairs admits of a very simple explanation. It happens that the periodic time of Venus bears a remarkable relation to the periodic time of the earth. The planet accomplishes thirteen revolutions around the sun in very nearly the same time that the earth requires for eight revolutions. If, therefore, Venus and the earth were in line with the sun in 1874, then in eight years more the earth will again be found in the same place; and so will Venus, for it has just been able to accomplish thirteen revolutions. A transit of Venus having occurred on the first occasion, a transit must also occur on the second.

It is not, however, to be supposed that every eight years the planets will again resume the same position with sufficient precision for a regular eight-year transit interval. It is only approximately true that thirteen revolutions of Venus are coincident with eight revolutions of the earth. Each recurrence of conjunction takes place at a slightly different position of the planets, so that when the two planets came together again in the year 1890 the point of conjunction was so far removed from the critical point that the line from the earth to Venus did not intersect the sun, and thus, although Venus passed very near the sun, yet no transit took place.