The Science of the Stars

by E. Walter Maunder

Full Moon Interval to New Moon
Dec. 1910 16 d 11 h. 5.1 m. A.M. 15 d. 5 h. 16.1 m.
Jan. 1911 14 " 10 " 26.0 " P.M. 15 " 11 " 18.7 "
Feb. " 13 " 10 " 37.5 " A.M. 15 " 13 " 53.6 "
March " 14 " 11 " 58.5 " P.M. 15 " 12 " 39.3 "
April " 13 " 2 " 36.6 " P.M. 15 " 7 " 48.4 "
May " 13 " 6 " 9.7 " A.M. 15 " 0 " 14.7 "
June " 11 " 9 " 50.7 " P.M. 14 " 15 " 29.0 "
July " 11 " 0 " 53.4 " P.M. 14 " 7 " 18.6 "
Aug. " 10 " 2 " 54.7 " A.M. 14 " 1 " 19.6 "
Sept. " 8 " 3 " 56.7 " P.M. 13 " 22 " 40.7 "
Oct. " 8 " 4 " 11.1 " A.M. 13 " 23 " 58.2 "
Nov. " 6 " 3 " 48.1 " P.M. 14 " 5 " 1.3 "
Dec. " 6 " 2 " 51.9 " A.M. 14 " 12 " 48.4 "
Jan. 1912 4 " 1 " 99.7 " P.M. 14 " 21 " 40.3 "

The astronomer who dealt with this difficulty was HIPPARCHUS (about 190-120 B.C.), who was born at Nicæa, in Bithynia, but made most of his astronomical observations in Rhodes. He attempted to explain these irregularities in the motions of the Sun and Moon by supposing that though they really moved uniformly in their orbits, yet the centre of their orbits was not the centre of the Earth, but was situated a little distance from it. This point was called "the excentric," and the line from the excentric to the Earth was called "the line of apsides."

But when he tried to deal with the movements of the planets, he found that there were not enough good observations available for him to build up any satisfactory theory. He therefore devoted himself to the work of making systematic determinations of the places of the planets that he might put his successors in a better position to deal with the problem than he was. His great successor was CLAUDIUS PTOLEMY of Alexandria, who carried the work of astronomical observation from about A.D. 127 to 150. He was, however, much greater as a mathematician than as an observer, and he worked out a very elaborate scheme, by which he was able to represent the motions of the planets with considerable accuracy. The system was an extremely complex one, but its principle may be represented as follows: If we suppose that a planet is moving round the Earth in a circle at a uniform rate, and we tried to compute the place of the planet on this assumption for regular intervals of time, we should find that the planet gradually got further and further away from the predicted place. Then after a certain time the error would reach a maximum, and begin to diminish, until the error vanished and the planet was in the predicted place at the proper time. The error would then begin to fall in the opposite direction, and would increase as before to a maximum, subsequently diminishing again to zero. This state of things might be met by supposing that the planet was not itself carried by the circle round the earth, but by an epicycle—i.e. a circle travelling upon the first circle—and by judiciously choosing the size of the epicycle and the time of revolution the bulk of the errors in the planet's place might be represented. But still there would be smaller errors going through their own period, and these, again, would have to be met by imagining that the first epicycle carried a second, and it might be that the second carried a third, and so on.

The Ptolemaic system was more complicated than this brief summary would suggest, but it is not possible here to do more than indicate the general principles upon which it was founded, and the numerous other systems or modifications of them produced in the five centuries from Eudoxus to Ptolemy must be left unnoticed. The point to be borne in mind is that one fundamental assumption underlay them all, an assumption fundamental to all science—the assumption that like causes must always produce like effects. It was apparent to the ancient astronomers that the stars—that is to say, the great majority of the heavenly bodies—do move round the Earth in circles, and with a perfect uniformity of motion, and it seemed inevitable that, if one body moved round another, it should thus move. For if the revolving body came nearer to the centre at one time and receded at another, if it moved faster at one time and slower at another, then, the cause remaining the same, the effect seemed to be different. Any complexity introduced by superposing one epicycle upon another seemed preferable to abandoning this great fundamental principle of the perfect uniformity of the actings of Nature.

For more than 1300 years the Ptolemaic system remained without serious challenge, and the next great name that it is necessary to notice is that of COPERNICUS (1473-1543). Copernicus was a canon of Frauenburg, and led the quiet, retired life of a student. The great work which made him immortal, De Revolutionibus, was the result of many years' meditation and work, and was not printed until he was on his deathbed. In this work Copernicus showed that he was one of those great thinkers who are able to look beyond the mere appearance of things and to grasp the reality of the unseen. Copernicus realised that the appearance would be just the same whether the whole starry vault rotated every twenty-four hours round an immovable Earth from east to west or the Earth rotated from west to east in the midst of the starry sphere; and, as the stars are at an immeasurable distance, the latter conception was much the simpler. Extending the idea of the Earth's motion further, the supposition that, instead of the Sun revolving round a fixed Earth in a year, the Earth revolved round a fixed Sun, made at once an immense simplification in the planetary motions. The reason became obvious why Mercury and Venus were seen first on one side of the Sun and then on the other, and why neither of them could move very far from the Sun; their orbits were within the orbit of the Earth. The stationary points and retrogressions of the planets were also explained; for, as the Earth was a planet, and as the planets moved in orbits of different sizes, the outer planets taking a longer time to complete a revolution than the inner, it followed, of necessity, that the Earth in her motion would from time to time be passed by the two inner planets, and would overtake the three outer. The chief of the Ptolemaic epicycles were done away with, and all the planets moved continuously in the same direction round the Sun. But no planet's motion could be represented by uniform motion in a single circle, and Copernicus had still to make use of systems of epicycles to account for the deviations from regularity in the planetary motions round the Sun. The Earth having been abandoned as the centre of the universe, a further sacrifice had to be made: the principle of uniform motion in a circle, which had seemed so necessary and inevitable, had also to be given up.

For the time came when the instruments for measuring the positions of the stars and planets had been much improved, largely due to TYCHO BRAHE (1546-1601), a Dane of noble birth, who was the keenest and most careful observer that astronomy had yet produced. His observations enabled his friend and pupil, JOHANN KEPLER, (1571-1630), to subject the planetary movements to a far more searching examination than had yet been attempted, and he discovered that the Sun is in the plane of the orbit of each of the planets, and also in its line of apsides—that is to say, the line joining the two points of the orbit which are respectively nearest and furthest from the Sun. Copernicus had not been aware of either of these two relations, but their discovery greatly strengthened the Copernican theory.

Then for many years Kepler tried one expedient after another in order to find a combination of circular motions which would satisfy the problem before him, until at length he was led to discard the circle and try a different curve—the oval or ellipse. Now the property of a circle is that every point of it is situated at the same distance from the centre, but in an ellipse there are two points within it, the "foci," and the sum of the distances of any point on the circumference from these two foci is constant. If the two foci are at a great distance from each other, then the ellipse is very long and narrow; if the foci are close together, the ellipse differs very little from a circle; and if we imagine that the two foci actually coincide, the ellipse becomes a circle. When Kepler tried motion in an ellipse instead of motion in a circle, he found that it represented correctly the motions of all the planets without any need for epicycles, and that in each case the Sun occupied one of the foci. And though the planet did not move at a uniform speed in the ellipse, yet its motion was governed by a uniform law, for the straight line joining the planet to the Sun, the "radius vector," passed over equal areas of space in equal periods of time.

These two discoveries are known as Kepler's First and Second Laws. His Third Law connects all the planets together. It was known that the outer planets not only take longer to revolve round the Sun than the inner, but that their actual motion in space is slower, and Kepler found that this actual speed of motion is inversely as the square root of its distance from the Sun; or, if the square of the speed of a planet be multiplied by its distance from the Sun, we get the same result in each case. This is usually expressed by saying that the cube of the distance is proportional to the square of the time of revolution. Thus the varying rate of motion of each planet in its orbit is not only subject to a single law, but the very different speeds of the different planets are also all subject to a law that is the same for all.