This he explained in his next great discovery by proving that an imaginary line, or radius-vector, extending from the centre of the Sun to the centre of the planet ‘describes equal areas in equal times.’ When near the Sun, or at perihelion, a planet traverses a larger portion of its arc in the same period of time than it does when at the opposite part of its orbit, or when at aphelion; but, as the areas of both are equal, it follows that the planet does not always maintain the same rate of speed, and that its velocity is greatest when nearest the Sun, and least when most distant from him.
By the application of his first and second laws Kepler was able to formulate a third law. He found that there existed a remarkable relationship between the mean distances of the planets and the times in which they complete their revolutions round the Sun, and discovered ‘that the squares of the periodic times are to each in the same proportion as the cubes of the mean distances.’ The periodic time of a planet having been ascertained, the square of the mean distance and the mean distance itself can be obtained. It is by the application of this law that the distances of the planets are usually calculated.
These discoveries are known as Kepler’s Laws, and are usually classified as follows:—
1. ‘The orbit described by every planet is an ellipse, of which the centre of the Sun occupies one of the foci.
2. ‘Every planet moves round the Sun in a plane orbit, and the radius-vector, or imaginary line joining the centre of the planet and the centre of the Sun, describes equal areas in equal times.
3. ‘The squares of the periodic times of any two planets are proportional to the cubes of their mean distances from the Sun.’[1]
These remarkable discoveries do not embrace all the achievements by which Kepler has immortalised his name, and earned for himself the proud title of ‘Legislator of the Heavens;’ he predicted transits of Mercury and Venus, made important discoveries in optics, and was the inventor of the astronomical telescope.
Galileo Galilei, the famous Italian astronomer and philosopher, and the contemporary of Kepler and of Milton, was born at Pisa on February 15, 1564.
His father, who traced his descent from an ancient Florentine family, was desirous that his son should adopt the profession of medicine, and with this intention he entered him as a student at the University of Pisa. Galileo, however, soon discovered that the study of mathematics and mechanical science possessed a greater attraction for his mind, and, following his inclinations, he resolved to devote his energies to acquiring proficiency in those subjects.
In 1583 his attention was attracted by the oscillation of a brass lamp suspended from the ceiling of the cathedral at Pisa. Galileo was impressed with the regularity of its motion as it swung backwards and forwards, and was led to imagine that the pendulum movement might prove a valuable method for the correct measurement of time. The practical application of this idea he afterwards adopted in the construction of an astronomical clock.