43. The Eccentricity of the Ellipse.—The ratio of the distance between the two foci to the major axis of the ellipse is called the eccentricity of the ellipse. The greater the distance between the two foci, compared with the major axis of the ellipse, the greater is the eccentricity of the ellipse; and the less the distance between the foci, compared with the length of the major axis, the less the eccentricity of the ellipse. The ellipse of Fig. 54 has an eccentricity of 1/8. This ellipse scarcely differs in appearance from a circle. The ellipse of Fig. 55 has an eccentricity of 1/2, and that of Fig. 56 an eccentricity of 7/8.
Fig. 54.
Fig. 55.
Fig. 56.
44. Kepler's First Law.—Kepler first discovered that all the planets move from west to east in ellipses which have the sun as a common focus. This law of planetary motion is known as Kepler's First Law. The planets appear to describe loops, because we view them from a moving point.
The ellipses described by the planets differ in eccentricity; and, though they all have one focus at the sun, their major axes have different directions. The eccentricity of the planetary orbits is comparatively small. The ellipse of Fig. 54 has seven times the eccentricity of the earth's orbit, and twice that of the orbit of any of the larger planets except Mercury; and its eccentricity is more than half of that of the orbit of Mercury. Owing to their small eccentricity, the orbits of the planets are usually represented by circles in astronomical diagrams.
