. The Adolfo Stahl lectures in astronomy, delivered in San Francisco, California, in 1916-17 and 1917-18, under the auspices of the Astronomical Society of the Pacific. he two-body problem. These matters will appear a littleclearer from the diagrams and tables which we shall nowdiscuss. Motions in the Solar System 181 Figure 11 shows the Earth and a minor planet in two cor-responding positions E^, Pj and Eo, Pg in their respective orbitswith reference to the Sun S. Both move in an easterly direc-tion approximately in circles. For each of these two bodies thecube of the distance from the Sun ex
. The Adolfo Stahl lectures in astronomy, delivered in San Francisco, California, in 1916-17 and 1917-18, under the auspices of the Astronomical Society of the Pacific. he two-body problem. These matters will appear a littleclearer from the diagrams and tables which we shall nowdiscuss. Motions in the Solar System 181 Figure 11 shows the Earth and a minor planet in two cor-responding positions E^, Pj and Eo, Pg in their respective orbitswith reference to the Sun S. Both move in an easterly direc-tion approximately in circles. For each of these two bodies thecube of the distance from the Sun expressed in astronomicalunits is equal to the square of its period of revolution expressedin years. The easterly or direct motion of the planet aroundthe Sun is therefore less rapid than that of the Earth. In thefirst position planet and Sun are on opposite sides of theEarth and the planet is said to be in opposition. P^ is seen fromEl in the position P/ on the celestial sphere. P, is seen fromE, at Po, which is west of P^. As seen from the Earth aplanet near opposition moving in a nearly circular orbit ap-pears to be moving westward or in a retrograde G H Fig. 12. The of Equal Areas in Elliptic Motion. Figure 12 shows an ellipse. The shaded sectors illustratethe law that equal sector areas are described in equal shaded areas are supposed to be equal. It takes the bodyjust as long to move in its curve from A to B as from C to D,from E to F, and from G to H. At A when it is near to theSun at perihelion its angular motion around the Sun S istherefore much more rapid than when it is far away from theSun at aphelion. The areas of two successive sectors of theconic are proportional to the times which it takes to describethem. But the ratios of the areas of triangles containedbetween three successive radii vectores, which form an 182 TfiE Adolfo Stahl Lectures important part in our discussion, are approximately propor-tional to the intervals only if these in
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