Page:A short history of astronomy(1898).djvu/163

motion of the planet in a circle round the sun, while the sun moves round the earth, or, more simply, the earth round the sun.

The synodic period of a superior planet could best be determined by observing when the planet was in opposition, i.e. when it was (nearly) opposite the sun, or, more accurately (since a planet does not move exactly in the ecliptic), when the longitudes of the planet and sun differed by 180° (or two right angles, chapter ii., § 43). The

Fig. 46.—The relative sizes of the orbits of the earth and of a superior planet.

sidereal period could then be deduced nearly as in the case of an inferior planet, with this difference, that the superior planet moves more slowly than the earth, and therefore loses one complete revolution in each synodic period; or the sidereal period might be found as before by observing when oppositions occurred nearly in the same part of the sky.^[1] Coppernicus thus obtained very fairly accurate

1. If p be the synodic period of a planet (in years), and s the sidereal period, then we evidently have I/p + I = I/s for an inferior planet, and I - I/p = I/s for a superior planet.