so small that its arc-measure may be substituted for its
sine; hence, for (1) and (2) we may write | A table should appear at this position in the text. See Help:Table for formatting instructions. |
for all the heavenly bodies except the moon.
From the observed parallactic displacement of the moon it is manifest, apart from the lunar phases, that the moon s orbit relatively to the earth lies within the sun's.
We have now, however, to consider bodies which, if they be regarded as moving around the earth, must move in orbits of very singular shape.
While observing the stars, which maintain apparently a constant position on the uniformly rotating star-sphere, the ancients early noted five bodies, which seem to travel among the stars like the sun and moon, but not always in one direction. To these bodies they gave the name of planets, or wanderers (a term which also included the sun and moon, so that there were seven in all). Three could be seen sometimes throughout the night, sometimes in the
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Fig. 17.—The Motion of Saturn, Jupiter, and Mars with respect to the Earth.
morning, sometimes in the evening. To these were given the names Saturn, Jupiter, and Mars ; and careful observation showed that these bodies, when visible all through the night, always travel among the stars in a direction con trary to that of the sun s yearly and the moon s monthly motion, but that this retrograde motion continues only for a certain length of time, being preceded and followed by an advancing motion, which is greater in amount than the retrograde motion, so that, on the whole, these bodies are carried round in the same direction as the sun and moon. The nature of these apparent motions will best be under stood by referring to fig. 17, and supposing an observer on the earth to watch Saturn, Jupiter, and Mars respec tively traversing the twisted paths there indicated, in the order shown by the dates, the loops being supposed to lie very nearly but not quite in the level of the paper, which represents the plane of the ecliptic. But this peculiarity was noticed, that when any planet was at the outermost parts of the successive loops (as, for instance, when Jupiter was as where the date 1712 is placed on his loops), the planet was lost to view in the sun s rays, lying nearly in the same part of the sky, whereas, when a planet was at
