Mars is observed to come in opposition, and likewise to have all other aspects with the Sun; he always preserves a round, full, and bright face, except when he is near his quadrate aspect, when he appears somewhat gibbous, like the Moon three or four Days before or after the full: Therefore the Orbit of ♂ must include the Earth within it, and also the Sun; for if he was betwixt the Sun and us at the time of his inferior conjunction, he would either quite disappear, or appear horned, as Venus and the Moon do in that position. Let S be the Sun, T the Earth, and A P Mars, both in his conjunction and opposition to the Sun, and in both positions full; and B C Mars at his quadratures, when he appears somewhat gibbous from the Earth at T. ’Tis plain hence, that the Orbit of Mars does include the Earth, otherwise he could not come in opposition to the Sun; and that it likewise includes the Sun, else he could appear full at his conjunction.
Mars when he is in opposition to the Sun, looks almost seven times larger in diameter than when he is in conjunction with him, and therefore must needs be almost seven times nearer to us in one position than in the other; for the apparent magnitudes of far distant objects increase or decrease in proportion to their distances from us: But Mars keeps always nearly at the same distance from the Sun; therefore it is plain that it is not the Earth, but the Sun, that is the center of his motion.
It is proved in the same way, that Jupiter and Saturn have both the Sun and the Earth within their Orbits, and that the Sun, and not the Earth, is the center of their motions; altho’ the disproportion of the distances from the Earth is not so great in Jupiter, as it is in Mars, nor so great in Saturn, as it is in Jupiter, by reason that they are at a much greater distance from the Sun.
Inferior and Superior Planets.
We have now shewn that all the Planets turn round the Sun, and that Mercury and Venus are included between him and the Earth, whence they are called the Inferior Planets, and that the Earth is placed between the Orbits of Mars and Venus, and therefore included within the Orbits of Mars, Jupiter, and Saturn, whence they are called the Superior Planets: And since the Earth is in the middle of these moveable bodies, and is of the same nature with them, we may conclude that she has the same sort of motions; but that she turns round the Sun is proved thus:
The Earth does not stand still, but turns round the Sun.
All the Planets seen from the Earth appear to move very unequally, as sometimes to go faster, at other times slower; sometimes to go backwards, and sometimes to be stationary, or not to move at all; which could not happen if the Earth stood still. Let S be the Sun, T the Earth, the great circle A B C D the Orbit of Mars, and the numbers 1, 2, 3, &c. its equable motion round the Sun; the correspondent numbers 1, 2, 3, &c. in the circle a, b, c, d, the motion of Mars, as it would be seen from the Earth. It is plain from this Figure, that if the Earth stood still, the motion of Mars, will be always progressive, (tho’ sometimes very unequal;) but since observations prove the contrary, it necessarily follows, that the Earth turns round the Sun.
The Annual and Diurnal Motions of the Planets, how computed.
The annual periods of the Planets round the Sun are determined by carefully observing the length of time since their departure from a certain point in the Heavens, (or from a fix’d Star) until they arrive to the same again. By these sort of observations the ancients determined the periodical revolutions of the Planets round the Sun, and were so exact in their computations, as to be capable of predicting Eclipses of the Sun and Moon. But since the invention of telescopes, astronomical observations are made with greater accuracy; and of consequence, our tables are far more perfect than those of the ancients. And in order to be as exact as possible, astronomers compare observations made at a great distance of time from one another, including several periods; by which means, the error that might be in the whole, is in each period subdivided into such little parts as to be inconsiderable. Thus the mean length of a Solar Year is known, even to Seconds.