A Short History of Astronomy, Arthur Berry [large screen ebook reader .TXT] 📗

The result of an investigation of this sort is often most conveniently expressed by means of a certain angle, from which the distance in terms of the radius of the earth, and hence in miles, can readily be deduced when desired.

The parallax of a heavenly body such as the moon, the sun, or a planet, being in the first instance defined generally (chapter II., § 43) as the angle (O M P) between the lines joining the heavenly body to the observer and to the centre of the earth, varies in general with the position of the observer. It is evidently greatest when the observer is in such a position, as at Q, that the line M Q touches the earth; in this position M is on the observer’s horizon. Moreover the angle O Q M being a right angle, the shape of the triangle and the ratio of its sides are completely known when the angle O M Q is known. Since this angle is the parallax of M, when on the observer’s horizon, it is called the horizontal parallax of M, but the word horizontal is frequently omitted. It is easily seen by a figure that the more distant a body is the smaller is its horizontal parallax; and with the small parallaxes with which we are concerned in astronomy, the distance and the horizontal parallax can be treated as inversely proportional to one another; so that if, for example, one body is twice as distant as another, its parallax is half as great, and so on.

It may be convenient to point out here that the word “parallax” is used in a different though analogous sense when a fixed star is in question. The apparent displacement of a fixed star due to the earth’s motion (chapter IV., § 92), which was not actually detected till long afterwards (chapter XIII., § 278), is called annual or stellar parallax (the adjective being frequently omitted); and the name is applied in particular to the greatest angle between the direction of the star as seen from the sun and as seen from the earth in the course of the year. If in fig. 69 we regard M as representing a star, O the sun, and the circle as being the earth’s path round the sun, then the angle O M Q is the annual parallax of M.

In this particular case Cassini deduced from Richer’s observations, by some rather doubtful processes, that the sun’s parallax was about 9″·5, corresponding to a distance from the earth of about 87,000,000 miles, or about 360 times the distance of the moon, the most probable value, according to modern estimates (chapter XIII., § 284), being a little less than 93,000,000. Though not really an accurate result, this was an enormous improvement on anything that had gone before, as Ptolemy’s estimate of the sun’s distance, corresponding to a parallax of 3′, had survived up to the earlier part of the 17th century, and although it was generally believed to be seriously wrong, most corrections of it had been purely conjectural (chapter VII., §§ 145).

162. Another famous discovery associated with the early days of the Paris Observatory was that of the velocity of light. In 1671 Picard paid a visit to Denmark to examine what was left of Tycho Brahe’s observatory at Hveen, and brought back a young Danish astronomer, Olaus Roemer (1644-1710), to help him at Paris. Roemer, in studying the motion of Jupiter’s moons, observed (1675) that the intervals between successive eclipses of a moon (the eclipse being caused by the passage of the moon into Jupiter’s shadow) were regularly less when Jupiter and the earth were approaching one another than when they were receding. This he saw to be readily explained by the supposition that light travels through space at a definite though very great speed. Thus if Jupiter is approaching the earth, the time which the light from one of his moons takes to reach the earth is gradually decreasing, and consequently the interval between successive eclipses as seen by us is apparently diminished. From the difference of the intervals thus observed and the known rates of motion of Jupiter and of the earth, it was thus possible to form a rough estimate of the rate at which light travels. Roemer also made a number of instrumental improvements of importance, but they are of too technical a character to be discussed here.

163. One great name belonging to the period dealt with in this chapter remains to be mentioned, that of René Descartes99 (1596-1650). Although he ranks as a great philosopher, and also made some extremely important advances in pure mathematics, his astronomical writings were of little value and in many respects positively harmful. In his Principles of Philosophy (1644) he gave, among some wholly erroneous propositions, a fuller and more general statement of the first law of motion discovered by Galilei (chapter VI., §§ 130, 133), but did not support it by any evidence of value. The same book contained an exposition of his famous theory of vortices, which was an attempt to explain the motions of the bodies of the solar system by means of a certain combination of vortices or eddies. The theory was unsupported by any experimental evidence, and it was not formulated accurately enough to be capable of being readily tested by comparison with actual observation; and, unlike many erroneous theories (such as the Greek epicycles), it in no way led up to or suggested the truer theories which followed it. But “Cartesianism,” both in philosophy and in natural science, became extremely popular, especially in France, and its vogue contributed notably to the overthrow of the authority of Aristotle, already shaken by thinkers like Galilei and Bacon, and thus rendered men’s minds a little more ready to receive new ideas: in this indirect way, as well as by his mathematical discoveries, Descartes probably contributed something to astronomical progress.