A Short History of Astronomy - Arthur Berry (read along books .txt) 📗
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Much more important, however, were his lunar theory and the tables based on it. The intrinsic mathematical interest of the problem of the motion of the moon, and its practical importance for the determination of longitude, had caused a great deal of attention to be given to the subject by the astronomers of the 18th century. A further stimulus was also furnished by the prizes offered by the British Government in 1713 for a method of finding the longitude at sea, viz. £20,000 for a method reliable to within half a degree, and smaller amounts for methods of less accuracy.
All the great mathematicians of the period made attempts at deducing the moon’s motions from gravitational principles. Mayer worked out a theory in accordance with methods used by Euler (chapter XI., § 233), but made a much more liberal and also more skilful use of observations to determine various numerical quantities, which pure theory gave either not at all or with considerable uncertainty. He accordingly succeeded in calculating tables of the moon (published with those of the sun in 1753) which were a notable improvement on those of any earlier writer. After making further improvements, he sent them in 1755 to England. Bradley, to whom the Admiralty submitted them for criticism, reported favourably of their accuracy; and a few years later, after making some alterations in the tables on the basis of his own observations, he recommended to the Admiralty a longitude method based on their use which he estimated to be in general capable of giving the longitude within about half a degree.
Before anything definite was done, Mayer died at the early age of 39, leaving behind him a new set of tables, which were also sent to England. Ultimately £3,000 was paid to his widow in 1765; and both his Theory of the Moon128 and his improved Solar and Lunar Tables were published in 1770 at the expense of the Board of Longitude. A later edition, improved by Bradley’s former assistant Charles Mason (1730-1787), appeared in 1787.
A prize was also given to Euler for his theoretical work; while £3,000 and subsequently £10,000 more were awarded to John Harrison for improvements in the chronometer, which rendered practicable an entirely different method of finding the longitude (chapter VI., § 127).
227. The astronomers of the 18th century had two opportunities of utilising a transit of Venus for the determination of the distance of the sun, as recommended by Halley (§ 202).
A passage or transit of Venus across the sun’s disc is a phenomenon of the same nature as an eclipse of the sun by the moon, with the important difference that the apparent magnitude of the planet is too small to cause any serious diminution in the sun’s light, and it merely appears as a small black dot on the bright surface of the sun.
If the path of Venus lay in the ecliptic, then at every inferior conjunction, occurring once in 584 days, she would necessarily pass between the sun and earth and would appear to transit. As, however, the paths of Venus and the earth are inclined to one another, at inferior conjunction Venus is usually far enough “above” or “below” the ecliptic for no transit to occur. With the present position of the two paths—which planetary perturbations are only very gradually changing—transits of Venus occur in pairs eight years apart, while between the latter of one pair and the earlier of the next pair elapse alternately intervals of 105-1∕2 and of 121-1∕2 years. Thus transits have taken place in December 1631 and 1639, June 1761 and 1769, December 1874 and 1882, and will occur again in 2004 and 2012, 2117 and 2125, and so on.
The method of getting the distance of the sun from a transit of Venus may be said not to differ essentially from that based on observations of Mars (chapter VIII., § 161).
The observer’s object in both cases is to obtain the difference in direction of the planet as seen from different places on the earth. Venus, however, when at all near the earth, is usually too near the sun in the sky to be capable of minutely exact observation, but when a transit occurs the sun’s disc serves as it were as a dial-plate on which the position of the planet can be noted. Moreover the measurement of minute angles, an art not yet carried to very great perfection in the 18th century, can be avoided by time-observations, as the difference in the times at which Venus enters (or leaves) the sun’s disc as seen at different stations, or the difference in the durations of the transit, can be without difficulty translated into difference of direction, and the distances of Venus and the sun can be deduced.129
Immense trouble was taken by Governments, Academies, and private persons in arranging for the observation of the transits of 1761 and 1769. For the former observing parties were sent as far as to Tobolsk, St. Helena, the Cape of Good Hope, and India, while observations were also made by astronomers at Greenwich, Paris, Vienna, Upsala, and elsewhere in Europe. The next transit was observed on an even larger scale, the stations selected ranging from Siberia to California, from the Varanger Fjord to Otaheiti (where no less famous a person than Captain Cook was placed), and from Hudson’s Bay to Madras.
The expeditions organised on this occasion by the American Philosophical Society may be regarded as the first of the contributions made by America to the science which has since owed so much to her; while the Empress Catherine bore witness to the newly acquired civilisation of her country by arranging a number of observing stations on Russian soil.
The results were far more in accordance with Lacaille’s anticipations than with Halley’s. A variety of causes prevented the moments of contact between the discs of Venus and the sun from being observed with the precision that had been hoped. By selecting different sets of observations, and by making different allowances for the various probable sources of error, a number of discordant results were obtained by various calculators. The values of the parallax (chapter VIII., § 161) of the sun deduced from the earlier of the two transits ranged between about 8″ and 10″; while those obtained in 1769, though much more consistent, still varied between about 8″ and 9″, corresponding to a variation of about 10,000,000 miles in the distance of the sun.
The whole set of observations were subsequently very elaborately discussed in 1822-4 and again in 1835 by Johann Franz Encke (1791-1865), who deduced a parallax of 8″·571, corresponding to a distance of 95,370,000 miles, a number which long remained classical. The uncertainty of the data is, however, shewn by the fact that other equally competent astronomers have deduced from the observations of 1769 parallaxes of 8″·8 and 8″·9.
No account has yet been given of William Herschel, perhaps the most famous of all observers, whose career falls mainly into the last quarter of the 18th century and the earlier part of the 19th century. As, however, his work was essentially different from that of almost all the astronomers of the 18th century, and gave a powerful impulse to a department of astronomy hitherto almost ignored, it is convenient to postpone to a later chapter (XII.) the discussion of his work.
GRAVITATIONAL ASTRONOMY IN THE 18TH CENTURY.
“Astronomy, considered in the most general way, is a great problem of mechanics, the arbitrary data of which are the elements of the celestial movements; its solution depends both on the accuracy of observations and on the perfection of analysis.”
Laplace, Preface to the Mécanique Céleste.
228. The solar system, as it was known at the beginning of the 18th century, contained 18 recognised members: the sun, six planets, ten satellites (one belonging to the earth, four to Jupiter, and five to Saturn), and Saturn’s ring.
Comets were known to have come on many occasions into the region of space occupied by the solar system, and there were reasons to believe that one of them at least (chapter X., § 200) was a regular visitor; they were, however, scarcely regarded as belonging to the solar system, and their action (if any) on its members was ignored, a neglect which subsequent investigation has completely justified. Many thousands of fixed stars had also been observed, and their places on the celestial sphere determined; they were known to be at very great though unknown distances from the solar system, and their influence on it was regarded as insensible.
The motions of the 18 members of the solar system were tolerably well known; their actual distances from one another had been roughly estimated, while the proportions between most of the distances were known with considerable accuracy. Apart from the entirely anomalous ring of Saturn, which may for the present be left out of consideration, most of the bodies of the system were known from observation to be nearly spherical in form, and the rest were generally supposed to be so also.
Newton had shewn, with a considerable degree of probability, that these bodies attracted one another according to the law of gravitation; and there was no reason to suppose that they exerted any other important influence on one another’s motions.130
The problem which presented itself, and which may conveniently be called Newton’s problem, was therefore:—
Given these 18 bodies, and their positions and motions at any time, to deduce from their mutual gravitation by a process of mathematical calculation their positions and motions at any other time; and to shew that these agree with those actually observed.
Such a calculation would necessarily involve, among other quantities, the masses of the several bodies; it was evidently legitimate to assume these at will in such a way as to make the results of calculation agree with those of observation. If this were done successfully the masses would thereby be determined. In the same way the commonly accepted estimates of the dimensions of the solar system and of the shapes of its members might be modified in any way not actually inconsistent with direct observation.
The general problem thus formulated can fortunately be reduced to somewhat simpler ones.
Newton had shewn (chapter IX., § 182) that an ordinary sphere attracted other bodies and was attracted by them, as if its mass were concentrated at its centre; and that the effects of deviation from a spherical form became very small at a considerable distance from the body. Hence, except in special cases, the bodies of the solar system could be treated as spheres, which could again be regarded as concentrated at their respective centres. It will be convenient for the sake of brevity to assume for the future that all “bodies” referred to are of this sort, unless the contrary is stated or implied. The effects of deviations from spherical form could then be treated separately when required, as in the cases of precession and of other motions of a planet or satellite about its centre, and of the corresponding action of a non-spherical planet on its satellites; to this group of problems belongs also that of the tides and other cases of the motion of parts of a body of
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