246. A few of Laplace's numerical results as to the secular variations of the elements may serve to give an idea of the magnitudes dealt with.
The line of apses of each planet moves in the same direction; the most rapid motion, occurring in the case of Saturn, amounted to about 15" per annum, or rather less than half a degree in a century. If this motion were to continue uniformly, the line of apses would require no less than 80,000 years to perform a complete circuit and return to its original position. The motion of the line of nodes (or line in which the plane of the planet's orbit meets that of the ecliptic) was in general found to be rather more rapid. The annual alteration in the inclination of any orbit to the ecliptic in no case exceeded a fraction of a second; while the change of eccentricity of Saturn's orbit, which was considerably the largest, would, if continued for four centuries, have only amounted to 11000.
247. The theory of the secular inequalities has been treated at some length on account of the general nature of the results obtained. For the purpose of predicting the places of the planets at moderate distances of time the periodical inequalities are, however, of greater importance. These were also discussed very fully both by Lagrange and Laplace, the detailed working out in a form suitable for numerical calculation being largely due to the latter. From the formulæ given by Laplace and collected in the Mécanique Céleste several sets of solar and planetary tables were calculated, which were in general found to represent closely the observed motions, and which superseded the earlier tables based on less developed theories.[1]
248. In addition to the lunar and planetary theories nearly all the minor problems of gravitational astronomy were rediscussed by Laplace, in many cases with the aid of methods due to Lagrange, and their solution was in all cases advanced.
The theory of Jupiter's satellites, which with Jupiter form
- ↑ Of tables based on Laplace's work and published up to the time of his death, the chief solar ones were those of von Zach (1804) and Delambre (1806); and the chief planetary ones were those of Lalande (1771), of Lindenau for Venus, Mars, and Mercury (1810–13), and of Bouvard for Jupiter, Saturn, and Uranus (1808 and 1821).
