A list of some of the principal astronomical researches of Lagrange and Laplace:—Libration of the moon. Long inequality of Jupiter and Saturn. Perturbations of Jupiter's satellites. Perturbations of comets. Acceleration of the moon's mean motion. Improved lunar theory. Improvements in the theory of the tides. Periodic changes in the form and obliquity of the earth's orbit. Stability of the solar system considered as an assemblage of rigid bodies subject to gravity.
The two equations which establish the stability of the solar system are:—
Sum (me2√d) = constant,
and
Sum (m tan2θ√d) = constant;
where m is the mass of each planet, d its mean distance from the sun, e the excentricity of its orbit, and θ the inclination of its plane. However the expressions above formulated may change for individual planets, the sum of them for all the planets remains invariable.
The period of the variations in excentricity of the earth's orbit is 86,000 years; the period of conical revolution of the earth's axis is 25,800 years. About 18,000 years ago the excentricity was at a maximum.
LECTURE XI
LAGRANGE AND LAPLACE—THE STABILITY OF THE SOLAR SYSTEM, AND THE NEBULAR HYPOTHESIS
Laplace was the son of a small farmer or peasant of Normandy. His extraordinary ability was noticed by some wealthy neighbours, and by them he was sent to a good school. From that time his career was one brilliant success, until in the later years of his life his prominence brought him tangibly into contact with the deteriorating influence of politics. Perhaps one ought rather to say trying than deteriorating; for they seem trying to a strong character, deteriorating to a weak one—and unfortunately, Laplace must be classed in this latter category.