The crowning trophies of gravitational astronomy in the r8th century were Laplace's explanations of the " great inequality ".
His inquiries afford the assurance of a nearly exact conformity among its members to strict gravitational law, only the moon and Mercury showing some slight, but so far unexplained, anomalies of movement.
They may thus be fairly regarded as constituting a binary system, though the gravitational attraction between some of the wider pairs must be very weak.
The problems of gravitational astronomy engaged the chief part of Hansen's attention.
From the observed motion of the node of Venus, as shown by the four transits of 1761, 1769, 1874 and 1882, is found Mass of (earth +moon) _Mass of sun 332600 In gravitational units of mass, based on the metre and second as units of length and time, Log.
For many purposes a gravitational system of measurement is most natural; thus we speak of a force of so many pounds or so many kilogrammes.
Although Adams's researches on Neptune were those which attracted widest notice, the work he subsequently performed in relation to gravitational astronomy and terrestrial magnetism was not less remarkable.
Leverrier, in 1858, calculated a value of 8.95" for the solar parallax (equivalent to a distance of 91,000,000 m.) from the " parallactic inequality " of the moon; Professor Newcomb, using other forms of the gravitational method, derived in 1895 a parallax of 8.76".
It is true that rotational instability alone is not competent to explain the separation into two components; but the existence of gravitational instability, pointed out by J.
Starting from a widely diffused nebula, more or less uniform, we find that, in consequence of gravitational instability, it will tend to condense about a number of nuclei.
The question remains, of course, as to how far the measurement of force here implied is practically consistent with the gravitational method usually adopted in statics; this will be referred to presently.
We learn also that on account of the variation of g with the locality a gravitational system of force-measurement is inapplicable when more than a moderate degree of accuracy is desired.
The full working out is in general difficult, the comparatively simple problem of three bodies, for instance, in gravitational astronomy being still unsolved, but some general theorems can be formulated.
Hence there is a certain point, fixed relatively to the assemblage, through which the resultant of gravitational action always passes; this resultant is moreover equal to the sum of the forces on the several particles.