596. The data requisite for computing the motions of the planets determined by observation for any instant arbitrarily assumed as the epoch or origin of the time, are

The masses of the planets ;

Their mean sidereal motions for a Julian year of 365.25 days ;

The mean distances of the planets from the sun ;

The ratios of the eccentricities to the mean distances;

The inclinations of the orbits on the plane of the ecliptic ;

The longitudes of the perihelia ;

The longitudes of the ascending nodes on the ecliptic;

The longitudes of the planets.

Masses of the Planets.

597. Satellites afford the means of ascertaining the masses of their primaries; the masses of such planets as have no satellites are found from a comparison of their inequalities determined by analysis, with values of the same obtained from numerous observations. The secular inequalities will give the most accurate values of the masses, but till they are perfectly known the periodic variations must be employed. On this account there is still some uncertainty as to the masses of several bodies. It is only necessary to know the ratio of the mass of each planet to that of the sun taken as the unit; the masses are consequently expressed by very small fractions.