308. The science of astronomy was cultivated very early, and many important observations and discoveries were made, yet no accurate inferences leading to the true system of the world were drawn from them, until a much later period. It is not surprising, that men deceived by appearances, occasioned by the rotation of the earth, should have been slow to believe the diurnal motion of the heavens to be an illusion ; but the absurd consequence which the contrary hypothesis involves, convinced minds of a higher order, that the apparent could not be the true system of nature.

Many of the ancients were aware of the double motion of the earth ; a system which Copernicus adopted, and confirmed by the comparison of a series of observations, that had been accumulating for ages ; from these he inferred that the precession of the equinoxes might be attributed to a motion in the earth's axis. He ascertained the revolution of the planets round the sun, and determined the dimensions of their orbits, till then unknown. Although he proved these truths by evidence which has ultimately dissipated the erroneous theories resulting from the illusions of the senses, and overcame the objections which were opposed to them by ignorance of the laws of mechanics, this great philosopher, constrained by the prejudices of the times, only dared to publish the truths he had discovered, under the less objectionable name of hypotheses.

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.

532. The position of a planet in space is fixed when its curtate distance Sp, fig. 77, its projected longitude γSp, and its latitude pm, are known. The determination of these three co-ordinates in functions of the time is the principal object of Physical Astronomy; these quantities in series ascending according to the powers of the eccentricities and inclinations are given in article 399, and those following, supposing the planet to move in a perfect ellipse ; but if values of the elements of the orbits corrected by their periodic and secular variations be substituted instead of their elliptical elements, the same series will determine the motion of the planet in its real perturbed orbit.

533. The projected longitude and curtate distance only differ from the true longitude and distance on the orbit by quantities of the second order with regard to the inclinations; and when the orbit at the epoch is assumed to be the fixed plane, these quantities as well as those of the latitude that depend on the product of the inclination by the eccentricity are so small that they are insensible, as will readily appear if it be considered that any inclination the orbit may have acquired subsequently to the epoch, can only have arisen from the small secular variation in the elements ; besides the epoch may be chosen to make it so, being arbitrary.