ELLIPTICAL MOTION, SECT. II. 



SECTION II. 



Elliptical Motion Mean and True Motion Equinoctial Ecliptic 

 Equinoxes Mean and True Longitude Equation of Centre In- 

 clination of the Orbits of Planets Celestial Latitude Nodes 

 Elements of an Orbit Undisturbed or Elliptical Orbits Great In- 

 clination of the Orbits of the New Planets Universal Gravitation the 

 Cause of Perturbations in the Motions of the Heavenly Bodies Problem 

 of the Three Bodies Stability of Solar System depends upon the Pri- 

 mitive Momentum of the Bodies. 



A PLANET moves in its elliptical orbit with a velocity varying 

 every instant, in consequence of two forces, one tending to the 

 centre of the sun, and the other in the direction of a tangent 

 (N. 38) to its orbit, arising from the primitive impulse given at 

 the time when it was launched into space. Should the force in the 

 tangent cease, the planet would fall to the sun by its gravity. 

 Were the sun not to attract it, the planet would fly off in the 

 tangent. Thus, when the planet is at the point of its orbit 

 farthest from the sun, his action overcomes the planet's velocity, 

 and brings it towards him with such an accelerated motion, that 

 at last it overcomes the sun's attraction, and, shooting past him, 

 gradually decreases in velocity until it arrives at the most distant 

 point, where the sun's attraction again prevails (N. 39). In this 

 motion the radii vector es (N. 40), or imaginary lines joining the 

 centres of the sun and the planets, pass over equal areas or spaces 

 in equal times (N. 41). 



The mean distance of a planet from the sun is equal to half 

 the major axis (N. 42) of its orbit : if, therefore, the planet de- 

 scribed a circle (N. 43) round the sun at its mean distance, the 

 motion would be uniform, and the periodic time unaltered, be- 

 cause the planet would arrive at the extremities of the major 

 axis at the same instant, and would have the same velocity, 

 whether it moved in the circular or elliptical orbit, since the 

 curves coincide in these points. But in every other part the 

 elliptical, or true motion (N. 44), would either be faster or 



