8 ELLIPTICAL MOTION. SECT. II. 



to velocity (N. 37), the reciprocal Attractions of a system 

 remain the same, whether its center of gravity be at 

 rest, or moving uniformly in space. It is computed that, 

 had the earth received its motion from a single impulse, 

 that impulse must have passed through a point about 

 twenty-five miles from its center. 



Since the motions of rotation and translation of the 

 planets are independent of each other, though probably 

 communicated by the same impulse, they form separate 

 subjects of investigation. 



SECTION II. 



Elliptical Motion Mean and True Motion Equinoctial Ecliptic Equi- 

 noxes Mean and True Longitude Equation of Center Inclination of 

 the Orbits of Planets Celestial Latitude Nodes Elements of an Orbit 

 Undisturbed or Elliptical Orbits Great Inclination 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 Primitive 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 center 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 toward him with 

 such an accelerated motion, that at last it overcomes the 

 sun's attraction ; and shooting past him, gradually de- 

 creases 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 centers 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 described a circle (N. 43) round the sun at 



