10 ELLIPTICAL MOTION. [SECT. IT. 



SECTION II. 



Elliptical Motion Mean and True Motion Equinoctial Ecliptic Equi- 

 noxes Mean and True Longitude Equation of Centre 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 Mo- 

 tions 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 varyr 

 ing 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 im- 

 pulse, 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 suns attraction again prevails (N. 39). In this motion 

 the radii vectores (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 described a circle (N. 43) round the sun at its mean 

 distance, the motion would be uniform, and the periodic 

 time unaltered, because the planet would arrive at the ex- 

 tremities of the major axis at the same instant, and would 



