NOMOS. 97 



tendency it moves in an orbit around the sun, and 

 by so doing shows that it has been deflected from the 

 straight line in which it would move naturally, by a 

 force which continually tended towards the sun. 

 This centripetal force, moreover, is attractive in its 

 character, because it tends to bring the planet towards 

 the sun ; its power is inversely proportional to the 

 square of the distance, because the planet moves in 

 an ellipse with the sun in one of the foci ; and the 

 same force attracts all the other planets and their 

 satellites, because in all the square of the periods is 

 inversely proportional to the cubes of the distance. 

 The particular form of the orbit is determined alto- 

 gether by the velocity with which the planet was ori- 

 ginally launched into space. If the velocity were pre- 

 cisely balanced by the attractive force, the orbit would 

 be a perfect circle, for at every point the planet would 

 be bent down from the tangent of the orbit the 

 straight line in which it tends to move in accordance 

 to the first law of motion into the circumference 

 of the circle. If the velocity was not precisely 

 balanced by the attractive force, the orbit would be 

 more or less eccentric. 



If, for example, the original projection be such as 

 to overbalance the centripetal force, the planet will 

 at first tend to escape from that purely circular orbit 

 in which it would have moved if the projection and 

 the attractive force were exactly counterbalanced. 

 At every successive moment, however, the planet 

 must move with diminished velocity away from the 

 sun, for the centripetal force will continually drag 

 upon it and tend to bring it back towards the sun ; 



H 



