CH. xviii. THE LAW OF GRAVITATION. 149 



in it than all the planets put together, and so it keeps them 

 moving round it. In the same way our earth has eighty 

 times more atoms in it than our moon, and so it keeps the 

 moon moving round it. 



In this way the force of gravity keeps all the different 

 planets in their paths or orbits. It does not set them 

 moving ; some other force unknown to us first started them 

 across the sky gravitation is only the force which determines 

 the direction in which they move. 



It was a grand thing to have discovered this force, but it 

 would have been of little value to Astronomy to know that 

 the heavenly bodies attracted each other unless it could also 

 be known how much influence they have upon each other. 

 This also Newton worked out accurately. You will remem- 

 ber that Kepler had shown that planets move in ellipses, 

 having the sun in one of the two foci (see Fig. TO, p. 97). 

 Knowing this, Newton was able to calculate how much the 

 sun attracts a planet when it is near, and how much when it 

 is far off, so as to make it move in an ellipse ; and he found 

 that exactly as much as the square of the distance increases, 

 so much the attraction decreases ; 

 that is, the attraction grows less 

 and less at a regular rate as 

 you go farther away from the 

 body that is pulling. 



For instance, suppose that 

 at the point i, Fig. 25, a planet 

 was one million of miles away 

 from the sun, and was being 

 attracted with immense force. 

 When it arrived at the point FlG - 2 5- 



3 it would be about twice as far, or two millions of miles 

 distant ; and the square of 2 being 4 (2 x 2 = 4), the attrac- 



