CII. XII. 



' KEPLER'S THREE LAWS} 



97 



orbits lie in a different direction. Kepler's first law, then, was 

 that planets move in ellipses. 

 Kepler's Second Law, 

 1609. His second law was 

 about the rate at which pla- 

 nets move. He found from 

 Tycho's tables that they all 

 moved more quickly when 

 they were near the sun 

 than when they were far 

 from it, and after an im- 

 mense number of calculations he found the following 

 rule. If you could draw a line from the sun to any planet 

 on the first day of each month of the year, you would en- 

 close a number of spaces, such as a, b, <r, d, etc., in Fig. n, 

 and each of these spaces would be the same size although not 



the same shape. For instance 

 the planet, when travelling from 

 i to 2 near the sun, would go 

 very quickly and pass over a 

 number of miles, while when 

 travelling from 6 to 7 it would 

 go slowly and pass over com- 

 paratively few miles. And yet 

 the space / will be exactly the 

 same size as the space a, only 

 it will be long and thin instead 

 of short and broad. Kepler's second law, therefore, was that 

 a line (radius vector} drawn from the centre of the sun to a 

 planet sweeps over equal areas in equal times. 



Not many months after Kepler published these two laws, 

 he heard of Galileo's discoveries with his telescope that 

 Jupiter had four satellites, and that Venus had phases like 



FIG. ir. 



