MIRACLES OF SCIENCE 



satellites with a good degree of accuracy. Such 

 measurement, stated in terms of angular distance, 

 would obviously have no definite meaning unless the 

 actual distance of the planet were known. But we 

 have already seen that these distances are matters 

 of precise knowledge, so the observations of the 

 atronomer as to the orbits of the various satellites of 

 the different planets can be translated into terms of 

 miles and thus supply the basis for simple computa- 

 tions through which the masses of the planets are 

 made known; otherwise stated, through which the 

 planets are weighed. 



Mathematicians have discovered that the computa- 

 tion in question may be very conveniently performed 

 if the problem is stated in the form of a proportion 

 in which the masses and the orbits of the satellites 

 of two different planetary systems are utilized. For 

 this purpose, the known mass and the orbital time 

 and distance of the earth and moon will naturally 

 form the standard of comparison. The formula im- 

 plied was stated as follows by the late Charles A. 

 Young, the famous Princeton astronomer: "The 

 united mass of a body and its satellite is to the united 

 mass of a second body and its satellite, as the cube 

 of the distance of the first satellite [from its pri- 

 mary] divided by the square of its period is to the 

 cube of the distance of the second satellite [from its 

 primary] divided by the square of its period." 



This formula obviously enables the astronomer to 

 compare, by the simplest mathematical computation, 

 the masses of any two bodies which have attendants 

 revolving round them. Thus the mass of any planet 



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