308 F. B. Taylor — Determinate Orbital Stability: 



mena of the Planetary system, including its structure and 

 its growth, when interpreted in the light of this principle. 



Some Functions of determinate Orhital Stability in Celestial 



Mechanics. 



1. The place of the determinate orbit of stability now 

 occupied by the Moon depends upon the masses of the 

 Sun and the Earth, and the distance of the Earth from the 

 Sun. A change in the value of one or more of these basic 

 conditions would necessarily change the value of some of 

 the factors entering into determinate stability, and would 

 change accordingly the distance of the determinate orbit 

 from the Earth. For example, an increase in the Earth ^s 

 mass, other conditions remaining the same, would set the 

 determinate orbit farther out from the Earth, while a 

 decrease would set it in nearer. Changes in the Earth's 

 distance from the Sun would produce similar effects 

 upon the place of the determinate orbit. Thus, if the 

 Earth, with its present mass, were revolving in the 

 present orbit of Mars the place of the determinate orbit 

 would be much nearer to the Earth. Mars is both smaller 

 in mass and farther out from the Sun than the Earth, 

 and as a consequence its two moons are remarkable for 

 their nearness to their primary. This phenomenon has 

 been something of a puzzle to astronomers and mathema- 

 ticians ever since these moons were discovered, but it 

 needs no other explanation. Phobos, the inner of the 

 two moons, is now in the orbit of determinate stability 

 for Mars. A change in the Sun's mass, other conditions 

 remaining the same, would have similar effects, but this 

 is not important for our present purpose. 



2. Mathematicians have found that each planet is 

 surrounded by a belt or zone of space in which the attrac- 

 tion of the planet is dominant over that of the Sun. This 

 space is called the planet's sphere of control. A theoreti- 

 cal outer limit to this sphere has been defined, but an inner 

 limit has not been suggested. However, since the Moon 

 revolves in the theoretical determinate orbit for a satellite 

 of the Earth, and would not be stable in any other orbit 

 nearer to the Earth, it is plain that the Moon's present 

 orbit marks the inner limit of stable revolution. In an 

 earlier publication,^ I have called the space between 



''The Planetary System. Published privately in 1903. Chapter X; The 

 satellite zone; pages 131-141. 



