earth's sphere of gravitative control 213 



In a complete analysis, the gravitative influence of a planet extends 

 indefinitely outward — at least in Newtonian dynamics — but at a certain 

 point the dominance of gravitative influence, in any given sense, passes 

 from the planet to some neighboring body or assemblage of bodies, and 

 so the phrase "sphere of control" seems preferable, as it carries its defini- 

 tion on its face. The control is not absolute or unqualified ; it is usually 

 subordinate to a higher control. It usually relates only to the immediate 

 control over bodies that have like motions, as when larger and smaller, 

 masses are moving about the sun in much the same way, the larger con- 

 trols the immediate movements of the smaller within its sphere of con- 

 trol, though the motions of both are controlled by the sun. This is merely 

 a generalization of Moulton's concrete definition, "the area within which 

 a planet can control a satellite." ^ The relationship is a relative one, and 

 there are some refinements of definition that need not embarrass us here. 

 The special conditions of any particular case must, of course, be recog- 

 nized in treating it. All that is important here is the essential concept 

 of the sphere of control and a realization of its functions in the life of 

 the body under study. 



The sphere of control of the earth is its dynamic domain. It forms 

 the truest and best delimitation of the earth as an organized body and as 

 a subject of study. It is the most distinctive feature of the greater earth. 

 It embraces more than five million times the space occupied by the ma- 

 terial earth. But the greater earth is really not so much this outlying 

 invisible part as it is the whole combination, the physical center supple- 

 mented by the outreaching d3aiamic domain. In ultimate analysis, the 

 material and the dynamic portions are, perhaps, only different phases of 

 the same ultimate entity, whatever that may be. At any rate, we know 

 of no way by which the two can be separated in our present state, though 

 we must treat them as more or less distinct. We have come here to ex- 

 change the products of our dynamic personalities; but we brought our 

 bodies with us; if we had not, I fear the value of our merely dynamic 

 efforts would have been negligible. 



Diagram I is introduced to illustrate the general relations of the sphere 

 of control of the earth to the sun. It is to be understood that the sun's 

 sphere of influence envelops the whole and stretches far beyond the limits 

 of the diagram. On the scale here used, the solid earth is a mere dot; 

 the small circle embracing it is the orbit of the moon, while the sphere of 

 control is outlined by the oval that embraces both these. At the left the 

 sun is represented on the same scale as the earth's sphere of control. The 

 volume of the latter is somewhat more than twice that of the sun. The 



' The spheres of activity of planets. Popular Astronomy, no. 60, 1899. 

 XV— Bull, Geol. Soc. Am., Vol. 32, 1920 



