Sphere of Influence

sphere of influence, term formerly applied to an area over which an outside power claims hegemony with the intention of subsequently gaining more definite control, as in colonization, or with the intention of securing an economic monopoly over the territory without assuming political control. A sphere of influence was usually claimed by an imperialistic nation over an underdeveloped or weak state that bordered an already existing colony. The expression came into common use with the colonial expansion of European powers in Africa during the late 19th cent. A sphere of influence was formalized by treaty, either between two colonizing nations who agreed not to interfere in one another's territory, or between the colonizing nation and a representative of the territory. Theoretically, the sovereignty of a nation was not impaired by the establishment of a sphere of influence within its borders; in actuality, the interested power was able to exercise great authority in the territory it dominated, and if disorders occurred it was in a position to seize control. Thus the creation of spheres of influence was frequently the prelude to colonization or to the establishment of a protectorate. The term in this sense is no longer recognized in international law, however. Currently, it is used by the more powerful nations of the world to denote the exclusive or predominant interest they may have in certain areas of the globe, especially for the purposes of national security.

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sphere of influence

In international politics, a state's claim to exclusive or predominant control over a foreign area or territory. Beginning in the late 1880s, European colonial powers undertook legal agreements consisting of promises not to interfere with each other's actions in mutually recognized spheres of influence in Africa and Asia. After colonial expansion ceased, geopolitical rather than legal claims to spheres of influence became common, examples being the U.S. claim to dominance in the Western Hemisphere under the much-earlier Monroe Doctrine and the Soviet Union's expansion of its sphere of influence to eastern Europe following World War II. See also Iron Curtain.

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Sphere of Influence 

The sphere of influence of a celestial body is the region in space where the gravitational attraction of the body predominates over the attraction of all other celestial bodies. The concept can be defined more precisely according to the particular problem being considered. In studying the motion of comets outside the solar system, for example, the sun’s sphere of influence is taken as the region in which the forces of attraction of the stars are so small in comparison with the attractive force of the sun that they can be neglected. In investigating the motion of comets, other small bodies, and space probes inside the solar system, the spheres of influence of the planets are considered.

If a small body is located within the sphere of influence of a planet, it is useful to study the body’s motion in a coordinate system associated with the planet; the effect of the sun’s attraction is treated as a perturbation (seeCELESTIAL MECHANICS). The sphere of influence of a planet is found by disregarding the attraction of the other planets and is the region in which F₁/R₁ < F/R. Here, R is the acceleration imparted by the sun to a body in heliocentric motion (motion referred to the center of the sun), F is the perturbing acceleration introduced into the body’s motion by the attraction of the planet, R₁ is the acceleration imparted by the planet to a body in planetocentric motion, and F₁ is the perturbing acceleration introduced into this motion by the attraction of the sun. Outside the planet’s sphere of influence, it is more useful to regard heliocentric motion as primary.

The surface bounding the sphere of influence of a planet is close in shape to a spheroid. The center of the spheroid coincides with the center of the planet, and the spheroid’s polar axis is directed toward the sun. The polar radius ρ_p and the equatorial radius ρ_e of the spheroid are given by the equations

where r is the radius vector of the planet and m is the planet’s mass divided by the mass of the sun. Since p_e = 1.15 p_p and r varies only slightly, the sphere of influence of the planet is in practice regarded as a planetocentric sphere with the radius

where a is the semimajor axis of the planet’s orbit.

Table 1. Spheres of influence of the planets
Planet	ρ(AU)
Mercury ...............	0.001
Venus ...............	0.004
Earth ...............	0.006
Mars ...............	0.004
Jupiter ...............	0.322
Saturn ...............	0.364
Uranus ...............	0.346
Neptune ...............	0.580

Table 1 gives the value of ρ in astronomical units (AU) for all the planets except Pluto. For Pluto, ρ = 0.22. Because, however, of the considerable variation in the radius vector r of Pluto, the radius of the sphere of influence varies from 0.18 to 0.30 AU.

In analyzing the motion of space vehicles heading toward the moon, the concept of the sphere of influence of the moon is used. The sphere of influence of the moon is defined in much the same way as that of a planet. In this case, the influences of the earth and the moon on the space vehicle are compared. The value of ρ for the sphere of influence of the moon is approximately 66,000 km.