sphere of influence

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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 colonizationcolonization,
extension of political and economic control over an area by a state whose nationals have occupied the area and usually possess organizational or technological superiority over the native population.
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, 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 sovereigntysovereignty,
supreme authority in a political community. The concept of sovereignty has had a long history of development, and it may be said that every political theorist since Plato has dealt with the notion in some manner, although not always explicitly.
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 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 protectorateprotectorate,
in international law, a relationship in which one state surrenders part of its sovereignty to another. The subordinate state is called a protectorate. The term covers a great variety of relations, but typically the protected state gives up all or part of its
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. 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.

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 ρp and the equatorial radius ρe 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 pe = 1.15 pp 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
Planetρ(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.

References in periodicals archive ?
Realism, spheres of influence, and an alliance of all states against the Fourth Generation comprise the policy prudence recommends.
The spheres of influence concept is usually identified with both realist and neorealist theories of international relations (IR), which argue that nation-states seek to maximize their power.
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Palmer said in a statement that he was disappointed the cities would act now on the spheres of influence, without considering the benefits of Las Lomas to the region.
The company's Spheres of Influence Contest asks businesses, organizations, and individuals to submit an entry that communicates the one idea in the company's new report that inspired them the most and then shows how they would use the $5,000 grand prize to carry that idea out into the world.
When it comes to logical spheres of influence under state law .
The founding in 2003 of GMAI-Auctentia has meant the culmination of an entire professional journey, given concrete representation over the years through the creation of and participation in numerous companies which have positioned themselves as authentic leaders in their respective spheres of influence and activity.
Speaking to a gathering at Witwatersrand University, Christopher said, ``The time has passed when Africa could be carved into spheres of influence, or when outside powers could view whole groups of states as their private domain.
Jean Delaney Nelson, vice president and chief information officer, Minnesota Life, was named to a list of 25 Twin Cities businesswomen who are credited for effecting change in their spheres of influence.
As we move from MOB (maintenance of benefits) concepts to managed benefits with deductible, coinsurance and copay by employees we must know where the spheres of influence are concentrated.
We are happy to work together with Sun and incorporate the key strengths both parties have in their respective markets and spheres of influence.