What is "sphere of influence"

n. The area (literal or figurative) influenced by a country, person, etc.

n. the geographical area in which one nation is very influential [syn: sphere]

In the field of international relations, a sphere of influence (SOI) is a spatial region or concept division over which a state or organization has a level of cultural, economic, military, or political exclusivity, accommodating to the interests of powers outside the borders of the state that controls it.

While there may be a formal alliance or other treaty obligations between the influence and influencer, such formal arrangements are not necessary and the influence can often be more of an example of soft power. Similarly, a formal alliance does not necessarily mean that one country lies within another's sphere of influence. High levels of exclusivity have historically been associated with higher levels of conflict.

In more extreme cases, a country within the "sphere of influence" of another may become a subsidiary of that state and serve in effect as a satellite state or de facto colony. The system of spheres of influence by which powerful nations intervene in the affairs of others continues to the present. It is often analyzed in terms of superpowers, great powers, and/or middle powers.

For example, during the height of its existence in World War II, the Japanese Empire had quite a large sphere of influence. The Japanese government directly governed events in Korea, Vietnam, Taiwan, and parts of China. The " Greater East Asia Co-Prosperity Sphere" could thus be quite easily drawn on a map of the Pacific Ocean as a large "bubble" surrounding the islands of Japan and the Asian and Pacific nations it controlled.

Sometimes portions of a single country can fall into two distinct spheres of influence. In the colonial era the buffer states of Iran and Thailand, lying between the empires of Britain/ Russia and Britain/ France respectively, were divided between the spheres of influence of the imperial powers. Likewise, after World War II, Germany was divided into four occupation zones, which later consolidated into West Germany and East Germany, the former a member of NATO and the latter a member of the Warsaw Pact.

The term is also used to describe non-political situations, e.g., a shopping mall is said to have a sphere of influence which designates the geographical area where it dominates the retail trade.

A sphere of influence (SOI) in astrodynamics and astronomy is the oblate-spheroid-shaped region around a celestial body where the primary gravitational influence on an orbiting object is that body. This is usually used to describe the areas in the Solar System where planets dominate the orbits of surrounding objects (such as moons), despite the presence of the much more massive (but distant) Sun. In a more general sense, the patched conic approximation is only valid within the SOI.

The general equation describing the radius of the sphere r of a planet:

$r_{SOI} \approx a\left(\frac{m}{M}\right)^{2/5}$

where

a is the semimajor axis of the smaller object's (usually a planet's) orbit around the larger body (usually the Sun). m and M are the masses of the smaller and the larger object (usually a planet and the Sun), respectively.

In the patched conic approximation, once an object leaves the planet's SOI, the primary/only gravitational influence is the Sun (until the object enters another body's SOI). Because the definition of r relies on the presence of the Sun and a planet, the term is only applicable in a three-body or greater system and requires the mass of the primary body to be much greater than the mass of the secondary body. This changes the three-body problem into a restricted two-body problem.

The sphere of influence is a region around a supermassive black hole in which the gravitational potential of the black hole dominates the gravitational potential of the host galaxy. The radius of the sphere of influence is called the "(gravitational) influence radius".

There are two definitions in common use for the radius of the sphere of influence. The first is given by

$r_h = \frac{GM_{\rm BH}}{\sigma^2}$

where M is the mass of the black hole, σ is the stellar velocity dispersion of the host bulge, and G is the gravitational constant.

The second definition is the radius at which the enclosed mass in stars equals twice M, i.e.

$M_\star(r<r_h) = 2 M_{\rm BH}$.

Which definition is most appropriate depends on the physical question that is being addressed. The first definition takes into account the bulge's overall effect on the motion of a star, since σ is determined in part by stars that have moved far from the black hole. The second definition compares the force from the black hole to the local force from the stars.

It is a minimum requirement that the sphere of influence be well resolved in order that the mass of the black hole be determined dynamically.

Sphere of influence may refer to:

• Sphere of influence (astrodynamics), the area, typically spherical, around a celestial body, e.g. a star, in which that body is the biggest gravitational influence
• Sphere of influence (black hole), a region around a black hole in which the gravitation of the black hole dominates that of the host bulge
• Sphere of influence, an area or region over which a state or organization has significant cultural, economic, military or political influence
• Sphere of influence is also a legal term in family law. A child can only be emancipated in some states when he or she goes outside of the sphere of influence of the parents, e.g. no longer needs their financial support.
• Sphere of Influence, a Japanese rapper
• Nobunaga's Ambition: Sphere of Influence, a 2013 Japanese turn-based strategy video game