Sphere of influence

The sphere of influence, or SOI, indicates the spherical space around a celestial body in which it has sole gravitational influence on a craft, Kerbal, or other object. This differs from real-world physics in which gravitational forces from multiple bodies may simultaneously have significant effects on an object.

This decision by the game developers at Squad allows simplifying the n-body problem to a one-body problem. In addition to giving predictability to contouring trajectories of an object in flight, it is easier for the player to understand. Although the two-body problem is also solvable, it isn't used in Kerbal Space Program because the orbits of the celestial bodies can't be changed.

One-body problem

Kerbal Space Program defines around each celestial body of the Kerbol System a spherical area in which this celestial body is the only body whose attraction has any influence on objects in flight. The trajectory is thus almost completely predictable.

All spheres of influence are arranged in a hierarchy to determine what SOI an object is currently in. Simplified the order is moons, then planets or dwarf planets, and lastly Kerbol's sphere of influence. If a craft is orbiting a moon it will be in the moon's sphere of influence and any gravitational influence by the planet or Kerbol will be ignored.

More complicated or generically said the object will always be in the most deepest sphere of influence. All bodies are in Kerbol's sphere of influence, so each planet's sphere of influence is within Kerbol's. If a craft would be in multiple spheres of influence, it is always in that sphere of influence which doesn't contain other spheres of influences the craft is in. So if a craft is for example orbiting Mun it is also in Kerbin's and Kerbol's spheres of influence. But is only in the Mun's sphere of influence, because when it would be in another sphere of influence there would be at least one sphere of influence – the Mun's – in that.

Furthermore, planets and moons orbit on predefined paths around their higher-order bodies. Physics calculations are not performed on celestial bodies, nor can forces be applied to them; they move on tracks such as-is.

N-body problem

From each body with mass, a mutual attractive force, gravitation comes from. In reality, gravitational fields are essentially infinite in distance though field strength decreases exponentially with distance. Nevertheless, the attraction affects every object's motion.

An example of a three-body system is the Earth-Moon system with the Sun. Each object in the vicinity is influenced by the attractions of these three celestial bodies, all of which influence trajectories differently as the object moves relative to each. The calculation of such trajectories is very complex; results generally are only approximate.

Two-body problem

The two-body problem is basically a simplified version of the n-body problem. Each body pair is observed which then orbits around their common center of mass, barycenter. For example a moon would not orbit the center of the planet which would result in a small orbit of the planet.

Effects

These simplifications result in particular trajectories, such as Lagrange points, not existing in-game.

Furthermore, trajectories have consistent curvatures because they can not be disturbed by changing amounts of influence while travelling relative to multiple bodies. Otherwise a supposedly stable trajectory could suddenly, after some time, turn out to be unstable and crash a rocket on a celestial body or be catapulted out of the system. This is because the game has to constantly check if which sphere of influence the craft is. If that change is not detected fast enough it might be skipping the change completely and the craft is not entering the sphere of influence. It might as well be deep inside the other sphere of influence which results in incorrect orbital parameters, because the object followed the trajectory around the parent body.

Trivia

• For the moons Mun, Tylo, Vall and Laythe, the SOIs are smaller than the semi-major axes of their synchronous orbit. Hence, synchronous orbits over these moons are not possible.
• Despite the exact solvability of all path equations, calculating them in-game gives unexpectedly changing and struggling trajectories. This is due to the technical limits of inaccuracy with floating point values in the computer.

Gallery

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  changes the trajectory by changing spheres of influence (SOIs)

See also

• Sphere of influence on Wikipedia