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 n-body problems to one-body problems. In addition to giving predictability to contouring behavior of a craft in flight, it is easier for the player to understand.

N-body problem

From each body with mass, a mutual attractive force 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 Sol (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.

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 completely predictable.

The spheres of influence in the game have been set by hand and the diameters of these gravitational spheres may not follow a single consistent rule based on the mass of the celestial body.

All spheres of influence are arranged in a hierarchy to determine what SOI an object is currently in. The order is Sun < Planet < Moon. So when an object is within the SOI radius of the moon, the forces of the planet and the sun will be ignored, even when the object is also within the SOI of a higher-order body.

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.

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.

Trivia

• For the moons Mun, Tylo, Vall and Laythe, the SOIs are smaller than the radius of their geosynchronous orbit. Hence, geosynchronous 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

<gallery> File: SOI.jpg | changes the trajectory by changing spheres of influence (SOIs) </ Gallery>