Planetary influence increases as the population on the planet grows. The influence is further modified by Race bonuses, technology, mining starbases (mining influence), planetary improvements, and universal effects (minus for xenophobes, positive for xenofiles). As the influence of a planet grows, so does the area the influence affects. The strength of influence lowers as distance increases until it drops off to zero.
Starbases have a static area of influence in that the circle generated does not grow over time as with planets. Economy, military, and mining starbases (except influence mining) have a minimal amount of influence which is enough to claim empty space but is easily overwhelmed if in enemy territory. Influence starbases and influence mining starbases grow in strength, but not size. Thus, a fully developed influence starbase will strongly affect anything within its range, but the range does not increase.
For any given sector, influence is summed for each race affecting that square. The race with the highest total is granted ownership. Planets and starbases within influence of another civilization are still owned by the original owner. However, planets under heavy influence may eventually revolt and switch allegiance to the stronger force.
Planets may start to revolt when the total influence applied to the planet from foreign sources exceeds four times that of friendly influence on the planet. With a low espionage, you can see how much influence an enemy planet generates and the ratio of foreign influence on it. The number in parentheses is the ratio, and over 1.00, the planet is considered in foreign territory. Over 4.00, and a pirate sign appears on the planet, signalling it is in revolt. Each turn, a planet in revolt may flip allegiance to the foreign influence. A higher influence ratio may increase the chance of flipping, while a high loyalty by the citizens (and possibly high approval?) will reduce the chance.
distance equation: ?