Collision between Satellites in Stationary Orbits

The collisions between stationary satellites, and those between a stationary satellite and abandoned stationary satellites which have nearly synchronous orbits with relatively large inclination are discussed. A general formula is introduced for calculating the probability of collision, as a function of time, three-dimensional sizes, orbital bounds, and numbers of satellites. Numerical calculation shows that the probability of collision is negligible if the sizes and numbers are comparable to those of existing satellites, whereas collision is possible for larger size, e.g., for a huge hypothetical gigawatt solar power satellite. The possibility would become large if the satellites continued to increase in number and to be abandoned in the stationary orbit at the present rate over a century, even if the size is ordinary, such as several meters.