Stationary configurations for co-orbital satellites with small arbitrary masses

We derive general results on the existence of stationary configurations for N co-orbital satellites with small but otherwise arbitrary masses m(i), revolving on circular and planar orbits around a massive primary. The existence of stationary configurations depends on the parity of N. If N is odd, then for any arbitrary angular separation between the satellites, there always exists a set of masses ( positive or negative) which achieves stationarity. However, physically acceptable solutions (m(i) > 0 for all i) restrict this existence to sub-domains of angular separations. If N is even, then for given angular separations of the satellites, there is in general no set of masses which achieves stationarity. The case N = 3 is treated completely for small arbitrary satellite masses, giving all the possible solutions and their stability, to within our approximations.