A theory of the Trojan asteroids

The paper constructs a long-periodic solution for the case of 11 resonance in the restricted problem of three bodies. The solution is smoothed by the exclusion of the internal resonant terms arising from the near-commensurability between the long and the short periods of the asteroid.Although the Brown (1911) conjecture regarding the termination of the family of the tadpoles at the Lagrangian pointL₃ is not supported by our analysis, the conjecture seems to hold in the limit asm0.