The force model for asteroid (3200) Phaethon

Asteroid (3200) Phaethon is an Apollo asteroid having very small (0.14 au) perihelion distance. We analyze the influence of various perturbing factors on the asteroid motion. Most of them were studied on the base of (O–C) residuals and/or the orbital evolution. This set of estimated perturbing accelerations contains: gravitational perturbations from all major planets, Pluto, the Moon, Ceres, Pallas, Vesta; the Earth, the Sun and Jupiter oblateness, the relativistic effects of the Sun and the solar radiation pressure. The perturbation estimation was done by five various methods. The purpose was to classify the perturbing accelerations as powerful, medium or weak ones, and the criteria for classification were built on the value of the mean accuracy of positional observations from the Earth. All five methods showed a good consistency. We found that the solar radiation pressure exerts a weak influence on the Phaethon motion, while the relativistic effects of the Sun and the Sun oblateness could be classified as medium perturbations. For the most complete and correct description of (3200) Phaethon motion we recommend to include gravitational influence from the planets and the Moon, the relativistic effects of the Sun and the Sun oblateness in the force model. Some other factors we considered separately. They are the recoil acceleration from the recurrent mass loss at perihelia, the Yarkovsky acceleration and relativistic effects of planets, Pluto and the Moon. It was obtained that their contributions to the total acceleration are negligible. We analyzed the next close encounter of Phaethon with the Earth in 2017 and found that neglecting gravitational perturbations from Neptune and Pluto, the Earth and Jupiter oblateness give an error less than 100 km in the asteroid position. Gravitational perturbations from the inner planets (including the Moon) and Jupiter are the strongest and neglecting one of them results in the asteroid position error 104–106 km