Determination of an instantaneous Laplace plane for Mercury's rotation

Mercury is the target of two space missions: MESSENGER, which carried out its first and second flybys of Mercury on January 14, 2008 and October 6, 2008, and the ESA/JAXA space mission BepiColombo, scheduled to arrive at Mercury in 2020. The preparation of these missions requires a good knowledge of the rotation of Mercury. This paper presents studies performed by the MORE/ROMEO Team of BepiColombo mission. In particular, we show here an analytical study of the rotation of Mercury, and the determination of a suitable Laplace plane that can be considered as a reference inertial plane for the duration of the mission. Our main results are a prediction of the short-period perturbations that should be detected in the longitudinal rotational motion of Mercury, and an easy method to define an instantaneous Laplace plane taking into account the very small precession of Mercury's orbit. This plane is afterward chosen as constant reference plane. An estimation of the (small) error induced by this choice is also computed.