An upgraded theory for Helene, Telesto, and Calypso

A tridimensional model including the perturbation due to Saturnʹs oblateness provides accurate solutions for the motions of Tethys and Dione ʹs Lagrangian satellites Telesto , Calypso, and Helene. Expanded around the Lagrangian points and compared to numerical simulations to check their reliabilities, the solutions are fitted to almost twenty years of data thanks to recently published observations. User-friendly compact series give Telesto, Calypso , and Heleneʹs positions and velocities in the mean ecliptic and equinox of J2000.