A relativistic orbit model for the LISA mission to be used in LISA TDI simulators

The LISA mission is an interferometer, formed by three spacecraft, that aims at the detection of gravitational waves in the [10(-4),10(-1)] Hz frequency band. Present LISA TDI simulators, aimed at validating the novel Time Delay Interferometry method, use a classical Keplerian orbit model at first order in eccentricity in the gravitational field of a spherical non-rotating Sun, without planets. We propose to use the same model but described in the framework of relativistic gravity, and we focus here on quantifying the differences between classical and relativistic orbits for the LISA spacecraft, under the same assumptions.