Explicit formulae for the two way time-transfer in the T2L2 experiment including the J2 contribution to the Earth potential in a relativistic framework

The topic of this paper is to study the two way time-transfer problem between a ground based station and a low orbit Earth's satellite, in the aim of an application to the T2L2 experiment. The sudy is driven in a fully relativistic framework. Because of the rapid increase in clock's precision/measurements, the first term beyond the Earth's potential monopolar term is explicitly taken into account. Explicit formulae, for both the distance and offset problems (definitions in the text) are proposed for the relevant applications.