Accurate determination of the successive moments of the sun: a new window open on the sun's interior

Despite its great importance for solar physics, mainly in the fields of solar fundamental astrometry, helioseismology, planetary motions and relativistic effects, the successive zonal harmonics of the Sun still remain elusive and subject to some controversy. Direct observations from the ground suffer from atmospheric effects and are not of enough accuracy. Up to now, space flights (SOHO) or balloon missions give consistent data but lead to spurious results due to the noise. As far as indirect observations are concerned, the more precise determination of the successive moments (mainly J₂, J₄ and even J₆), will be provided unambiguously by the study of the orbit of a spacecraft flying close to the Sun or around Mercury. This has been scheduled, but not yet achieved. In this paper we will first emphasize why it is important to know the successive zonal harmonics of the Sun with a high accuracy. We will show how their precise knowledge permits to obtain informations on the Sun's interior, mainly the shear's regions (tacholine or leptocline). Then we will give an up-to-date review of both theories (including the heliosismology approach) and data. We will explain some of the difficulties, mainly due to the differential rotation and we will give an insight of what the PICARD's mission will bring in that field. Then we will propose a novel concept for a Sun's mission, which would lead to the most accurate determination of the successive solar moments (that could be part of another project), and thus opening a new window on the Sun's interior.