Impact of the quadrupole moment of the Sun on the dynamics of the Earth-Moon system

Range of values of the Sun's mass quadrupole moment of coefficient J(2) ari sing both from experimental and theoretical determinations enlarge across l iterature on two orders of magnitude, from around 10(-7) until to 10(-5). T he accurate knowledge of the Moon's physical librations, for which the Luna r Laser Ranging data reach an outstanding precision level, prove to be appr opriate to reduce the interval of J(2) values by giving an upper bound of J (2). A solar quadrupole moment as high as 1.1 10(-5) given either from the upper bounds of the error bars of the observations, or from the Roche's the ory, is not compatible with the knowledge of the lunar librations accuratel y modeled and observed with the LLR experiment. The suitable values of J(2) have to be smaller than 3.0 10(-6). As a consequence, this upper bound of 3.0 10-6 is accepted to study the imp act of the Sun's quadrupole moment of mass on the dynamics of the Earth-Moo n system. Such an effect (with J(2) = 5.5 +/- 1.3 x 10(-6)) has been alread y tested in 1983 by Campbell & Moffat using analytical approximate equation s, and thus for the orbits of Mercury, Venus, the Earth and Icarus. The app roximate equations are no longer sufficient compared with present observati onal data and exact equations are required. As if to compute the effect on the lunar librations, we have used our BJV relativistic model of solar syst em integration including the spin-orbit coupled motion of the Moon. The mod el is solved by numerical integration. The BJV model stems from general rel ativity by using the DSX formalism for purposes of celestial mechanics when it is about to deal with a system of a extended, weakly self-gravitating, rotating and deformable bodies in mutual interactions. The resulting effects on the orbital elements of the Earth have been comput ed and plotted over 160 and 1600 years. The impact of the quadrupole moment of the Sun on the Earth's orbital motion is mainly characterized by variat ions of (Omega) over dot, (omega) over dot, and (E) over dot. As a conseque nce, the Sun's quadrupole moment of mass could play a sensible role over lo ng time periods of integration of solar system models.