  Recently, Rozelot & Eren pointed out that the first solar gravitational
moment (J2) might exhibit a temporal variation. The suggested explanation is
through the temporal variation of the solar rotation with latitude. This issue
is deeper developed due to an accurate knowledge of the long-term variations in
solar differential rotation regarding solar activity. Here we analyze solar
cycles 12-24, investigating the long-term temporal variations in solar
differential rotation. It is shown that J2 exhibits a net modulation over the
13 studied cycles of approximately (89.6 +- 0.1) yr, with a peak-to-peak
amplitude of approximately 0.1 x 10-7 for a reference value of 2.07 x 10-7).
Moreover, J2 exhibits a positive linear trend in the period of minima solar
activity (sunspot number up to around 40) and a marked declining trend in the
period of maxima (sunspot number above 50). In absolute magnitude, the mean
value of J2 is more significant during periods of minimum than in periods of
maximum. These findings are based on observational results that are not free of
errors and can be refined further by considering torsional oscillations for
example. They are comforted by identifying a periodic variation of the J2 term
evidenced through the analysis of the perihelion precession of planetary orbits
either deduced from ephemerides or computed in the solar equatorial coordinate
system instead of the ecliptic coordinate one usually used.
