The motion of the Solar System is chaotic to the extent that the precise positions of the planets are predictable for a period of only about 20 Myr (ref. 1). The Earth’s precession, obliquity and insolation parameters over this time period(1-6) can be influenced by secular variations in the dynamic ellipticity of the planet which are driven by long-term geophysical processes, such as post-glacial rebound(5,7-10). Here we investigate the influence of mantle convection on these parameters, We use viscous flow theory to compute time series of the Earth’s dynamic ellipticity for the past 20 Myr and then apply these perturbations to the nominal many-body orbital solution of Laskar et al.(5). We find that the convection-induced change in the Earth’s flattening perturbs the main frequency of the Earth’s precession into the resonance associated with a secular term in the orbits of Jupiter and Saturn(5), and thus significantly influences the Earth’s obliquity. We also conclude that updated time series of high-latitude summer solar insolation diverge from the nominal solution for periods greater than the past similar to 5 Myr. Our results have implications both for obtaining precise solutions for precession and obliquity and for procedures that adopt astronomical calibrations to date sedimentary cycles and climatic proxy records.