Celestial mechanical simulations from a purely classical point of view of the solar system, including our Moon and the Mars moons - Phobos and Deimos - are carried out for 2 millions of years before present. Within the classical approximation, the results are derived at a very high level of accuracy. Effects from general relativity for a number of variables are investigated and found to be small. For climatic studies of about 1 Myr, general relativity can safely be ignored. Three different and independent integration schemes are used in order to exclude numerical anomalies. The converged results from all methods are found to be in complete agreement. For verification, a number of properties such as spin axis precession, nutation, and orbit inclination for Earth and Mars have been calculated. Times and positions of equinoxes and solstices are continously monitored. As also observed earlier, the obliquity of the Earth is stabilized by the Moon. On the other hand, the obliquity of Mars shows dramatic variations. Climatic influences due to celestial variables for the Earth and Mars are studied. Instead of using mean insolation as in the usual applications of Milankovitch theory, the present approach focuses on the instantaneous solar radiation power (insolation) at each summer solstice. Solar radiation power is compared to the derivative of the icevolume and these quantities are found to be in excellent agreement. Orbital precessions for the inner planets are studied as well. In the case of Mercury, it is investigated in detail.