What is SO important about finding all possible orbits (states)? Isn't it sufficient to just identify the one that the earth is currently tracking? No, it isn't! The fact that the earth is, for example, currently tracking orbit A (see Fig. 5.2) does not imply that it will do SO forever. Impact of a meteorite or any other external influence may drive the earth from orbit A to orbit B. Since orbit B is a valid solution to the unperturbed equation of motion, the earth would be perfectly happy on this second orbit and would make no attempt to return to the original orbit A. External influences can hence drive the core system from one state to another. When the external influences persist, this process continues, driving the earth, for instance to a third orbit (state) C. The state-changing behavior discussed above represents the basic idea underlying os- cillator perturbation analysis. Due to a small but non-zero E in (5.2), the equation of motion, and therefore the earth's behavior, slightly deviates from that of the unper- turbed core system. This can be dealt with by considering the perturbing force term ef The same holds for all parabolas and hyperbolas. 5.1.3 Perturbed system behavior: changes in the earth's orbit perihelion 0.32%/century earth Figure 5.3: The joint forces exerted by the other planets in the solar system cause, amongst others, a precession of the earth's orbit around the sun. The position of the perihelion advances about 0.32° per century. as an external influence that drives the core system from one state (orbit) to another. In Fig. 5.2, ef causes the earth, for instance, to change from state (orbit) A to state (orbit) B. Since ef is small, the equations that govern this state-changing behavior can be extracted using perturbation series expansion techniques [Kev81]. These equations describe how the characteristics of the earth's elliptic orbit, like plane of revolution and eccentricity, change over time. The smallness of the perturbing force ef has another important consequence: the rate at whi