ch the earth is changing states (orbits) is much slower than the speed with which the earth is traversing the orbits associated with these states. It takes centuries before a significant change in state (orbit) is observed. Hence, changes in the system's state occur on a time scale that is much slower than that of the earth's periodic revolution around the sun. It is therefore said that the revolution around the sun occurs on a fast- varying time scale while the earth's dynamic (state-changing) behavior occurs on a slow-varying time scale. Of course, from a human point of view, an oscillation with a period of a year isn't particularly fast. However, the words fast and slow must be inter- preted in the context of the system that is investigated. In the context of the evolution of our solar system, changes taking place in a year's time are to be considered very fast. In order to give a feeling as to the consequences of the perturbing force ef, we consider the impact of the joint forces exerted by the other planets in the solar system. As shown in Fig. 5.3, these forces induce a precession of the earth's orbit around the sun [Hest87]. The position of the earth's perihelion³ advances about 0.32° per century. One also observes periodic changes in the eccentricity of the earth's orbit, making it first more and then again less elliptical. These changes in the shape and position of the earth's orbit are called the Milankovitch cycles [Hays76]. These cycles have a period of about 100,000 years. They are of prime importance for glaciation and the occurrence 3 The perihelion is that point of the earth's orbit that is closest to the sun. 5.1 THE STORY BEHIND THE MATH 1 year Figure 5.4: The position of the perihelion of the earth's orbit as a function of time (solid line). This position is expressed as an angle with respect to some reference position. On average, we observe a steady increase (dotted line) with time. In addition, there is a small fast-varying fluctuation. state changing solve filter state changing filter state