h around the sun. As is the case for an electronic oscillator, the earth's motion contains a periodic fast-oscillating component: its elliptic motion around the sun. Here, "fast" implies a time scale of the order of a year. Due to small perturbations in the solar system's gravi- tational field, the shape and period of the earth's elliptic orbit slowly change over time. Here, slow indicates a time span of ten-thousands of years. These slow-varying changes are governed by mechanisms similar to the ones that govern the transient dynamics of an electronic oscillator's amplitude and phase. As such, the same mechanisms that govern an oscillator's phase noise behavior caused the ice ages. 5.1.1 Earth: a big oscillator One of the first oscillations ever to be studied in depth is the earth's motion around the sun. The modern point of view on this subject started with the work of Copernicus (1543), Kepler (1609), Galilei (1616) and Newton (1687). Lagrange (1784), Laplace (1799) and Poincaré (1892) made important contributions to the topic, for example, on the use of perturbation series techniques. Fig. 5.1 shows the problem setup for computing the earth's trajectory around the sun. Gravity attracts the earth towards the sun with a force that is inversely proportional to the square of the distance of separation r. However, the presence of other planets, the non-spherical shape of both the sun and the earth and some other effects introduce an additional but small force component ef (r,t). The total force exerted on the earth therefore equals F(r,1,e)= (5.1) Here, r is the unit vector pointing from the earth to the sun while r = rr. Furthermore, E denotes a small number indicating that the second term in (5.1) is, typically, much smaller than the first component. The term ef (r,t) is, therefore, called a perturbation term. Given the driving force (5.1), the earth's motion can now be solved from (5.2) 5.1.2 Unperturbed system behavior: neglecting small forces ef(r,t) earth Figure 5.1: Gravity attracts the earth towards the sun