Rotational Dynamics of Viscoelastic Planets

Abstract

The rotation of the Earth is not regular. It changes on virtually every time scale we know in both position of the rotation axis and rotation rate. Even in our daily lives we sometimes experience the consequences of such changes, such as the second that is subtracted or added to clocks at the beginning of a new year. Although this second is not much more than a curiosity for most of us, the rotational changes it implies can influence our lives in a more fundamental sense. There are indications that the emergence of the great ice ages some two million years ago was triggered by a gradual shift of the rotation axis over the Earth’s surface, combined with wandering of the continents and associated changes in ocean currents (note that we are talking here about the onset of ice ages — the period of the 100,000 year cycles of ice build-up and decay is determined by astronomical causes). In the 19th century, both the rate of rotation and the position of the rotation axis were shown to be variable. Nowadays we know that these changes occur on all time scales: from shorter than a day to geological ones of hundreds of millions of years. The changes in position of the rotation axis can be divided into two main categories: those in which the position of the axis changes with respect to the distant stars but not with respect to the Earth’s surface, and vice versa. For the latter category, it looks to a hypothetical observer in space as though the Earth shifts underneath its rotation axis as a solid unit while the rotation axis itself remains fixed with respect to the stars, while for an observer on Earth it looks as though the rotation axis is wandering over the Earth’s surface. Displacements of the axis of rotation with respect to the fixed stars (changes in which the whole planet is moving rigidly as one unit) are mainly due to external forces, notably the gravitational interactions between the Earth and the Sun, the Moon and the other planets of the solar system. The astronomically well-known precession and nutation are examples of this. The external forces exert a net torque on the equatorial bulge of the Earth, as a consequence of which the rotation axis spins. The most important periods are about 26,000 years (precession) and 18.6 years (nutation)