Secular variation
The secular variation of a time series is its long-term, non-periodic variation. Whether a variation is perceived as secular or not depends on the available timescale: a variation that is secular over a timescale of centuries may be a segment of what is, over a timescale of millions of years, a periodic variation. Natural quantities often have both periodic and secular variations. Secular variation is sometimes called secular trend or secular drift when the emphasis is on a linear long-term trend.
The term is used wherever time series are applicable in history, economics, operations research, biological anthropology, and astronomy such as VSOP .
Etymology
The word secular, from the Latin root saecularis, has two basic meanings: I. Of or pertaining to the world, and II. Of or belonging to an age or long period. The latter use appeared in the 18th century in the sense of "living or lasting for an age or ages". In the 19th century terms like secular acceleration and secular variation appeared in astronomy, and similar language was used in economics by 1895.Astronomy
In astronomy, secular variations are distinguished from periodic phenomena. In particular, astronomical ephemerides use secular to label the longest duration or non-oscillatory perturbations in the motion of planets, contrasted with periodic perturbations which exhibit repetition over the course of a given time frame. In this context it is referred to as secular motion. Solar System ephemerides are essential for the navigation of spacecraft and for all kinds of space observations of the planets, their natural satellites, stars and galaxies.Most of the known perturbations to motion in stable, regular, and well-determined dynamical systems tend to be periodic at some level, but in many-body systems, chaotic dynamics result in some effects which are unidirectional.
Solar System
Secular phenomena create variations in the orbits of the Moon and the planets. The solar emission spectrum and the solar wind follow secular trends due to migration through the galactic plane. Consensus has determined these to have been among the smallest of factors to influence climate and extinction during human evolution, dwarfed by complex solar cycles and magnetic cycles.Moon
The secular acceleration of the Moon depends on tidal forces. It was discovered early but it was some time before it was correctly explained.Earth
Depending on the time frame, perturbations can appear secular even if they are actually periodic. An example of this is the precession of the Earth's axis considered over the time frame of a few hundred or thousand years. When viewed in this timeframe the so-called "precession of the equinoxes" can appear to be a secular phenomenon since the axial precession takes years. Thus monitoring it over a much smaller timeframe appears to simply result in a "drift" of the position of the equinox in the plane of the ecliptic of approximately one degree per 71.6 years, influencing the Milankovitch cycles.Planets
Secular variation also refers to long-term trends in the orbits of all of the planets. Several attempts have from time to time been undertaken to analyze and predict such gravitational deviations for planets, observing ordinary satellite orbits. Others are referred to as post-keplerian effects.Variations Séculaires des Orbites Planétaires is a modern numerical model that tries to address the problem.