Insolation and Earths Orbital Periods

Solar irradiance received on a horizontal surface depends on the solar output, the semimajor axis of the elliptical orbit of the Earth around the sun (a), the distance from the Earth to the sun (r), and the zenith distance (z). The spectrum of the distance, r, for a given value of the true longitude, lambda, displays mainly the precessional periods and, with much less power, half precession periods, eccentricity periods, and some combination tones. The zenith distance or its equivalent, the elevation angle (E), is only a function of obliquity (epsilon) for a given latitude, phi, true longitude, and hour angle, H. Therefore the insolation at a given constant value of z is only a function of precession and eccentricity. On the other hand, the value of the hour angle, H, corresponding to this fixed value of z varies with epsilon, except for the equinoxes, where H corresponding to a constant z also remains constant through time. Three kinds of insolation have been computed both analytically and numerically: the instantaneous insolation (irradiance) at noon, the daily irradiation, and the irradiations received during particular time intervals of the day defined by two constant values of the zenith distance (diurnal irradiations). Mean irradiances (irradiations divided by the length of the time interval over which they are calculated) are also computed for different time intervals, like the interval between sunrise and sunset, in particular. Examples of these insolations are given in this paper for the equinoxes and the solstices. At the equinoxes, for each latitude, all insolations are only a function of precession (this invalidates the results obtained by Cerveny [1991)). At the solstices, both precession and obliquity are present, although precession dominates for most of the latitudes. Because the lengths of the astronomical seasons are secularly variable (in tenus of precession only), a particular calendar day does not always correspond to the same position relative to the sun through geological time. Similarly, a given longitude of the Sun on its orbit does not correspond to the same calendar day. For example, 103 kyr ago, assuming arbitrarily that the spring equinox is always on March 21, autumn began on September 13, and 114 kyr ago, it began on September 27, the length of the summer season being 85 and 98 calendar days, respectively, at these remote times in the past