Long-Term Ephemerides for the Sun

Scope and Purpose

Due to the relative smooth and regular motion of the Earth around the Sun, compact long-term ephemeris data for the Sun can be compiled. This section describes how such tables can be constructed and also how they are used. These compact Sun Ephemeris may be used as a backup alternative if a regular Nautical Almanac is not available. The accuracy of the obtained GHA and Declination data is better than 2'. The effort to obtain the ephemeris data is higher compared to using a regular Almanac in which the data is recorded at integral hour intervals with an accuracy of 0.1' for both GHA and Declination.

Background

Time is experienced in the first place by the rotation of the Earth resulting in the day-night succession and in the second place by the orbiting of the Earth around the Sun manifesting itself primary in the succession of the different seasons over the year but also in the changing star constellations at night. Unfortunately there is no direct relationship between the two time periods of one day and one year. For the Earth, it takes about 365.25 rotations to arrive at the same point on it's orbit around the Sun.

To make things more complicated, the duration of a true solar day varies in length over the course of a year. This became already obvious in ancient times as people tried to keep track of time with mechanical instruments such as wax candles, water clocks or pendulum clockworks. Mechanical timekeeping requires a constant time flow and thus a constant length of a day. This resulted in the development of the concept of a Mean Solar Day in contrast to the True Solar Day. A Mean Solar Day has a fixed duration of about 365th of the orbit period. The difference between Mean Solar day and True solar day is the Equation-of-Time (EoT). The value for the EoT varies in a range or ±16 min or in a range of ±4° expressed in degrees. Expressed in time, the EoT indicates the time difference between Noon based on Mean Solar time and True Solar Noon as shown by a sun dial.

Construction of the Tables

The main table, from which the primary ephemeris information is obtained, is based on the values of the Equation-of-Time and Declination of the Sun recorded for the beginning of each day (00:00 hour) over one year. This main table is constructed for a reference year, which may be chosen at about half of the required time range. The data for the other years is obtained by entering the main table with a slightly adjusted time called Orbit Time. This time adjustment or hour offset (in integral hours) is obtained from table (a) at the entry for the year of interest.
From one year to the next year, the time adjustment decrements by about 6 hours to flip forward by about 24 hours in the course of a leap year. For a leap year two time adjustment values are in place. The first value is valid for the first two months including the 29th of February. The second value is valid from March till the end of the year.

The other tables (b), (c) and (d) are used to interpolate the data obtained from the main table.

Explanation of the Tables

The time correction of table (a) is the time difference compared to the GMT of the reference year, needed to obtain the same E and Dec data as recorded for the reference year. With this correction the Orbit Time is obtained, which is the adjusted GMT time required to enter the fundamental table.

Precession

The axis of the Earth is undergoing a precessional motion similar to that of a top spinning with its axis tilted. In about 25800 years the axis completes a cycle and returns to the position from which it started. Since the celestial equator is 90° from the celestial poles, it too is moving. The result is a slow westward movement of the equinoxes and solstices, which has already carried them about 30°, or one constellation, along the ecliptic from the positions they occupied when named more than 2000 years ago. Since sidereal hour angle is measured from the vernal equinox, and declination from the celestial equator, the coordinates of celestial bodies would be changing even if the bodies themselves were stationary. This westward motion of the equinoxes along the ecliptic is called precession of the equinoxes. The total amount, called general precession, is about 50 seconds of arc per year. It may be considered divided into two components: precession in right ascension (about 46.10 seconds per year) measured along the celestial equator, and precession in declination (about 20.04" per year) measured perpendicular to the celestial equator. The annual change in the coordinates of any given star, due to precession alone, depends upon its position on the celestial sphere, since these coordinates are measured relative to the polar axis while the precessional motion is relative to the ecliptic axis.
Due to precession of the equinoxes, the celestial poles are slowly describing circles in the sky. The north celestial pole is moving closer to Polaris, which it will pass at a distance of approximately 28 minutes about the year 2102. Following this, the polar distance will increase, and eventually other stars, in their turn, will become the Pole Star. The precession of the Earth’s axis is the result of gravitational forces exerted principally by the Sun and Moon on the Earth’s equatorial bulge. The spinning Earth responds to these forces in the manner of a gyroscope. Regression of the nodes introduces certain irregularities known as nutation in the precessional motion.