## Long-Term Solar AlmanacPre-requisite for Celestial Navigation is the availability of some basic almanac data. For an Earth-bound observer the apparent motion of the Sun and the stars are closely related to civil time and seasons. This allows to compile compact long-term (10 years and more) almanac data which are accurate enough to make them suitable for rough navigation. An appropriate version of such an almanac can easily be kept in the sextant box. ## The Motion of the Earth
The apparent motion of the Sun originates from two independent motions of the Earth in space:
the spinning of the Earth on it's axis of rotation and the orbiting of the Earth around the Sun.
Roughly speaking, the spinning of the Earth is related to time through the day, whereas
the date through the year is related to the orbiting around the Sun.
Since ancient times it is known that the periodicity of these two basic motions have no
common factor and the quest to keep a certain synchronism between (solar) time and date led to
the science of calender making.
Today this synchronism is arranged through the concept of leap days (rough adjustment) and
leap seconds (fine adjustment). If the Almanac for a specific year is available, and the exact time offset for the current year with respect to the validity year of the Almanac is known, the Ephemeris Data for the Sun can be used but the UT has to be adapted according to the time offset between the years that are involved. Almanac Data can be re-used in the original form after roughly four years. Based on this, a scheme for a compact, and long-term Almanac can be constructed. Notice, that this is only valid for the Ephemerides of the Sun. ## Determining GHA of the Sun from UTC
The GHA = 180° + 15°/h x (UTC + EoT) range: 0° through 360°
Time is expressed in hours and GHA in degrees.
The factor 15 is related to the Earth rotation: 360° in 24 hours (15°/h).
The value of EoT is in the range ±16min.
Expressed in degrees of GHA, this corresponds to a range of ±4°. ## Long-Term Solar Almanac
A long-term Solar Almanac has the EoT and Declination data for a certain reference year.
The Almanac Data for the other years is determined by correcting the applied UTC time
scale by an appropriate time offset (which will be approximately a multiple of 6 hours).
To account for this, an adapted time scale called "Orbit Time" (OT) is used to
enter the Solar Almanac. An example of a Long-Term Solar Almanac is available. An analysis of the accuracy over the valid time frame of 20 years, shows an error in GHA of less than 2'. For the Declination, the values are accurate within 3'. So the expected accuracy of these long-term almanacs is about twenty times less than the accuracy of a standard Nautical Almanac in which GHA and Declination values are given with 0.1' accuracy. However, for a backup method, this should be tolerable. ## Table Structure
The main table gives "E" (5° + Equation of Time) and Declination of the Sun
for the argument "Orbit Time" OT, which is formed by applying the "h"
correction from the "Corrections for OT" to the nearest integral hour of
UTC. In leap years, the upper value of the correction is to be used for
January and February and the lower value for the rest of the year. Thus,
OT’s corresponding to 2016 February 29 - 16h 31m UTC and 2016 March
01 - 05h 29m UTC, are February 29 - 09h 00m and March 01 - 21h 00m
respectively. ## Example of how to use the Tables
Given the long-term Almanac 2017-2036, find the GHA and Declination
of the Sun on 2020 January 18 at 03h 30m 35s UTC. OT = UTC (nearest integral hour) + Corr. (Table "Corrections for OT") = Jan. 18 / 04h - 6h = Jan. 17 / 22h. Main Table, Jan. 17 OT, E 2° 32’ (-4’) Dec S 20° 50’ (-12’) Interp. Table, 22h OT, -4’ -11’ -------- ------- Corrected Jan. 17 22h OT, E 2° 28’ Dec S 20° 39’ Diur. Arc 03h 30m UTC 227° 30’ Diur. Arc 00m 35s UTC 0° 09’ -------- GHA 230° 07' |

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