## Interpolation and Conversion Tables for Celestial Navigation
The Hour-Minute-Seconds and Degree-ArcMinute-ArcSeconds system used to
express values of time and angle goes back to the Babylonian sexagesimal
number system (base 60). Being used to the Indian-Arabic decimal number system,
this sexagesimal system is not very well suited for doing even simple multiplication.
This multiplication is needed for example while doing linear interpolation
on the integral-hour GHA and Declination values from Nautical Almanac Tables.
Also for determining a calculated altitude in the table-based sight reduction
process such an interpolation is needed. ## Purpose and Scope
The Interpolation and Conversion Tables presented here are designed to
be used for both the interpolation of the Nautical Almanac data (GHA and
Declination) as well as for the interpolation of the data from the Sight
Reduction Tables (Altitude).
## ArrangementThe tables have an entry for each Minute / Second combination (from 00Min/00Sec to 59Min/59 Sec). Each entry represents a fraction of an hour. The complete Table consists of 3600 entries: one for each second of the hour. For each entry four data values are given arranged in two sub tables (the example shown below gives the first entries of the "16 Min" data):
## TablesThe complete Interpolation Tables consists of 20 pages each containing the data for a 3-Minute span. The fraction of the hour is recorded both in integral Minutes and Seconds and in decimal Minutes.
## Use and Application of the Interpolation TablesThe tables presented here are designed for the following two problems typically occurring in the process of elaborating a Line-of-Position from a Sextant measurement: For the fraction of the hour of the time of observation, find interpolated increment of the GHA corresponding to the principle 15°/hour increase of the GHA of celestial objects. Given the increment on a GHA-, Declination- or Altitude value for the next hour, find the correct fraction of this increment corresponding to the given fraction of the hour of the time of observation.
The
In the first line the increment/decrement for one hour interval (e.g. from the Nautical
Almanac) or one degree of Declination (e.g. from the Sight Reduction Tables) is recorded
(d).
In both, the Nautical Almanac and the Sight Reduction Tables this value is given in
decimal Minutes.
Since the increment "d" for the hour interval is positive, also the resulting fractional increase "c" is positive. |

Cover << Sail Away << Celestial Navigation << . | last updated: 09-Sep-2005 |