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Celestial Navigation TheoryThe Navigational TriangleA flat plane triangle can be solved using trigonometry. Knowing 2 sides and an angle, SAS, the third side and a second angle can be determined. The Celestial Triangle, which is laid out on the face of the planet, is a spherical triangle. In this triangle we also know 2 sides and an angle, Latitude, Declination and LHA. Pub 229 is a set of tables which solves the triangle using spherical trigonometry. Enter the table with: 1. Latitude We extract : 1. Hc (height computed) Hc is compared to Ho (height observed) along with Z converted to Zn and then plotted from your Assumed Position to give a line of position. The Celestial Triangle’s three points are defined by the Pole, your DR Position (latitude and longitude) and the Objects Geographical Position (GHA and Declination) The Component Parts Ho  Height Observed: This is the Sextant observation (Hs) corrected for height of the eye above sea level and for refraction. (Dip, Altitude Correction) Lat  Latitude: This is your DR Latitude rounded to the nearest whole latitude. Dec  Declination: This is exact Declination for the body observed at the time of the sighting. LHA  Local Hour Angle: This is Meridian Angle (t). The Angle between your Longitude and the objects GHA (Greenwich Hour Angle). It is expressed as a whole number. LHA = GHA  West Long or + East Long Navigational TriangleAP  Assumed PositionDR  Position GP  Geographical Position, GHA and Dec of the Body PUB 229 Entering Argument: LHA Local Hour Angle LHA= GHA  W Long GHA + E Long Note: Long is changed to make LHA a whole number, Lat and new Long become AP. LAT DR  Lat rounded to nearest whole Lat. DEC  Exact Declination of body. HS  Height Shot HA  Apparent Altitude Corrected for Index Error and Dip Angle HO  Height Observed All Corrections Applied The angle that would be formed at the center of the earth between the Observer’s celestial horizon and the line of sight to center of the body.HC  Height Computed for DR position Index Correction: Corrections for inaccuracy in reading the sextant. Add or subtract.Dip Angle: Height of Eye. Difference between the Horizontal reference plane and the visible horizon. Always subtracted.Altitude Corrections: Entered with HA (apparent altitude). A correction that take the following factors in account: Always added for lower limb.Refraction: Correction for bending of light rays coming from the body shot.SemiDiameter: Correction for 1/2 of the body’s diameter.Augmentation: Increase in apparent size of the sun and moon as a result of the increase in apparent altitude.Parallax: The difference in apparent altitude as viewed from the surface of the Earth and in the center of the Earth.Additional Corrections: Correction for nonstandard conditions. Barometric pressure and temperature.Moon: Altitude Correction is done in two parts using apparent altitude and H.P. (horizontal parallax). Follow instruction on correction table. Always added. See Celestial Navigation Diagram Click image for more detail
Download Sunline Worksheet Download Local Apparent Noon Worksheet Download Latitude by Polaris Worksheet Great Circle CalculatorDistance:L1 = Departure Latitude Initial Course Angle:
Points along the route. Determine Lat for known Long.
Cosine – HaversineSight ReductionHc = Height Computed Great Circle Publication 229 Solution: Enter 229 with: Lat = Latitude of point of departureNotes: 1. If HC and Z are of body above the horizon Then D = 90  HC (D = Distance) (Z = Initial Course)2. If HC and Z are of body below the horizon Then D = 90 + HC and C = 180  Z 

