LESSON 15:Celestial Coordinate SystemsLearning ObjectivesKnow the ultimate goal of celestial navigation.Know the definitions of terms and components associated with the terrestrial, celestial, and horizon coordinate systems.Know the relationship between the terrestrial, celestial, and horizon coordinate systems.Apply correct procedures to describe the location of a celestial body in reference to the celestial and horizon coordinate systems.

The Goal of Celestial NavigationThe solution of spherical triangles of sides based on the observed positions of celestial bodies, in order to determine the position of a vessel.100 years ago, this involved some complicated spherical trigonometry.Today, it requires the use of tables or a navigational calculator (HP makes one).

1. Terrestrial Coordinate SystemA quick review:

Basic AssumptionsFirst, assume the earth does not move, but instead the celestial bodies rotate about it in a predictable manner.The celestial sphere: celestial bodies are assumed to be on the inner surface of a vast, hollow sphere of infinite radius, which has the earth at its center.

2. Celestial Coordinate SystemThe celestial coordinate system is best understood as a projection of the terrestrial coordinate system, outward into space onto the celestial sphere.

Declination

Celestial Coordinate SystemCelestial Equator (Equinoctial)Celestial MeridiansHour CirclesHour Circle of AriesDeclinationcelestial equivalent of latitudeHour Anglescelestial equivalent of longitude

Hour AnglesThree different references are used:

Sidereal Hour Angle (SHA)Hour Circle of a celestial body, as referenced from the hour circle of Aries (measured westerly)Greenwich Hour Angle (GHA)Hour circle of a celestial body, as measured relative to Greenwich Celestial Meridian Local Hour Angle (LHA)Hour circle of a celestial body, as measured relative to the local celestial meridian

Hour AnglesGHA = GHA(Aries) + SHA

3. Horizon Coordinate SystemIn the terrestrial and celestial coordinate systems, the basic references are the poles and the equator.The horizon coordinate system, however, is based on the observers position.This system is necessary because stars are sighted with respect to the observers position.

Horizon Coordinate SystemZenith and Nadiranalogous to north and south polesVertical Circleanalogous to meridian (terrestrial system) or hour circle (celestial system)Prime Vertical (east and west)Principal Vertical (north and south)

Horizon Coordinate System

Horizon Coordinate SystemCelestial Horizonanalogous to the equatorTrue Azimuth (Zn)analogous to longitudeAltitudeanalogous to latitudeSextant Altitude (hs)Measured altitudes of celestial bodiesVisible or Sea HorizonUsed as a reference for celestial body altitude measurementsObserved Altitude (Ho)Conversion of Sextant Altitude, since sea horizon is not at celestial horizon.

The Celestial TriangleThese three coordinate systems (TERRESTRIAL, CELESTIAL, AND HORIZON) are then combined to form the celestial triangle, which is used to determine our position.One leg from each triangle forms the new triangle on the celestial sphere.

The Celestial Triangle

The Celestial TriangleAzimuth Angle (Z)Meridian angle (t)

Coordinate System Comparison