1. LESSON 15: Celestial Coordinate Systems Learning ObjectivesLearning Objectives –Know 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.

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

3. 1. Terrestrial Coordinate System A quick review:A quick review:

4. Basic Assumptions First, assume the earth does not move, but instead the celestial bodies rotate about it in a predictable manner.First, 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.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.

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

6. Declination

7. Celestial Coordinate System Celestial Equator (Equinoctial)Celestial Equator (Equinoctial) Celestial MeridiansCelestial Meridians Hour CirclesHour Circles Hour Circle of AriesHour Circle of Aries DeclinationDeclination –celestial equivalent of latitude Hour AnglesHour Angles –celestial equivalent of longitude

8. Hour Angles Three different references are used:Three different references are used: Sidereal Hour Angle (SHA)Sidereal Hour Angle (SHA) –Hour Circle of a celestial body, as referenced from the hour circle of Aries (measured westerly) Greenwich Hour Angle (GHA)Greenwich Hour Angle (GHA) –Hour circle of a celestial body, as measured relative to Greenwich Celestial Meridian Local Hour Angle (LHA)Local Hour Angle (LHA) –Hour circle of a celestial body, as measured relative to the local celestial meridian

9. Hour Angles GHA = GHA(Aries) + SHA

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

11. Horizon Coordinate System Zenith and NadirZenith and Nadir –analogous to north and south poles Vertical CircleVertical Circle –analogous to meridian (terrestrial system) or hour circle (celestial system) Prime Vertical (east and west)Prime Vertical (east and west) Principal Vertical (north and south)Principal Vertical (north and south)

12. Horizon Coordinate System

13. Celestial HorizonCelestial Horizon –analogous to the equator True Azimuth (Z n )True Azimuth (Z n ) –analogous to longitude AltitudeAltitude –analogous to latitude Sextant Altitude (h s )Sextant Altitude (h s ) –Measured altitudes of celestial bodies Visible or Sea HorizonVisible or Sea Horizon –Used as a reference for celestial body altitude measurements Observed Altitude (H o )Observed Altitude (H o ) –Conversion of Sextant Altitude, since sea horizon is not at celestial horizon.

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

15. The Celestial Triangle

16. Azimuth Angle (Z)Azimuth Angle (Z) Meridian angle (t)Meridian angle (t)

17. Coordinate System Comparison