Published on November 13, 2007
Slide1: Advanced Navigation Celestial Theory Slide2: Objectives: 1. To become familiar with the relationships of the earth to the solar system and the universe. 2. To become familiar with the celestial and horizon coordinate systems, and how they relate to the terrestrial coordinate system. 3. To gain a working knowledge of the celestial and navigation triangles. Slide3: Objectives: 4. To become familiar with the concept involved with a circle of equal altitude. Elements of the Celestial Sphere: Elements of the Celestial Sphere THE CELESTIAL SPHERE: Infinite radius An imaginary sphere of infinite radius with the earth at it’s center. THE CELESTIAL SPHERE Zenith - Nadir: Zenith - Point on the celestial sphere directly above the observers head Zenith - Nadir Nadir - Point on the celestial sphere directly below the observers feet CELESTIAL BODIES: PLANETS STARS MOON SUN Celestial bodies are located throughout the celestial sphere. We are interested in the relative positions and motions of these bodies on this imaginary sphere. CELESTIAL BODIES CELESTIAL POLES: North Celestial Pole South Celestial Pole CELESTIAL POLES CELESTIAL EQUATOR: Also known as the EQUINOCTIAL. It’s the intersection of the extended plane of the equator and the celestial sphere. CELESTIAL EQUATOR HOUR CIRCLES: A great circle on the celestial sphere perpendicular to the celestial equator and passing through both celestial poles. HOUR CIRCLES CELESTIAL MERIDIAN: A great circle of the celestial sphere, through the celestial poles and the zenith. CELESTIAL MERIDIAN DECLINATION: Angular distance of a point on the celestial sphere north or south of the celestial equator Celestial Equator DECLINATION Parallel of Declination:: Parallel of Declination A circle parallel to the celestial equator. Bodies are considered to travel along the parallel of declination as the earth rotates. Parallel of Declination: HOUR ANGLE: HOUR ANGLE The angular distance measured laterally along the celestial equator in a westerly direction through 360º The Sun at the time of the vernal equinox seems to be located in the constellation Aries: First Point of Aries: Ecliptic Aries The Sun at the time of the vernal equinox seems to be located in the constellation Aries: First Point of Aries Sidereal Hour Angle: SHA SHA Sidereal Hour Angle SHA of A Star: Because stars and Aries move at the same rate, the SHA is constant SHA SHA SHA of A Star GREENWICH HOUR ANGLE: First meridian GHA GHA SUN GHA GREENWICH HOUR ANGLE GREENWICH HOUR ANGLE: SHA OF ARIES GHA STAR GHA = GHA + SHA GREENWICH HOUR ANGLE Local Hour Angles: LHA LHA Local Hour Angles LOCAL HOUR ANGLE: SHA LHA LHA LHA = LHA + SHA LOCAL HOUR ANGLE HOUR ANGLES: . HOUR ANGLES Sidereal Hour Angle (SHA): Measured in a westerly direction from the hour circle of Aries to the hour circle of the body Greenwich Hour Angle (GHA): Angular distance measured west of the Greenwich Celestial Meridian. Local Hour Angle (LHA): Angular distance west of the observers celestial meridian to the body Location on the Celestial Sphere: A point on the Celestial Sphere may be identified at the intersection of: * it’s parallel of declination (Declination) * it’s hour circle identified by the angular distance west (0º - 360º) of a reference hour circle. Location on the Celestial Sphere Location of Stars: The location of Stars are referenced by their Declination and Sidereal Hour Angle. Location of Stars The Location of Bodies: The location of the Sun, Moon, planets and First point of Aries are referenced by their Declination and Greenwich Hour Angle. The Location of Bodies Slide26: NOW LET’S ADD MOTION TO THE SCENE EARTH MOTION: EARTH MOTION DIURNAL MOTION: IT APPEARS TO BE FROM EAST TO WEST DIURNAL MOTION BECAUSE OF THE DIURNALMOTION (EARTH’S ROTATION) : BECAUSE OF THE DIURNAL MOTION (EARTH’S ROTATION) ALL THE CELESTIAL BODIES SEEM TO MOVE AT ONE RATE, THEREFORE THE GHA’s WILL CHANGE AT ONE RATE AND THE RATE IS: 15DEG -------1HR 360DEG ------24HRS THE CELESTIALCOORDINATE SYSTEMDESCRIBES THE POSITION OF CELESTIAL BODIES. WE ALSO NEEDED A SYSTEM FROM THE OBSERVER’SPERSPECTIVE: THE CELESTIAL COORDINATE SYSTEM DESCRIBES THE POSITION OF CELESTIAL BODIES. WE ALSO NEEDED A SYSTEM FROM THE OBSERVER’S PERSPECTIVE Elements of the Horizon Coordinate System: Elements of the Horizon Coordinate System OBSERVER’S HORIZON: the plane perpendicular to that axis passing through the observer. OBSERVER’S HORIZON Slide33: HORIZON ZENITH NADIR Slide34: -N- the projection of the poles over the horizon will give us the other coordinate Slide35: OBS. HORIZON ZENITH NADIR CELESTIAL HORIZON: Another plane parallel to the observer’s horizon but passing through the center of the earth CELESTIAL HORIZON Slide37: HORIZON ZENITH NADIR CELESTIAL HORIZON Slide38: HORIZON ZENITH NADIR CELESTIAL HORIZON Slide39: Observer’s Horizon ZENITH NADIR CELESTIAL HORIZON Since the radius of the earth is considered negligible with respect to the celestial sphere, the visible horizon is considered to be the same as the celestial horizon.: Since the radius of the earth is considered negligible with respect to the celestial sphere, the visible horizon is considered to be the same as the celestial horizon. Slide41: ZENITH NADIR CELESTIAL HORIZON The angular distance above the horizon that a celestial body is measured is called that body’s altitude.: The angular distance above the horizon that a celestial body is measured is called that body’s altitude. Slide43: OBSERVER’S HORIZON CEL. BODY ALTITUDE Sextant Angle (Hs): The altitude measured by the sextantApparent altitude (Ha): The Sextant Altitude corrected for inaccuracies in the instrument and height of eyeObserved altitude (Ho): All further corrections are applied: Sextant Angle (Hs): The altitude measured by the sextant Apparent altitude (Ha): The Sextant Altitude corrected for inaccuracies in the instrument and height of eye Observed altitude (Ho): All further corrections are applied Slide45: CELESTIAL HORIZON ALTITUDE VERTICAL CIRCLE A Vertical Circle is a great circle on the celestial sphere that passes through the zenith and nadir. It is perpendicular to the celestial (visible) horizon.: A Vertical Circle is a great circle on the celestial sphere that passes through the zenith and nadir. It is perpendicular to the celestial (visible) horizon. North Cardinal Point: The projection of the North pole over the horizon that we measure the true azimuth North Cardinal Point Slide48: CEL. BODY ALTITUDE -N- TRUE AZIMUTH The Principle Vertical Circle is a vertical circle that passes through the north and south celestial poles.: The Principle Vertical Circle is a vertical circle that passes through the north and south celestial poles. Slide50: PRINCIPAL VERTICAL TRUE AZIMUTH CELESTIAL HORIZON ALTITUDE Z Slide51: THE PLACE WHERE A LINE LINKING THE CELESTIAL BODY Slide52: PUNCHES IT’S SURFACE AND THE CENTER OF THE EARTH Slide53: THE NAME OF THAT POINT IS THE GEOGRAPHIC POSITION GP Questions?: Questions?