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Geodetic Astronomy. genn 2 1 5. Astronomy: is the science dealing with celestial bodies and phenomena. Astrology: is the belief that the positioning of the stars and planets affect the way events occur on Earth. Geodetic astronomy: is the art and science of determining, by astronomical observations, the positions of points on the Earth’s surface and the azimuth of the geodetic lines connecting such points. DEFINITIONS. Practical astronomy: is the theory and use of astronomical instruments, methods of observing, reduction of observations, and discussion of astronomical data. Parallax (p) is the difference in the direction of a celestial object as seen from two widely separated points. UNITS OF STELLAR DISTANCE. • Astronomical unit (AU): the average distance between Earth and the Sun. 1 AU is equals to 1.496 x 1011 m. • Parallax second (parsec or pc): the fundamental unit of distance in astronomy. A star with a parallax of 1 arcsecond has a distance of 1 parsec. 1 pc is equals to 206,265 A.U. is equals to 3.086 x 1016 m. The distance (D) of a star in parsecs is just the reciprocal of its parallax (p) in arcseconds; that is. D is equals to 1 over p. Thus, a star with a parallax of 0.1 arcsecond would be found at a distance of 10 parsecs. • Light-year (l.y.): is an alternative unit of astronomical distance and is the distance traveled by light in 1 year. 1 l.y. is equals to 9.461 x 10 to the power of 15 m and 1 pc is equals to 3.262 l.y. Stars are too distant for any difference of position to be perceptible from two places on the Earth’s surface, except when observed from widely different viewpoints during the year. Annual or stellar parallax: • is the angle subtended at the star by the mean radius of the Earth’s orbit around the Sun. • no star has an annual parallax greater than 1 arcsecond. Constellation is a group of stars that appears to form a pattern; the International Astronomical Union (IAU) recognizes 88 constellations covering the entire northern and southern sky. In the northern hemisphere, the most famous star is found in the asterism Little Dipper — the Polaris (a.k.a. the pole star or the North Star). Using Ursa Major to locate Polaris (generated from Stellarium). Asterism is a star pattern that is not officially recognized by the IAU as a constellation. To identify Polaris in the night sky, look for the constellation Ursa Major, commonly known for its asterism, the Big Dipper. Draw a line connecting its two outermost stars (Dubhe and Merak) then extend this line to about five times until it reaches Polaris. CELESTIAL Coordinate System versus TERRESTRIAL Coordinate System. Fundamental differences. number 1. only directions are considered in celestial Coordinate System. number 2. celestial geometry is spherical rather than ellipsoidal. Celestial sphere is an imaginary, hollow sphere of infinite radius whose center is the Earth. Elements of the Celestial Sphere. Altitude (h) is the angular distance measured along a vertical circle, from the horizon to the body. It is generally obtained by measuring a vertical angle with a total station (or theodolite), and correcting for refraction and parallax if the Sun is observed. Astronomical (PZS) triangle: is the spherical triangle whose vertices are the pole P, zenith Z, and astronomical body S. Because of the body’s movement through its diurnal circle, the three angles in this triangle are constantly changing. Azimuth (A): is the angular distance measured along the horizon, in a clockwise direction from either the north or south point of the meridian, to the vertical circle through the body. Celestial Axis: is the prolongation of the Earth’s polar axis. Celestial Equator: is the great circle on the celestial sphere whose plane is perpendicular to the axis of rotation of the Earth. It corresponds to the Earth’s equator enlarged in diameter. Celestial Meridian: a.k.a. local or observer’s meridian, is that unique hour circle containing the observer’s zenith. It is both an hour circle and a vertical circle. It is composed of two branches: a. the upper branch contains the zenith and is the arc PZQ’H’P’. b. the lower branch includes the nadir and is the arc PHQNP’. Codeclination: is equal to 90° minus the declination or (90° minus delta); a.k.a. polar distance (p) and are always positive. Colatitude: is equal to 90° minus the latitude or (90° minus phi ). Declination (delta): is the angular distance, measured along the hour circle, above or below the celestial equator; it is plus (+) when the body is north of the equator and minus (-) when south of it. Equinoctial Colure: is the hour circle that passes through the NCP and SCP and the vernal and autumnal equinoxes. Great Circle: is any circle on the celestial sphere whose plane passes through the center of the sphere. Horizon: is a great circle on the celestial sphere whose plane is perpendicular to the direction of the plumb line. Hour Angle (t): exists between a meridian of reference and the hour circle passing through a celestial body. Hour angles are measured westward (in the direction of apparent travel of the Sun or star) from the upper branch of the meridian of reference. Hour Circle: is any great circle on the celestial sphere that passes through the north and south celestial poles. Therefore, hour circles are perpendicular to the plane of the celestial equator. They correspond to meridians (longitudinal lines) and are used to observe hour angles. Latitude (phi): is the angular distance, measured along the meridian, from the equator to the observer’s position. It is also the angular distance between the polar axis and horizon, or arc HP. Depending on the observer’s position, latitude is measured north or south of the equator. Local Meridian: is Celestial Meridian. Longitude (A): is the angular distance measured along the arc of the equator between a reference meridian and the meridian circle passing through the station; can be expressed in degrees of arc or in hours of time. Meridian: the great circle of the celestial sphere which passes through the celestial poles and the observer’s zenith. This circle is both a vertical and an hour circle. Nadir (N): is the point on the celestial sphere vertically beneath the observer and exactly opposite the zenith. North Celestial Pole (NCP): is the point where the Earth’s rotational axis, extended from the north geographic pole, intersects the celestial sphere. Parallactic angle (y): the angle formed by the intersection of the vertical circle and the hour circle and the least used element of the PZS triangle. Polar Distance (p): is the complement of declination. See Codeclination. South Celestial Pole (SCP): is the point where the Earth’s rotational axis, extended from the south geographic pole, intersects the celestial sphere. Vertical Circle: is any great circle of the celestial sphere passing through the zenith and nadir and represents the line of intersection of a vertical plane with the celestial sphere. Zenith (Z): the point where the plumb line projected above the observer’s horizon meets the celestial sphere. Zenith Distance (z): is the complement of altitude. also called Coaltitude.