GE 109 LECTURE 2 ENGR. MARVIN JAY T. SERRANO LECTURER

In surveying, the use of true or astronomical directions has several advantages over the use of magnetic or assumed directions. One reason is that permanence is given to the direction of boundaries of land compared to magnetic directions which are constantly changing; Astronomical directions are useful for correlating surveys, checking angles of traverse and triangulation lines, and in orienting important maps as well as radio and radar antennae. True directions may be obtained by sighting on the sun or on one of several thousand stars whose positions are known.

Since earth rotates around its axis from west to east, all celestial bodies appear to revolve around the earth from east to west. Therefore when one faces north, the stars revolve around the north celestial pole in a counter clockwise direction. A which rotates around the celestial north pole and never goes below the observers horizon is called a circumpolar star. The star is circumpolar if θ+δ is greater than +90° (observer in northern hemisphere), or θ+δ is less than −90° (observer in southern hemisphere). Designation of a star as circumpolar depends on the observer's latitude. At the equator no star is circumpolar. At the North or South Pole all stars are circumpolar, since only one half of the celestial sphere can ever be seen. For an observer at any other latitude a star whose declination is greater than 90° minus the observer's latitude will be circumpolar, appearing to circle the celestial pole and remaining always above the horizon.

Polaris is a circumpolar star since it rotates very closely celestial north pole. The star is of important significance to engineers and surveyors since its most commonly used to determine the true direction of the line on earth surface. It is fairly bright star about 1 degree from the north celestial pole. The North Star (Polaris, or sometimes Dhruva Tara (fixed star), Taivaanneula (Heaven's Needle), or Lodestar) is a Second Magnitude multiple star about 430 light-years from Earth. Because it is very close to the North Celestial Pole, it appears stationary over the Northern Horizon. The height of the North Star above the horizon is equal to the latitude of the observer. It cannot be seen by an observer on or below the Equator although, as a practical matter, it will be too close to the horizon to be observed south of 10 degrees of North Latitude.

It is the last star in the tail of the constellation Ursa Minor and is located in the sky by finding first the constellation of Ursa Major ("Big Bear" or sometimes the "Big Dipper" or "Plough"). The two outermost stars in the cup of the "dipper" (Merak and Dubhe) are called the "pointers" because they describe a straight line that points to the North Star. The constellation of Cassiopeia, which looks like a big "W", is always opposite Ursa Major. The North Star is located approximately midway between the central star of Cassiopeia and Ursa Major. Polaris rotates in a counter clockwise direction and makes a complete revolution in approximately every 24 hours.

UPPER CULMINATION WESTERN ELONGATION LOWER CULMINATION EASTERN ELONGATION

RELATIONS AMONG LATITUDE (  ), ALTITUDE (H), AND DECLINATION (  ) LATITUDE (  ) – the angular distance measured from the equator along the meridian of longitude to the vertical line through the observer’s station  DECLINATION (  ) – the angular distance measured from the equator along the hour circle to the celestial body ALTITUDE (h) – the angular distance measured from the horizon along the hour circle to the celestial body   POLAR DISTANCE (P) – the angular distance measured from the polar axis along the hour circle to the celestial body h UPPER CULMINATION (NORTH OF ZENITH)  = h – P f = h +  - 90 f = 90 – z – P f =  - z P ZENITH DISTANCE (z) – the angular distance measured from the vertical axis along the hour circle to the celestial body z

RELATIONS AMONG LATITUDE (  ), ALTITUDE (H), AND DECLINATION (  ) LATITUDE (  ) – the angular distance measured from the equator along the meridian of longitude to the vertical line through the observer’s station  DECLINATION (  ) – the angular distance measured from the equator along the hour circle to the celestial body ALTITUDE (h) – the angular distance measured from the horizon along the hour circle to the celestial body  POLAR DISTANCE (P) – the angular distance measured from the polar axis along the hour circle to the celestial body h LOWER CULMINATION  = h + P f = 90 – z + P f = 180 – z –  P ZENITH DISTANCE (z) – the angular distance measured from the vertical axis along the hour circle to the celestial body z

RELATIONS AMONG LATITUDE (  ), ALTITUDE (H), AND DECLINATION (  ) LATITUDE (  ) – the angular distance measured from the equator along the meridian of longitude to the vertical line through the observer’s station  DECLINATION (  ) – the angular distance measured from the equator along the hour circle to the celestial body ALTITUDE (h) – the angular distance measured from the horizon along the hour circle to the celestial body   POLAR DISTANCE (P) – the angular distance measured from the polar axis along the hour circle to the celestial body h UPPER CULMINATION (SOUTH OF ZENITH)  =  + z f =  + (90 – h) f = 180 – P - h P ZENITH DISTANCE (z) – the angular distance measured from the vertical axis along the hour circle to the celestial body z

RELATIONS AMONG LATITUDE (  ), ALTITUDE (H), AND DECLINATION (  ) LATITUDE (  ) – the angular distance measured from the equator along the meridian of longitude to the vertical line through the observer’s station  DECLINATION (  ) – the angular distance measured from the equator along the hour circle to the celestial body ALTITUDE (h) – the angular distance measured from the horizon along the hour circle to the celestial body   POLAR DISTANCE (P) – the angular distance measured from the polar axis along the hour circle to the celestial body h UPPER CULMINATION (SOUTH OF ZENITH – BELOW THE EQUATOR)  = 90- h -  P ZENITH DISTANCE (z) – the angular distance measured from the vertical axis along the hour circle to the celestial body z