Horizon Coordinates A: Azimuth. The angle measured beginning at cardinal pt. north eastward along the horizon to the base of the vertical circle of the object. Azimuth is measured in units of degrees. h = 90o h: Altitude. The angle measured upward from the horizon along the vertical circle of an object to the object itself. The angle is measured in degrees. Z Vertical Circle h = 30o A = 270o W A = 310o 45o = h A = 180o N N A = 0o S A = 135o h = 0o E A = 90o

The Celestial Sphere Z NCP Meridian altitude of the C.E. = observer’s co-latitude Altitude of the NCP = observer’s latitude W (DVC) 52 38 S N N Definition: Co-latitude = 90o - latitude HORIZON DIURNAL CELESTIAL E CIRCLE EQUATOR SCP

Celestial Coordinates Z R.A.: Right Ascension. The angle measured beginning at the vernal equinox eastward (counter-clockwise) along the celestial equator to the base of the hour circle of the object. R.A. is measured in units of hours, minutes and seconds. V.E. R.A. = 0h HOUR CIRCLE NCP  = 90o (at NCP) R.A. = 5h W  = 40o S N N V.E.: Vernal Equinox. The point on the celestial equator from which Right Ascension is measured. The vernal equinox moves at the same rate as the stars (361o west every day with respect to the horizon).  = 0o (on C.E.) HORIZON δ: Declination. The angle measured upward (if positive) or downward (if negative) from the celestial equator along the hour circle of an object to the object itself. The angle is measured in degrees. CELESTIAL E EQUATOR SCP  = -90o (at SCP)

Hour Angle The angle in units of hours, minutes and seconds between the celestial meridian and the hour circle of an object. The angle is positive if measured westward, negative if measured eastward. HOUR ANGLE (positive) = 4h Z HOUR ANGLE (negative) = - 3h15m NCP HOUR CIRCLE W S N N A positive hour angle states the amount of time since an object went through upper transit. HORIZON CELESTIAL A negative hour angle states the amount of time until an object goes through upper transit. E EQUATOR SCP

Sidereal Time H.A. = S.T. – R.A. The angle in units of hours, minutes and seconds between the celestial meridian measured westward to the hour circle of the vernal equinox. Z R.A. = 5h15m HOUR ANGLE (negative) V.E. = - 3h15m NCP HOUR CIRCLE W S N N Sidereal time states the amount of time since the vernal equinox went through upper transit. It equals the hour angle of the vernal equinox. HORIZON CELESTIAL E EQUATOR SCP H.A. = S.T. – R.A.