Formula for altitude of star

• alt = angle of altitude of star
• lat = latitude of observer
• d = declination of star
• H = hour angle of star = (t - RA)(360/24)
• RA = right ascension of star
• t = local sidereal time
• RA and t are measured on a scale from 0 to 24; the formula above converts the angle H to degrees (0 to 360 scale)
• t = 12 + (366.25CT+ 24DV)/365.25
• CT = local clock time, measured by 24 hour scale (0=midnight, 12=noon)
• DV = days since vernal equinox
• if the star is on the meridian, then
  t=RA, and H=0:
  sin alt=sin lat sin d + cos lat cos d
  sin alt=cos(lat - d)
  alt=90 - lat+d
  if H=0, and lat=d, then the star will be at the zenith

Amount of time (in hours) between rising and setting of a star

• T=time in hours between rising and setting
• lat=latitude of observer
• d=declination of star
• if lat=0, then T=12 (from the equator, all stars are in the sky 12 hours between rising and setting)
• if d=0, then T=12 (stars on the celestial equator, where d=0, are in the sky 12 hours between rising and setting for observers from all over the Earth)
• if d and lat are both positive, then T is greater than 12 (from the northern hemisphere, stars that are north of the celestial equator are in the sky longer than 12 hours between rising and setting)
• if d=90 - lat, then
  tan lat tan d =1
  and T=24. These stars never set-- they are circumpolar
• if d=lat-90, then
  tan lat tan d =-1
  and T=0. These stars just touch the southern horizon at one time, but they never rise above it (assuming the observer is in the northern hemisphere). Any stars with declinations south of this cannot be seen from this latitude.