Circumpolar bodies

For a body to be circumpolar, the body should always be above the rational horizon i.e the body should not set. Therefore, a circumpolar body will have upper transit (upper meridian passage) which is above the elevated pole and lower transit (lower meridian passage) which is below the elevated pole.

Condition required for a body to be circumpolar:

• Lat + Dec > 90° (For the body not to set)
  
• Latitude and declination should be the same name.
  

1. North Latitude – Lat < Dec

2. North Latitude – Lat > Dec

3. South Latitude – Lat < Dec

4. South Latitude – Lat > Dec

Upper and Lower transit of circumpolar bodies

Upper transit (NX) or (SX) of a circumpolar body is above the elevated pole.

For North latitudes,

Upper transit (NX) bearing is North, when lat < dec

= Altitude of pole + Polar distance (NP + PX)

= Latitude + Polar distance (Lat + PX)

= Declination circle + lower transit (XX’ + NX’)

= 90° – Zenith Distance (ZX)

Upper transit (SX) bearing is South, when lat > dec

= 180° – (Altitude of pole + Polar distance)

= 180° – (NP + PX) = 180° – (Latitude + Polar distance)

= 180° – (Lat + PX) = 180° – (Declination circle + lower transit)

= 180° – (XX’ + NX’)

For South latitudes,

Upper transit (SX) bearing is South, when lat < dec

= Altitude of pole + Polar distance (SP + PX)

= Latitude + Polar distance (Lat + PX)

= Declination circle + lower transit (XX’ + SX’)

= 90° – Zenith Distance (ZX)

Upper transit (NX) bearing is North, when lat > dec

= 180° – (Altitude of pole + Polar distance) = 180° – (SP + PX)

= 180° – (Latitude + Polar distance)= 180° – (Lat + PX)

= 180° – (Declination circle + lower transit) = 180° – (XX’ + SX’)

Lower transit (NX’ or SX’) is below the elevated pole.

For The North latitudes,

Lower transit (NX’) bearing is North, same as the elevated pole or latitude or declination. 

= Altitude of pole – Polar distance (NP – PX’)

= Latitude – Polar distance (Lat – PX’)

= 90° – (PX’ + PZ)

For The South latitudes,

Lower transit (SX’) bearing is South, same as the elevated pole or latitude or declination.

= Altitude of pole – Polar distance (SP – PX’)

= Latitude – Polar distance (Lat – PX’)

= 90° – (PX’ + PZ)

If the altitudes of a circumpolar body at upper and lower meridian passage are observed,

– then the observer’s latitude and

– body’s declination can be calculated.

• Draw the rational horizon, place the body at the upper transit (X) and lower transit (X’)
  
• Place elevated pole midway between the 2 positions and draw declination circle, with the pole as the centre and the circle passing through X and X’.
  
• Draw equinoctial, WQE, where PQ is 90°
  
• Diameter of declination circle (XX’) = Upper altitude (NX) – lower altitude (NX’) (when Lower & Upper mer pass, brg is same)or 
  = 180° – (Upper altitude (SX) + lower altitude (NX’)) (when Lower & Upper mer pass, brgs are opposite)
• The diameter, divided by 2 gives the polar distance PX and PX’.
  

  (PX or PX’) = XX’ / 2
  

• Polar distance (PX) = altitude of the pole (NP) – lower meridian altitude (NX’)
  
• Polar distance (PX) = 90° – Declination
  
• 90° – polar distance (PX) = Declination, named same as elevated pole.
  
• Polar distance(PX) + lower meridian altitude (NX’)
  = Altitude of the pole (NP)
  

  = Latitude of an observer, named same as the elevated pole.