Sextant altitude correction true altitude celestial bodies


Sextant is a precession instrument which is used to measure the altitudes of celestial bodies. I have explained earlier about Marine sextant.                                                                             Click for more about Marine Sextant

Sextant is an instrument which has many errors and corrections. Sextant altitude obtained by sextant may not be accurate, thus requires some corrections according to the celestial body we are observing.

Corrections to be applied to the sextant altitude: 

  1. Index error :  Index error occur when the horizon glass and the index glass not being  parallel to each other when the index bar is at zero . Index error is zero if both the glasses are parallel to each other. To measure the index error the mariners use either the horizon or sun during the day time. If the reading is positive, the error is on the arc and is to be substracted from sextant altitude. If the reading is negative , the error is off the arc and is to be added to the sextant altitude. Sextant altitude corrected for index error is called observed altitude.                                                                                                          
  2. Height of eye correction(Dip) : Dip is the angle between plane of  sensible horizon of observer and his visible horizon. Dip occurs because the observer is not at sea level . The correction increases with the increase of height from the sea-level. Dip is always negative and should be subtracted from the observed altitude. Dip is given in the nautical almanac altitude correction tables according to the height of eye of the observer. Observed altitude corrected for dip gives us apparent altitude.                                        
  3. Total Correction:  This correction is contributed by various factors like refraction, semi diameter , parallax in altitude, Augmented SD. This varies according to the celestial body you are observing like sun, stars ,planets, moon, etc . Applying the total correction to the apparent altitude will give True altitude.
  • Refraction: It is deviation of a light when it passes from one medium to the other . When the light is passing from a rarer medium to denser medium the light bends towards the normal. The atmosphere near to the earth surface is denser and as it goes higher the atmosphere becomes rarer. So a ray from any celestial body passes from a rarer medium top a denser medium. Therefore it bends towards the normal. Any light is subject to refraction and it is applicable to every celestial body observed. Refraction is negative and is to be substracted.                                                                                    
  • Semi- Diameter: Celestial bodies like sun and moon are large visible discs , so it is impossible to measure the altitude of their centres. Hence the upper limb or lower limb of sun and moon are taken for measuring the altitude. If the upper limb is taken the half of apparent diameter of the body is substracted from the altitude to get the altitude of the centre and vice versa.                                                                                               
  • Parallax : After applying index error, dip, refraction and semi diameter correction we will get the altitude above the sensible horizon. To get the altitude above observer's rational horizon parallax correction is to be applied. Parallax in altitude is the angle at the centre of the body contained between centre of the earth and observer on the surface of earth , when the body is at any altitude. Parallax of bodies will reduce as their distance from earth increases. Therefore moon has the highest parallax and stars because of its large distance from earth, parallax is negligible. Parallax is always positive and is to be added.
Various Corrections to be applied for each celestial bodies:

  • Stars: Index error , dip , refraction(Given in Nautical almanac altitude correction tables under stars and planets)                                                                                            
  • Planets: Index error , dip , refraction , parallax (Given in Nautical almanac altitude correction tables under stars and planets. An additional parallax correction is given for planets venus and mars )                                                                                                     
  • Sun : Index error , dip , refraction , semi diameter, parallax                                                
  • Moon :Index error , dip , refraction , parallax, Augmented semi - diameter  

                        
 Steps to apply corrections from sextant altitude to true altitude:

  • Obtain the sextant altitude from the sextant.
  • Apply the index error off the arc or on the arc to get observed altitude
  • Obtain dip from nautical almanac according to the height of eye and apply it to observed altitude to get apparent altitude
  • Obtain total correction from nautical almanac according to the celestial body that you are observing and apply it to obtain the true altitude .