Best practice for celestial fix

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  1. It is useful to understand that when selecting celestial bodies for observation. it can be difficult to accurately determine the true altitude of bodies lying low near the horizon due to refraction
  2. Except for sights of the Sun, Moon, and sometimes Venus and Jupiter, all other bodies used in celestial navigation sights can be measured only during nautical twilight.
  3. The process of taking sights is weather dependent. An accurate sight requires that both the body and the horizon below it be visible at the time the sight is taken.
  4. Figure  shows two LOPs for two objects whose azimuths are separated by 15º. The LOPs also intersect with an acute angle of 15º. The result is: it is difficult to deter mine where the two LOPs cross along the axis bisected by the acute angle. That is, there is a large uncertainty in the fix position in that direction. The uncertainty in the fix along the axis bisected by the oblique angle is approximately the same as it would be if the LOPs met at right angles.

LOP Separated by 15°

  1. Figure shows the two LOPs are perpendicular to each other. The result is that the uncertainty in the fix is the same in all directions. The closer the separation of the azimuths of two sights comes to perpendicularity the better the chance a fix will have minimum uncertainty. Finding two bodies with azimuths separated by exactly 90º is unlikely, so an acute angle of at least 30º is recommended to reduce the uncertainty along the axis that bisects the acute angle of two LOPs.

LOP Separated by 90°

  1. Sights well distributed in azimuth also act to cancel out systematic errors in determining Ho such as an incorrect index correction (IC) or error in dip. For example, Figure below shows three LOPs made from bodies separated by 120º in azimuth. A systematic error in determining Ho will move the LOPs in a direction perpendicular to the LOPs themselves, indicated by the arrows. A systematic error will move all of the LOPs the same amount in directions distributed 120º in azimuth. The result is the most likely position for the fix remains at the center of the “cocked hat”.

Azimuths Separated by 120°

  1. In below Figure, the three LOPs were plotted from bodies distributed by 60º in azimuth. The resulting “cocked hat” looks identical to the one in Figure 1802a. A systematic er ror, however, will move all of the LOPs the same amount in directions distributed in azimuth by 60º on either side of the center of the distribution. The result is that the most likely position for the fix is no longer at the center of the “cocked hat”. The most likely position may even lie outside of the “cocked hat” altogether if the systematic error is more than a few tenths of an arc minute.

Azimuths Separated by 60°

  1. Bodies at high altitudes are difficult to observe. They can be a challenge to acquire, to “bring to the horizon” with a sextant, and to determine their approximate azimuth to measure an accurate Hs. As the body gets closer to the zenith the assumption that the circle of equal distances can be approximated by an LOP breaks down. Sights of a body taken at high altitudes may also require the use of more complicated procedures, such as the use of second differences when calculating Hc. Taking sights of body at high altitudes, greater than 75º, should be avoided for these reasons.
  2. There are three things a navigator can do to reduce any systematic errors caused by uncorrected refraction:
  3. Make sure the observations are well distributed in azimuth. At sea, it is usually the case that the factors that contribute to refraction are similar in all directions. Taking sights well distributed in azimuth will cause the systematic errors to cancel out.
  1. Take the sights from a place close to the sea surface, if possible. Almost all of the abnormal refraction encountered is caused by that part of the atmosphere between the observer’s eye and the sur face of the sea. Reducing the observer’s height decreases the distance to the horizon. An observer close to the sea surface will have a nearby horizon, which is more likely to have similar refraction conditions in all directions.
  1. Observe celestial bodies with similar altitudes, all greater than 15°. Bodies at the same altitude have the same total values for refraction. So, the systematic effect of errors in computed refraction will tend to cancel out if the bodies are well distributed in azimuth. The change in refraction angle is small, except near the horizon, so relative altitude is a mi nor consideration when choosing which bodies to use.
  1. One method to reduce the random error in determining an LOP is to take a number of observations of the same body over a short period of time. Averaging these observations together into a single sight, taking into account the change in Hs with time, reduces random error with the square root of the number of observations. Averaging four observations into a sight reduces the random error to one half that of a single observation sight and averaging nine observations into a sight reduces the random error to one third that of a single observation.
  2. Taking sights of more than two bodies can significantly reduce the random error of a fix just as taking more than a single observation can reduce the random error in an LOP.
  3. in the Torrid Zone (tropics) the Sun’s azimuth changes slowly for most of the morning and most of the afternoon switching rapidly from east to west around local apparent noon. To achieve a good running fix, sights need to be obtained before, near-to, and after local apparent noon.
  4. At high latitudes (north or south), on the other hand, the motion of the Sun is mostly in azimuth, at approximately 15º/hr. So, a good running fix from the Sun can be made from two sights as long as at least two and fewer than ten hours have elapsed between sights and the Sun is high enough above the horizon to take an accurate sight.
  5. Occasionally, it is necessary to take a Sun sight when it is near the horizon, to make a compass check for example. Precomputing the time and Zn of sunrise or sunset are useful to provide an approximate time and azimuth for making such an observation.
  6. When the Moon is more than a few days from New Moon it is bright enough to be easily visible during the day time. It is also well separated from the Sun. It is best situated for daytime sights around the times of First Quarter (age 6 to 8 days) and Last Quarter (age 21 to 23 days).
  7. Near Full Moon the Sun and Moon are opposite each other in the sky, so the resulting LOPs may be nearly parallel and the resulting fix would be poor. Instead, sights of the Full Moon should be combined with sights of celestial bodies other than the Sun.
  8. The most important consideration in selecting bodies for a fix is to ensure that the bodies are well distributed in azimuth. A fix from twilight observations alone requires sights of a minimum of two celestial bodies. Separating the bodies by at least 30º degrees in azimuth is desired to improve the acute angle of the intersection between LOPs.
  9. A fix made from at least three bodies that are well distributed in azimuth minimizes systematic errors in determining Ho. Observing four to six bodies significantly reduces the un certainty of a fix.
  10. select bodies with an altitude greater than 15º to minimize systematic errors in refraction, and with an altitude less than 75º to prevent errors arising from the break down in the approximation that an LOP is equivalent to a circle of equal altitude.

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