In celestial navigation, lines of position are rarely obtained simultaneously. This is especially true during the day when the sun may be the only available celestial body. A celestial line of position may be advanced for 3 or 4 hours, if necessary, to obtain a celestial running fix. It may also be advanced by advancing the AP in the direction and distance an amount consistent with the ship's travel during the interval between two successive observations. In the latter procedure, the azimuth line is drawn through the advanced AP without any change in direction. The advanced LOP is drawn perpendicular to the azimuth, a distance from the AP equal to the intercept, and toward or away from the GP, as appropriate.Plotting the Celestial Fix
At morning and evening twilight, the navigator may succeed in observing the altitudes of a number of celestial bodies in a few minutes and establish a celestial fix. If 2 or more minutes elapse between observations, the navigator must consider:
1. Elapsed time
2. Speed of ship
3. Scale of the chart or plotting sheet
To determine whether or not a more accurate fix can be obtained by advancing AP's to a common time. It is possible during the day to obtain a celestial fix rather than a celestial running fix if two or more of the three following bodies are visible:
1. Sun
2. Moon
3. Venus
LOP from Celestial Observations
A ship has many possible locations on a line of position. In other words, the ship's position must be somewhere along that line. A fix, by position is the intersection of two or more lines of position, but this is not the ship's exact position, because one can always assume some errors in observation, plotting. The celestial navigator must establish the lines of position by applying the results of the observations of heavenly bodies. A line of position obtained at one time may be used at a later time. All you need to do is move the line parallel to itself, a distance equal to the run of the ship in the interim, and in the same direction as the run. Such a line of position cannot be as accurate as a new line, because the amount and direction of its movement can be determined only by the usual DR methods.
If two new lines cannot be obtained, however, a old line, advanced and intersected with a new one, may be the only possible way of establishing a fix. Naturally, the distance an old line may be advanced without a substantial loss of accuracy depends on how closely the run can be reckoned. In celestial navigation, as in piloting, you essentially are trying to establish the intersection of two or more lines of position. A single observation is insufficient to obtain a fix, however it can be used with a loran line, etc. to provide a fix.
Two Circles
Observation of two bodies at the same time gives the navigator two circles of equal altitude. The circles intersect each other at two points, and because the ship is somewhere on each one of them, she must be at one or the other points of intersection. A circle on the surface of the earth, on every point of which the altitude of a given celestial body is the same at a given instant, the pole of this circle is the geographical position of the body, and the great-circle distance from this pole to the circle is the zenith distance of the body.
Line of Position
In practice, you may not be able nor will you need to plot the whole of a circle of equal altitude. The position is usually known within 10 miles and possibly even less than that. Inside these limits, the curve of the arc of a circle of equal altitude is hardly perceptible, and the arc is plotted and regarded as a straight line. Such a line, comprising enough of the arc of a circle of equal altitude to cover the probable limits of a position, is called a Sumner line of position or just a line of position.
Two Lines of Position
The prefered method of establishing two lines of position is by observing two different bodies, although two lines may be obtained from the same body by observations taken at different times. As in piloting, the nearer the two lines approach at right angles to each other, the more accurate the fix. When two lines are determined by observing the same body, the first line established is brought forward the distance run on the course steered. For example, if a ship steams 27 miles on course 315° between the first and second observations, obviously the position is on a line parallel with the first one established, but drawn 27 miles away (to scale) on the course line 315°. Intersection of the line established by the second observation with the advanced line of the first observation is a fix. The fix progressively decreases in accuracy, depending on how far the first line is advanced. You should not advance such a time for more than 5 hours of a run.
Determining a Line of Position
At this point you might be entitled to complain that much has been said concerning what a line of position tells you, but very little has been said about how you should determine it in the first place. I will get to that part now. You probably have grasped the idea that what you want to find out is which circle of equal altitude you are on, and what this altitude is. To draw such a circle, you would need a chart covering an extensive area, unless the heavenly body's altitude approached 90° you do not determine the entire circle but only a portion of its arc, this is so small that it is plotted and regarded as a straight line. An assumed position (AP) is selected according to the rule of 30' of your DR position for the time of sight. Observation of a body provides sextant altitude. Sextant altitude is then corrected to obtain observed altitude (Ho). The body's altitude from the assumed position (called the computed altitude (Hc) and its azimuth angle are determined from tables. The azimuth angle is then converted to azimuth.
After selecting an AP, draw the azimuth through the AP. Along the azimuth measure off the altitude intercept (difference between the observed altitude and the computed altitude). At the end of this measurement, draw a perpendicular line, which is the LOP. You must know whether altitude intercept (a) should be measured from AP TOWARD the body or from AP AWAY from the body. Sometimes the initials for Coast Guard Academy (CGA) can be helpful. If the computed altitude is greater than the observed altitude, altitude intercept (a) is measured away from the body. In other words applying the CGA "memory aid," you have computed, greater away (CGA). Another memory aid is Ho Mo To when it is towards.
Selecting Bodies for Observation
Before going into problems and tables, mention should be made of a few items concerned with selecting astronomical bodies for observation. Observing two heavenly bodies in rapid succession is the most convenient method of finding two lines of position necessary to establish a fix. Noting three bodies gives three lines, and these three define the fix more accurately (as in piloting). Accuracy of the fix established by intersecting lines of position depends upon the angle between the lines. The nearer this angle approaches 90°, the more accurate the fix. Actually, sights seldom are taken on two or more bodies simultaneously. Instead, the navigator decides which bodies to observe, then takes a round of sights, each one timed exactly. Resulting lines of position are advanced or retarded in the amount of the ship's run between the time of observation and the time of the desired fix.
The ideal situation for lines of position established by observing three bodies would be that where the bodies lie 120° apart in azimuth. An ideal fix using four bodies would include two north / south lines and two east / west lines of position to form a box. Lines perpendicular to the course are valuable for checking the run. Those lines parallel to it are helpful in deciding the accuracy of the course made good. Concerning altitude, best results are obtained by observation of bodies whose altitudes are between 10° and 65° In general, observations are taken from bodies whose altitudes are between 10° and 80°.
Advancing and Retarding the LOP
Several methods may be used to advance a line of position.The most frequent method consists of advancing the AP in the direction of your course and for the distance of the run, and drawing the new LOP. To retard a LOP, just do the reciprocal of your course for the distance run.
Estimated Position by Celestial Navigation
If appreciable time has elapsed since the determination of the last fix of the ship's position at sea, the error in the DR plot may change where the ship's actual position is well away from the DR plot. A single line of position can be useful in establishing an estimated position. If an accurate line is obtained, the actual position is somewhere on this line. In the absence of better information, a perpendicular from the previous DR position or EP to the line of position establishes the new EP. The foot of the perpendicular from the AP has no significance in this regard, since it is used only to locate the line of position.
The establishment of a good EP is dependent upon accurate interpretation of all information available. Generally, such ability can be acquired only by experience. If, in the judgment of the navigator, the course has been made good, but the speed has been uncertain, the best estimate of the position might be at the intersection of the course line and the LOP. If the speed since the last fix is considered accurate, but the course is considered uncertain, the EP might be at the intersection of the line of position and an arc centered on the previous fix and of a radius equal to the distance traveled.
