![]() ![]() Therefore distance of the true position from the apparent positionĪlternatively, we could simply find the difference between the two altitudes and convert this to nautical miles as follows: Alt. Suppose that, at the same time as measuring the altitude at the true position, we find from the Sight Reduction Tables that the tabulated altitude at the Assumed Position is 67o.92 then the zenith distance would be: Zenith Distance = 90o – Alt = 90o – 67o.92 = 22o.08 = 1324’.8 = 1324.8 n.m. Using this information, the calculation for finding the zenith distance at the true position would be as shown below: Zenith Distance = 90 o– Alt = 90 o – 68o.06 = 21 o .94 = 1316’.84 = 1316.4 n.m.Ĭalculating the Zenith Distance at the Assumed Position. Suppose the Sun’s altitude, as measured at the true position, was 68 o.06. For the following example, suffice it to say that we have measured the altitude at the True Position and calculated the altitude at the Assumed Position.Ĭalculating the Zenith Distance at the True Position. We can calculate the altitude at the assumed position by using either spherical trigonometry or by sight reduction techniques. position) position at the time that the altitude was measured at the true position, we would then be able to compare the two altitudes and calculate the difference between them. Now, If we calculate what the altitude would have been at the Assumed Position (the D.R. So, measuring the altitude gives us a method of calculating the zenith distance and the zenith distance gives us the distance AU in nautical miles. We can see that the zenith distance is equal to 90 o – Altitude. The true position of the yacht is represented by A in the diagram Z represents the zenith of the true position X represents the position of the Sun U represents the geographical position of the Sun ZX is the zenith distance and AU is equal to the angular distance ZX in nautical miles. We cannot physically measure the distance from the yacht to the GP but we can measure the altitude of the Sun at the true position and from that we can calculate the zenith distance as can be explained with the aid of the diagram below. However there is another way of solving the problem. A chart on which such a large circle could be drawn would require such a small scale that accurate position-fixing would be impossible. ![]() Because of the great distance of the Sun from the Earth, the radius of the position circle will be very large (approximately 3000 nautical miles or so). However, there is a problem with this idea which makes it impracticable. In this way, it would seem that our true position would correspond to the intersection of these lines on the chart. The problem is to establish at which precise point on the position circle the yacht lies.Īt first, it might seem that all we need to do is to observe the bearing of the Sun at the same time that we measure its altitude and then draw the line of bearing on the chart along with the position circle. The diagram below shows that, at any point on the circumference of the circle, the Sun’s altitude will be 35 o and our distance from the GP will be equal to the radius. Such a circle is known as a ‘position circle’ and when it is based on a sighting of a celestial body, as in this case, it is known as an Astronomical Position Line. Suppose we are in a yacht and we measure the altitude of the Sun and find it to be 35 o what does this tell us? All that we know is that the yacht lies somewhere on the circumference of a circle centred at the geographical position of the Sun. The difference between the two altitudes will be equal to the distance between the two positions and this distance is known as the intercept. Hilaire method after the French Navigator who devised it in 1875, is a method of establishing a fix by measuring the altitude of a celestial body from the true position and comparing this with the calculated altitude at the DR position or the EP. The Intercept method, also known as the Marcq St. One of these methods is the Intercept Method. Although it is usual these days to calculate an observed position in astro navigation by using the Rapid Reduction Method, there are other methods which do not necessitate the purchase of expensive reduction tables. ![]()
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