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    Re: Single LOP is enough?
    From: Frank Reed
    Date: 2020 Sep 15, 12:41 -0700

    The key detail here: that azimuth that you see in the intercept method is calculated from your input! It cannot help you fix your position all by itself because it can have any value, dependent on the DR or AP or other position that you feed into the calculation process. We don't have any means of observing azimuths with great accuracy, but if we did, we could use them for celestial position fixes.

    Let's imagine a super-compass enabling us to observe the azimuth of a star to the nearest tenth of a minute of arc. Typical real compasses can get you the azimuth to the nearest degree under good conditions and often worse. So this super-compass would be on the order of 500 to 1000 times better at measuring azimuths than anything we have today. 

    Now observe the Sun with your (common) sextant and also your super-compass. You get an altitude of, let's say, 60°15.5' (after applying altitude corrections), and from your super-compass you get an azimuth of perhaps 175°12.0'. Then you look up the Sun's astronomical data, and you select and arbitrary position near where you think you are to use as an "AP". From that AP you calculate that the Moon's altitude should be 60°10.0' and it's azimuth should be 175°09.5'. That tells us that our vessel is 5.5 nautical miles towards the Sun, and it is also some miles (there's a little math involved) to the left of the arbitrary AP (to the left when facing the Sun). With those two observed pieces of information, we could fix our position. But there are no super-sextants, at least not in commercial production.

    There's a general principle at work here. We want two numbers out of our navigation process: latitude and longitude (or some equivalent x, y coordinates). To get two quantities out, we need to feed two observed quantities in. In normal celestial navigation, we observe two altitudes to get latitude and longitude. With super-compass celestial navigation, we could observe one altitude and one azimuth at the same time to get latitude and longitude. Two in, two out.

    Frank Reed

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