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Re: Curve fitting for noon Sun
Date: 2020 Jan 12, 18:41 -0500
Hi Rafael

While a parabolic fit will do, there is a far, far easier way to do it.

Plot your points as shown, on a piece of paper.  Fair in a curve with a pencil.  Fold the paper so the left and right halves are superimposed.  Viola!  The time of Meridian Passage!  Totally unscientific, yet completely practical.

Further, you can skip just about all of this for the sun's meridian passage.  The sun will hang there, with hardly any perceptible change.  Simply determine when you think LAN will occur as a function of your longitude and time zone.  Measure a few times in rapid succession at that time, to remove outliers.  Viola!  The maximum altitude for the sun that day is determined

On Sun, Jan 12, 2020, 6:33 PM Rafael C. Caruso <NoReply_Caruso@fer3.com> wrote:

I am a beginner in the study of celestial navigation, despite being of retirement age, and this is my first NavList posting. My initial celestial navigation project was to try to determine latitude by noon sun, to start with an easy measurement (particularly when carried out from the boardwalk in Belmar, New Jersey, rather than aboard a sailboat). The results were very encouraging, since the measurement error with respect to GPS latitude was only 3.3 minutes of arc, probably a case of beginner's luck.

I followed the method I read in a couple of textbooks, which recommend taking a series of measurements before and after local apparent noon. What I did not read is which type of curve should be used for fitting these data points. As the data points seemed to describe a parabola (figure NoonSun), I used a polynomial of degree 2, which has the advantage of being easy to deal with (figure NoonSunFit). It also allows a calculation of the time at which the curve reaches its maximum, and of the altitude reached at the maximum.

My question is: does Sun altitude as a function of time describe a parabola? Or another curve? Or it doesn't matter as long as the fit is acceptable? Many thanks in advance for your input.

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