Thursday, June 16, 2011

Observing Local Noon

The Summer Solstice is fast approaching and so some details on observing local noon might be a suitable topic for this blog. I used the setup below to capture images of the Sun projected onto a plywood board with graph paper affixed to it to serve as a coordinate grid. The observations were made about local noon on 27 May 2011.

The coordinates, (λ,μ), of the Sun were found by doing a 2D interpolation of an image's pixel coordinates for the Sun relative to the corner coordinates of the 1 inch grid which contained the Sun's image. This was easier than finding a formula to convert pixel coordinates to grid coordinates for each image. λ increases along the line of sight and μ increases to the left both from the bottom right corner. The Sun followed the track indicated in the next image. The large red dot at the bottom indicates the point below the aperature of the lens which is needed to determine a minimum distance corresponding to the Sun's maximum altitude.

Plotting the distance of the Sun from the point below the aperature of the lens versus time results in a curve with a fairly well defined minimum. Estimating the time of the minimum and doing a polynomial fit about this time gives a simple polynomial. The curve shown is that of a 6 degree polynomial fit.

The time of local noon is determined by the best fit and comparing this time with that of the Greenwich local noon allows one to determine the hour angle of one's position. I'll try to give more details on this procedure in future blogs.

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