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## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

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Re: Sight Reduction Formula
From: George Huxtable
Date: 2003 Oct 20, 00:37 +0100

```I said
>>
>> example above). Rectangular to polar conversions are conventionally
>> intended to produce an angle which increases anticlockwise from the x-axis,
>> whereas we require an angle that increases clockwise from the y axis, so a
>> bit of thoughtful tinkering may be called for.

And Paul Hirose responded-

>One solution is to lie to the machine. Where it wants x, give it y,
>and vice versa. Leave the signs unchanged. That will generate azimuths
>increasing clockwise from zero at north.

Yes, that's exactly what was done in the examples given, as copied below..

>Many Casio calculators provide the POL (polar) function, with two inputs,
>and when you apply
>
>X = POL (( Cos Lat * Tan Dec - Sin Lat * Cos HA) , (- Sin HA))
>
>then what appears in the Y variable is a quantity between -180 and +180,
>unambiguously >defining the azimuth. (Negative azimuths can have 360 added
>to put them into familiar >form.)

The Casio POL function asks for the Cartesian X-coordinate first, then the
Y coordinate, but in the example above they are provided in the opposite
order, just as Paul suggests. The function expects the X-coordinate to be
positive going left, and the Y-coordinate to be positive going upward.
Because hour angle increases positively going to the right, however, the
Sin HA term has to be given a minus sign.

If anyone else still owns a working HP-21 that isn't in a museum, I should
warn that the description of Polar/Rectangular coordinate conversion in its
handbook (or at least in my 1975 version) is in error and doesn't
correspond to the way the machine actually behaves.

George.

================================================================
contact George Huxtable by email at george---.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
================================================================

```
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