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Frank Reed wrote:

> The angle to be subtracted from TA to obtain OA is, in this routine-
> Arc-tan ( cos TA / ((23455 * D) - sin TA))
>
> I mentioned that you can also do this calculation by iteration. Now
> for a bit of trivia: the Arctan formula, which is plenty accurate
> enough for practical puposes, is actually an approximation. There is
> no closed form solution for OA above. There cannot be since the
> equation is identical in form to Kepler's Equation.

Frank,

I believe you are mistaken. There is no resemblance to Kepler's
equation. The characteristic feature of the latter is that the variable
E (eccentric anomaly) appears as a term E as well as a term sin E,
making it impossible to express E as explicit function of the mean
anomaly. We don't have this sort of thing in the above formula for the
parallax. It is explicit and rigorous (for what it is supposed to do).
No iteration required.

Herbert Prinz

   

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