(HP-67) Barkers's Equation

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An extract from An Efficient Method for Solving Barkers's Equation, British Astronomical Association, R. Meire, Journal of the British Astronomical Association, Vol. 95, NO.3/APR, P.113, 1985

"In a parabolic orbit, the true anomaly v (as a function of the time) can be obtained by solving a cubic equation for tan y, the so-called Barker equation. A modified method of solution is described and it is shown that this new form is very efficient from a computational point of view: it needs less program statements, is faster, and it has greater accuracy than the normally used trigonometric solution.
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In programming this trigonometric method on a computer or on a calculator, a problem occurs with the cubic root in equation (6) if W < 0. We must include a conditional test in the program to solve this problem. As an example, Appendix A shows the program for an HP-67 calculator, and it can be seen that the cubic root problem takes four additional steps.
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Appendix B gives the program for the HP-67 calculator. Although the trigonometric solution has a certain 'beauty', it cannot compete with this new solution (equation (12)) from a practical point of view."

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there are THREE pages to the article. Use the navigation links at the bottom to 'see' ALL three. The program listings are on page 115.