Minor Axis and Offset Derivation

Ralph Dakin published exact expressions for minor axis and offset in Sky and Telescope years ago, but these expressions are arranged for convenience of calculation rather than exposition. Hence, the equations are a little mysterious and subject to error when published in secondary sources. This situation was not helped by an unfortunate typographical error in the original article. The mistake was corrected a few months later, but the repair was often missed and incorrect expressions progressed further in amateur literature (Dakin 1962, erratum 1963).

These quantities are not difficult to derive, and something can be learned from seeing the analytic geometry logic, so they are derived anew here. The formulas that follow are superficially different than Dakin's expressions, but they produce the same answers. The differences probably are caused by the way the coordinate systems are set up. Such modifications often lead to ostensibly different formulas.

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