Suppose a vessel begins fishing at latitude 42° 48.163, longitude -70° 40.159 and stops fishing at 42° 50.013/-70° 40.534. It moves at 3.0 knots for 45 minutes. The vessel does not tow in a straight line, but no intermediate positions are available. I theorize that all possible vessel paths between those two points can be described by an ellipse. However, despite many hours searching for a formula or methodology to define that ellipse, I have been unsuccessful.

I recently realized a formula for an ellipse from two geolocations, plus a speed and a duration, might be useful for tag/recapture studies, since tag and recapture locations, and time at liberty are known, and average speed can be estimated. A two-dimensional ellipse of fish movement could be then be defined.

Does anyone have knowledge of a formula, or any other insight?

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