On Minor Circle Turns

摘要

In a recent issue of the Journal of the Aerospace Sciences W. H. T. Loh introduced a definition of a minor circle turn. In the present paper, an alternative definition was suggested which appears useful in that it removes some of the restrictions found in the work by Loh. Loh's definition of a minor circle turn requires the vehicle to fly in a plane which is oriented normal to the axis of the earth and which is elevated above the equator at that distance where the plane intersects the surface of the earth at the desired latitude. While this is satisfactory for near-earth trajectories and for gentle minor circle turns, it does not appear to be capable of handling the cases where the altitudes are large and where the latitudes of the turn approach ninety degrees. To surmount this difficulty, the author defined a minor circle trajectory as that path where the vector pointing toward the center of the earth from the vehicle always cuts the surface of the earth at a constant latitude. This is equivalent to requiring the path of the vehicle to lie on the surface of a cone whose solid angle is the supplement of twice the latitude.