Optimum range of a wingless rocket about a rotating earth

Abstract

The motion of a wingless rocket in a vacuum about a spherical non-rotating earth describes the elliptic orbit of a material point of mass in a central field of force. The corrections for the rotation of the earth are applied to this solution to determine the effects on optimum range. Since there is no simple mathematical solution for optimizing the range, it is necessary to obtain ranges for several angles of elevation at each initial velocity and then find the optimum range by using interpolation formulas. Only the case of firing at the equator is computed although the formulas and the computational procedure outlined can be applied at any latitude. Firing to the East gives the greatest range for a given initial velocity and firing to the West gives the least range. The angle of elevation is lowest firing East and highest firing West, although for low velocities the difference is not great and for the 5,000 mph. solution a constant angle of elevation gives ranges varying at most only one-tenth of a mile from the maximum for any direction of fire. However, for the 15,000 mph. solution all the factors are critical in obtaining the maximum range.