Accession Number : AD0284799

Title :   ON TAKE-OFF FROM CIRCULAR ORBIT BY SMALL THRUST

Corporate Author : POLYTECHNIC INST OF BROOKLYN N Y

Personal Author(s) : TING,LU ; BROFMAN,SHERWOOD

Report Date : AUG 1962

Pagination or Media Count : 1

Abstract : Analytic solutions for the trajectories of taking off from a circular orbit by low thrust at a finite angle to the radial vector are presented. The solution is uniformly valid for the entire time interval measured from the initial instant of take-off, t=0, to t=O(1/epsilon) subjected to the upper limit set by the assumption of small thrust, where epsilon is the ratio of thrust to the central force at t=0. The zero order solution, which is in error to the order epsilon, is a function of the 'slow' time variable tau equals epsilon t and reduces to Tsien's solution (Jet Propulsion, v.23 (4):233-236, 1953) for circumferential thrust. Due to the long time interval, t=0 to O(1/epsilon) the standard techniques for the next order solution break down. The present solution is obtained by splitting it into two parts; one is a non-oscillatory function of tau and the other is an oscillatory function of t with varying periods. With this scheme it is possible to simplify the equations by estimating the order of magnitude of the terms for the entire interval. For the first order solution the non-oscillatory part is uniquely determined from an integral equation while the oscillatory term cannot be uniquely determined. This indeterminacy is removed by the requirement of the vanishing of the secular terms in the second order solution when the same scheme of splitting the solution is applied. Comparison with several results repeated to obtain higher order solutions. (Author)

Descriptors :   *CELESTIAL MECHANICS, *ORBITS, DIFFERENTIAL EQUATIONS, MATHEMATICAL ANALYSIS, THRUST, TIME

Distribution Statement : APPROVED FOR PUBLIC RELEASE