Optimal Low Thrust, Three Burn Orbit Transfers with Large Plane Changes

Citation

Zondervan, Keith Peter (1983) Optimal Low Thrust, Three Burn Orbit Transfers with Large Plane Changes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/NXPK-GE17. https://resolver.caltech.edu/CaltechETD:etd-08152005-091409

Abstract

During the last twenty-five years, much attention has been devoted to the problem of optimal orbit transfer. The problem has been conveniently divided into two categories - unlimited thrust (or acceleration) orbit transfers and limited thrust (or acceleration) orbit transfers. The unlimited thrust orbit transfers use infinite thrust, zero burn time burns and hence have also come to be known as impulsive burn orbit transfers. In general it has been found that optimal (i.e., minimum fuel, time-free) solutions to these types of transfers require two or possibly three burns. The limited thrust transfers, in contrast, do not use impulsive burns but use burns which have a finite thrust level and a nonzero burn time and, hence, are also known as finite burn orbit transfers.

If our attention is restricted to finite multi-burn transfers which have burn times less than an orbital period, two classes of transfers emerge. These classes of transfers are either Geometrically Similar to the 2-Burn Impulsive (GS2BI) transfers or Geometrically Similar to the 3-Burn Impulsive (GS3BI) transfers. For example, if a 2-burn impulsive solution has a perigee burn followed by an apogee burn, the GS2BI finite burn transfer would use one or more perigee burns followed by one or more apogee burns.

Recent-studies have presented optimal solutions to GS2BI finite burn orbit transfers for various thrust to weight ratios. The current study presents the optimal solutions to GS3BI finite burn orbit transfers between a 28.5° inclined low-earth orbit and a series of 63.4° inclined circular orbits and a series of 63.4° inclined elliptical orbits with twelve hour periods. Also presented are optimal solutions to GS3BI finite burn orbit transfers between 97° inclined high-earth orbits and a 57° inclined low-earth orbit. Optimal solutions are found to be bounded by a lower limit on the initial thrust to weight ratio. It is shown that as the final perigee altitude is increased, the GS3BI finite burn transfer degenerates to a GS2BI finite burn transfer much as it would for the impulsive case.

Analysis of the optimal steering during various burns reveals a natural division of the steering strategies into two categories based on whether a burn results in a predominant change in the orbit size-or-the orbit plane. The similarity of these optimal steering strategies to previously obtained simple "near-optimal" steering strategies is discussed.

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