Computer program includes time minimizing function required for propellant constrained minimum time impulsive transfer between coplanar circular orbits or unrestricted orbits. Basic formulation is extended to include inclined circular or inclined elliptic orbits

Davis, D. A.

English

NASA Technical Reports Server

October 1971	 Brief 71-10376 
NASA TECH BRIEF 
Marshall Space Flight Center
	
_4V 
NASA Tech Briefs announce new technology derived from the U.S. space program. They are issued to encourage 
commercial application. Tech Briefs are available on a subscription basis from the National Technical Information 
Service, Springfield; Virginia 22151. Requests for individual copies or questions relating to the Tech Brief program may 
be directed to the Technology Utilization Offi ce, NASA, Code KT, Washington, D. f. 20546. 
New Procedure for Determining Minimum Time Orbit Transfers 
.
The problem: 
To determine the minimum time for orbital trans-
fer in a central force field when a fixed amount of 
propellant is available. 
The solution: 
The Minimum Time Orbit Transfer Program, which 
includes the time-minimizing function required for 
the propellant-constrained minimum time impulsive 
transfer between orbits. 
How it's done: 
The program considers transfers between coplanar 
circular orbits or unrestricted orbits. The total 
velocity change from orbit to orbit is defined, and 
the minimum time required for the given propellant 
constraint is derived. The different propellant 
constraints lead to the three basic operational modes. 
In mode one, only a single velocity change is allowed, 
enabling the minimum time intercepts between 
orbits to be calculated. In mode two, two impulses 
are assumed, and the sum of these impulses is 
limited to a preselected value. Modes one and two, 
then, are dependent upon a single parameter search. 
In mode three, the configuration of the vehicle is 
assumed known, and the analytical solution for 
elliptic and hyperbolic transfers can be derived. 
Lambert's theorem provides the relationship 
needed for determining the transfer times associated 
ith those trajectories which can link two orbits in 
all three modes.
When the program is used without the minimiza-
tion procedure, all possible propellant constrained 
trajectories are generated. Through mode three, 
vehicular sizing may be explored. In addition, 
the basic formulation may be easily extended to in-
clude inclined circular orbits or inclined elliptic 
orbits. In such cases, there is an appreciable increase 
in the number of parameters which must be varied 
to determine the minimum time transfer. 
Notes: 
1. This program is written in FORTRAN IV for use 
on the IBM OS/360 computer. 
2. Requests for further information may be directed 
to:
COSMIC 
112 Barrow Hall 
University of Georgia 
Athens, Georgia 30601 
Reference: B71-10376 
Patent status: 
No patent action is contemplated by NASA 
Source: D. A. Davis of

The Boeing Company

under contract to

Marshall Space Flight Center

(MFS-14804) 
Category 09 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned.rights.
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New procedure for determining minimum time orbit transfers

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