Modified program has been developed using improved variation of Encke method which avoids accumulation of round-off errors and avoids numerical ambiguities arising from near-circular orbits of low inclination. Variety of interplanetary trajectory problems can be computed with maximum accuracy and efficiency

Lefton, L.

Levine, N.

Whitlock, F. H.

Wolfe, H.

English

NASA Technical Reports Server

October 1972	 B72-10604 
NASA TECH BRIEF 
Goddard Space Flight Center 
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 Office, NASA, Code KT, Washington, D.C. 20546. 
Interplanetary Trajectories, Encke Method (ITEM) 
The problem: 
To compute with maximum accuracy and efficiency 
a variety of interplanetary trajectory problems. 
The solution: 
The Encke method has been shown to require 
minimum time in trajectory computation with minimum 
loss of accuracy. The ITEM program has been developed 
using an improved variation of the Encke method which 
avoids accumulation of round-off errors and avoids 
numerical ambiguities arising from near-circular orbits 
of low inclination. 
How it's done: 
ITEM trajectory computation consists of two parts, 
the exact splution to the Kepler two-body problem, and 
integrated additions to this solution which account for 
perturbation effects. 
Since perturbations only are integrated, the allowable 
integration interval is fairly large over most of the 
path. Even in the vicinity of the Earth, or another planet,. 
a relatively large interval (compared to other schemes) 
may be used without limiting stability or accuracy of 
the solution. 
Round-off errors are controlled by keeping perturba-
tion displacement small. The two-body orbit is rectified 
whenever the perturbations exceed a specified maximum 
value established by comparison with the corresponding 
unperturbed value. .Further, the reference body is 
changed as necessary, with the Earth, another planet or 
the Sun selected as the reference body whenever that 
body would otherwise contribute the largest perturbing 
force.
Numerical ambiguities, such as would be introduced 
by circular orbits or zero inclination, are avoided by 
defining the problem in terms of parameters which have 
real physical significance (position and velocity vectors) 
directly related to measurable quantities. 
Flexibility is provided by means of numerous options 
available to the user through a detailed system of control 
cards which can be selected in adapting the program to 
wide variations in problem type and complexity. In 
addition, a subroutine, MODIF, permits the user to 
modify program parameters which normally are con-
stant. 
Notes: 
1. This program is written in FORTRAN IV to be 
utilized by the IBM-360 computer. 
2. Inquiries concerning this program should be directed 
to:
COSMIC 
112 Barrow Hall 
University of Georgia 
Athens, Georgia 30601 
Reference: GSC-1 1576 
Source: Fred H. Whitlock
Goddard Space.Flight Center and

Henry Wolfe, Leon Lefton, and

Norman Levine of
Analytical Mechanics Associates, Inc. 
under contract to
Goddard Space Flight Center 
(GSC-1 1576) 
Category 09, 06 
This document was prepared under the sponsorship of the National 	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States
	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States
	 will be free from privately owned rights.
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Interplanetary Trajectories, Encke Method (ITEM)

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