Computer program was devised to compute free-fall trajectories of satellites, allowing for injection errors and midcourse velocity perturbations. Program consists of trajectory perturbing program and N-body integrating conic program which can also be used as 2-body patch conic program

Hoeft, R. F.

Ojeda, L.

Setter, R. N.

English

NASA Technical Reports Server

March 1973
	 B73-10012 
NASA TECH BRIEF 1	 Lewis Research 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. 
N-BODY U AND K MATRIX PROGRAM 
The Problem: 
A program was needed to compute the free-fall 
trajectories of satellites allowing for injection errors and 
midcourse velocity perturbations. 
The Solution: 
A main program and a system of subroutines designed 
to include all the necessary variables. 
How It's Done: 
Two-body equations of motion provide solutions to 
the problem of describing the motion of a small particle 
(space vehicle) near a large particle (celestial body). A 
0 two-body solution establishes a reference conic section or sections (circle, ellipse, parabola, or hyperbola) and describes the motion of a small particle along this 
reference path. However, a two-body representation is not 
sufficiently accurate when a precise description of orbits 
is required. In the case of earth-satellite motion, for 
example, the two-body representation neglects such 
effects as the earth's oblateness and the attractions of the 
sun, moon, and planets. These influences are known as 
perturbations and must be incorporated into the equa-
tions of motion when computing precision trajectories. 
The U and K Program computes linear partial deriva-
tive matrices for mapping injection errors and midcourse 
velocity perturbations into lunar and interplanetary target 
miss parameters. The program consists of a trajectory 
perturbing program and an N-body integrating conic 
program which can also be used as a 2-body patch conic 
program. The N-body mode produces precise space 
trajectories; the 2-body does not. However, for the 
purpose of computing partial derivative mapping matrices, 
the 2-body mode closely approximates the results of the 
N-body mode.
Notes: 
1. This program is written in FORTRAN IV for the 
CDC-6400 computer. 
2. Inquiries concerning this program should be directed 
to:
COSMIC 
Computer Center 
112 Barrow Hall 
University of Georgia 
Athens, Georgia 30601 
Reference: LEW-1 1438 
Source: R.N. Setter, L. Ojeda, and

R.F.Hoeft
General Dynamics Corp.

under contract to

Lewis Research Center
(LEW-1 1438) 
Category 09 
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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N-body U and K matrix program

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