Program determines if rendezvous in near space is possible, and performs an analysis to determine the approximate required values of the magnitude and direction of two thrust applications of the upper stage of a rocket firing. The analysis is performed by using ordinary Keplerian mechanics

Barling, W. H., Jr.

Brothers, W. J.

Darling, W. H., Jr.

English

NASA Technical Reports Server

December 1967
	 Brief 67-10479 
NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Fortran IV Program for Two-Impulse Rendezvous Analysis 
The problem: 
To develop a program that will determine whether 
rendezvous in near space is possible with a given set of 
circumstances and, if rendezvous is feasible, to per-
form an analysis that will determine the approxi-
mate required values of the magnitude and direction 
of two thrust applications on the upper stage of a 
rocket firing. In particular, rendezvous maneuvers 
requiring two burns (one to intercept and one to 
match velocities) are to be treated for stipulated total 
propellant allotments. 
The solutioti: 
The analysis is performed by using ordinary Kepler-
ian mechanics for vacuum flight above a spherical 
earth subject to a few physical and operational limi-
tations. The thrust-to-weight ratio is assumed to be 
high enough that the burns are short compared to 
orbit periods. Target orbit characteristics are allowed 
to be arbitrary as are first stage burnout conditions. 
The plane of the launch trajectory is assumed to differ 
somewhat from the plane of the target orbit. The 
result is a nearly straight-through set of calculations. 
How it's done: 
From the description of the general mission, certain 
implicit asumptions can be drawn. The first burn of 
the upper stage can be treated as an in-plane (IP) 
maneuver with slight out-of-plane (OP) corruptions. 
The second burn will have a substantial out-of-plane 
component which is virtually set by the initial launch 
conditions. It is likely that the first stage booster will 
burn out at a fairly low altitude and the inertial veloc-
ity magnitude will be suborbital. Thus, the magnitude 
of the first burn of the upper stage will be larger than 
the in-plane component of the second burn in order to 
inject the satellite into orbit. 
With the above estimates, the problem can be
stated by writing the velocity equivalent of the propel-
lant allotment as 
Lv = AV I + -/ ( v 2) 2 1 + 
where A v 1
 is the magnitude of the first burn and the 
radical represents the magnitude of the combined 
in-plane and out-of-plane second burn. The magni-
tude of the out-of-plane component of the second 
burn depends only on the angle between the orbit 
planes and the inertial velocity magnitude of the 
target orbit. It is thus possible to estimate (v2)op 
prior to solving the in-plane part of the maneuver. 
Thus the gross rendezvous problem becomes essen-
tially two-dimensional with a quasi-fixed out-of-plane 
component. 
In accordance with the assumptions, the analysis is 
divided into two parts: the in-plane maneuvers and 
the corrections for out-of-plane maneuvers. 
Notes: 
I. This program is written in Fortran IV for use on 
the Univac 1107. 
2. Inquiries concerning this program may be made 
to:
COSMIC 
Computer Center 
University of Georgia 
Athens, Georgia 30601 
Reference: B67-10479 
Patent status: 
No patent action is contemplated by NASA. 
Source: W. H. Barling, Jr. and W. J. Brothers 
of Lockheed Missile and Space Company 
under contract to 
Marshall Space Flight Center 
(M FS- l3971) 
Category 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.
https://ntrs.nasa.gov/search.jsp?R=19670000479 2020-03-11T20:53:33+00:00Z


Fortran 4 program for two-impulse rendezvous analysis

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server