Procedure for calculating three components of vector field from spherical harmonic using either geocentric or geodetic coordinates as input and output is described. Three subroutines of computer program are explained. Program is written in FORTRAN for IBM 360 computer

Mead, G. D.

Stassinopoulos, E. G.

English

NASA Technical Reports Server

October 1972
	 B72-10674 
NASA TECH BRIEF 
Goddard Space Flight Center 
NASA Tech Briefs announce now 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. 
Geometric Field-Line Calculations 
The problem: 
To calculate the three components of the vector field 
from a spherical harmonic expansion using either geo-
centric or geodetic coordinates as input and output. The 
program also contains field-line tracing routines useful in 
several applications, for example: locating the position of 
conjugate points, determining mirror point locations for 
particles at a given position with a given pitch angle, etc. 
The solution: 
The three components of the vector field are returned 
as output in either geocentric or geodetic coordinates 
according to how they were entered, whereas the field-line 
tracing routine returns a line that passes through a point 
and is everywhere parallel to the location field direction as 
determined by the model. 
How it's done: 
The program is actually three subroutines, ALLMAG, 
GDALMG, and LINTRA. ALLMAG is a fundamental 
routine that calculates three components of the vector 
field from a spherical harmonic expansion. The relevant 
mathematical formulation is readily available in related
texts and is not included here. The coordinates entered 
into ALLMAG must be geocentric. If input must be 
geodetic, then the subroutine GDALMG must be called to 
convert the coordinates to the proper input parameters. 
In the line-tracing, LINTRA, routine, the method used 
is to solve differential equations defining a field-line in 
order to obtain the correct values for field-line values. 
Notes: 
1. This program is written in FORTRAN IV for use on an 
IBM-360/(40, 75, and 91), IBM-7094, UNIVAC . l 108, 
and CDC-6600. 
Inquiries concerning this program should be directed 
to:
COSMIC 
112 Barrow Hall 
University of Georgia 
Athens, Georgia 30601 
Reference: GSC . l 1597 
Source: E. G'. Stassinopoulos and
Gilbert D. Mead
Goddard Space Flight Center 
(GSC-1 1597) 
Category 09 
This document was prepared under the sponsorship of the National
	 Government assumes any liability resulting from the use of th 
Aeronautics and Space Administration. Neither the United States
	 information contained in this document, or warrants that such u-c• 
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=19720000673 2020-03-17T03:42:29+00:00Z
N73-S 
R1. 1313 
KSC HQ3 
-1-


Geometric field-line calculations

Abstract

Similar works

Full text

Available Versions

NASA Technical Reports Server