SATELLITE ORBIT DETERMINATION AND ANALYSIS
(S.O.D.A) – A VISUAL TOOL OF SATELLITE ORBIT FOR
SPACE ENGINEERING EDUCATION & RESEARCH
1
Muhammad Shamsul Kamal Adnan, 2Md. Azlin Md. Said, 3M. Helmi Othman,
4
Siti Maheran Johari
School of Aerospace Engineering, Universiti Sains Malaysia, 14300, Nibong Tebal, Penang. Tel: 604-5937788 ext. 6513 / Fax 604-5941026
1Lecturer, 2Associate Professor, 3Research Officer & 4Student
ABSTRACT
This paper discusses the establishment and relevant accomplishments of a simple facility used for students learning aids based on the Keplarian Orbit parameters. Three major areas in Orbital Mechanics are discussed in this paper, Orbit of a satellite, Field of View (FOV) of a satellite and Constellation of Satellites. In order to have the visual simulation of satellite orbit, 6 classical orbital elements have to be identified, i.e., Semi-major axis, Eccentricity, Inclination angle, Longitude of ascending node, argument of perigee, and true anomaly. Coverage area of a satellite is called Field of View. FOV can be calculated if the distance of the satellite from the center of the Earth is known. Orbit Constellation using Walker’s Method is simulated and display through the visual simulation for enhancing the concept of constellation design. Through the establishment of the simple facility as presented here, it is strongly felt that the required space technologies are gained with the minimum amount of budget investment. It is also felt that this is a good way for developing and getting involved in space activities in, Malaysia, especially for universities where the student training in space technology plays the main role in professional education.
Keywords: Keplerian Orbit Elements, Visual Simulation, Space Education,
Constellation, Walker’s Method
1.0 INTRODUCTION
The establishment of Aerospace Program at Malaysian Universities, such as School of Aerospace Engineering, Universiti Sains Malaysia, it is hoped that it will provide not just aerospace education, but also as one of the national sources for aerospace program. In this paper, the approaches of space education, human resources and expertise are being explained to support the national aerospace program. One of the fundamental aspect of space technology is the knowledge of orbiting bodies especially satellites orbiting around the Earth.
In this paper, an effort is made in understanding the basis of Keplerian elements which are the basis in Space Mechanics, and the fundamental of satellites constellation using the concept of Walker’s Constellation, are displayed conceptually using Matlab to produce of visual simulation of satellite’s orbit.
2.0CLASSICAL ORBIT ELEMENTS (KEPLARIAN ORBIT ELEMENTS)
For precise calculation, Orbital Elements are divided into 6 parameters as shown in Figure (1). To completely describe an orbit mathematically, these six quantities of orbital elements, which are (a) Semi-Major Axis, a, (b) Eccentricity, e, (c) Inclination angle, I, (d) Longitude of the Ascending Node, Ω, (e) Argument of Perigee (Periapsis), ω, (f)True Anomaly, ν, must be calculated [1].
3.0FIELD OF VIEW
Orbital elements of a satellite enable to visualize the orbit and its orientation in the IJK inertial reference frame and FOV is often important in knowing the ground trace of a satellite. FOV can be defined as the area that can be viewed by a satellite from a certain height [2]. Mathematically, FOV can be calculated in Figure 2. The summary equations involved in obtaining the FOV, are
2 2
R d
h= − (1)
Using the triangles comparison method, r can be calculated, which will lead to the value b
[3]. R : d = b : R Æ d R b 2 = , wherebr=bzr (2)
Finally, the Coverage Area or Field of View can be obtained as (Figure 2). CAreaθ =br+rcosθ⋅xr+rsinθ.yr (3)
4.0SATELLITE’S CONSTELLATION USING WALKER’S METHOD
Walker’s Constellation is the optimal constellation consists of circular orbits (e = 0) and symmetrical. In principal, Walker’s method is used to obtain an optimal constellation where the constellation must follow the followings (Figure 3), (a) The orbits are circular (e=0) with the same altitude (b) the orbits are inclined to the certain angle from the earth equatorial surface (c) Provide the same coverage, whether it is the zonal coverage or global coverage continuously (d) Consists of minimum numbers of satellite. Using the Walker’s method, there are several parameters need to be determined, such as, (a) T = numbers of satellite in the constellation orbit (b) P = numbers of the orbits surface with same inclination (c) F = relative phase parameter (d) I = inclination for all orbits [4].
5.0 CONCLUSION
This paper provides a fundamental introduction to the techniques of Keplerian elements, which lead to the foundation of a visualization program. As a fundamental introduction to space engineering education, this paper enhances the credibility of the student to understand the fundamental orbital mechanics as a part of learning tools and offers a good opportunity to encourage students becoming interested in space technology. Figure (4) until Figure (10) shows the simulation of satellite orbit of SODA and it is strongly believed provides a good stem of training and education for students pursuing space technology as the main interest.
Although there are many kinds of software available in the market today about space technology, but these types of software are expensive and non-economical for learning aid. In contrast, SODA is an affordable learning-training tool for the aerospace students. Furthermore, it enhances the creativity of R&D in ‘Aerospace’.
ACKNOWLEDGENTS
The authors would like to thank Universiti Sains Malaysia and USM Short Term Grant No 6035116 and 6053076 in supporting this paper.
REFERENCES
[1] Bate R.R, Mueller D.D., White J.E. Fundamentals of Astrodynamics. New York: Dover Publications
Inc. (1971)
[2] Kee C. D. Lecture Notes on Astrodynamics. Seoul. (1997)
[3] M.S. Kamal., Park C. K. Visual Simulation of Satellite Orbit. Seoul National University. Thesis. (1998)
Table 1. Initial location of 12 satellites in Walker’s Constellation 12/3/2. Sat. No. Plane No. RAAN, deg Initial Mean Anomaly, deg 1 1 0 0 2 1 0 90 3 1 0 180 4 1 0 270 5 2 120 60 6 2 120 150 7 2 120 240 8 2 120 330 9 3 240 120 10 3 240 210 11 3 240 300 12 3 240 30
Figure (1). Keplerian Orbit Elements
Figure (2). Fundamental diagram of FOV
Figure (3). Example of the Walker’s Constellation concept 12/3/2
Figure (4). Input parameters of Keplerian elements
Figure (5). A 3-D Visual simulation of satellite orbiting the Earth.
Figure (6). Field of View. The small yellow dot indicates the position of the satellite and the big red circle indicates the coverage area from the satellite.
Figure (7). A 2-D static ground track.
Figure (8). A 3-D static ground track
Figure (9). Launch window of Constellation (12/3/2)
Figure (10). The simulation of Walker’s Constellation 12/3/2 concept.