JOURNAL OF TELECOMMUNICATIONS, VOLUME 19, ISSUE 1, MARCH 2013

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© 2013 JOT

www.journaloftelecommunications.co.uk

Determination and visualization of the

trajectories of Satellites

S. Berrezzoug, A. Boudjemai, and F.T. Bendimerad

Abstract— The detailed definition and optimization of satellites required to build the most advanced knowledge in a wide range

of disciplines (mechanical space, radio frequency, thermal exchange, control, etc.).. Therefore, for the design of a satellite,

many and various technical problems must be solved, including the orbital position of the satellite. The purpose of this study is

to develop a method of calculating orbits and the use of algorithms to compute the ground track of the satellite allowing

visualization of the latter in a terrestrial planisphere.

Index Terms— Satellite, Orbit, Orbital element, Position of the satellite, Altitude, Ground track.

—————————— ——————————

1 INTRODUCTION

HE use of satellites in orbit requires frequent and accurate assessment of their positions. In this context, the orbit is the starting point of all the work.

So the purpose of orbit determination is to get the coordinates of a satellite "or orbital elements" in function of time.

A reminder of the orbital parameters and the ground track of the satellite will be presented before moving to software developed and the results of the application.

2 ORBITAL ELEMENTS

The design of a system for tracking a satellite necessarily requires knowledge of its orbit. To do this we must accu-rately describe the position of a satellite in space. Parame-ters to fully define the orbit are called "Keplerian orbital elements" in the name of the astronomer Johannes Kepler (Fig1). [1] Five parameters are independent of time, they allow the identification of the orbital plane relative to the earth and the determination of its shape and position in this plan. These parameters are: a (Semi-major axis), e (eccentricity), i (inclination), Argument of perigee) and (Longitude of ascending node or Right ascension of the ascending node). [2] The sixth parameter is a function of time, it identifies the position of the satellite in its orbit, we choose the angle (true anomaly), E (eccentric anomaly) or M (mean anoma-ly). \

3 DETERMINATION OF VECTOR POSITION FROM

ORBITAL PARAMETERS

Cartesian coordinates of the artificial satellite in the orbital plane are [3] :

(1)

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S. Berrezzoug is PhD student with the Telecommunications Laboratory LTT, Department of Electrical Engineering, Tlemcen University, Algeria.

A. Boudjemai Jr. is Research Team Leader with The CDS (Satellite Devel-opment Center), Oran, Algeria

F.T. Bendimerad is Professor with the Department of Electrical Engineer-ing and director of Telecommunications Laboratory, University of Tlemcen, Algeria.

T

FIG1 : ORBITAL ELEMENTS

0

2

z

Esine1asinry

)eE(cosacosrx

7

(2)

There must be an equation that takes into account the time law of motion of the satellite in orbit. Such an equa-tion will predict at any time the position of the satellite; it is also called "Kepler's equation" given by [1]:

)tt(nEsineEM p (3)

where : pt : Date of perigee passage and

n: average movement T

2

an

3

The three parameters (i,) allow to calculate the position of the satellite in the equatorial plane [4] :

(4)

with:

xx a PA , yy PaA , zz a PA , et

xx ea Q)1(B 2 , yy Q)e(aB 21 ,

zz ea Q)1(B 2

4 GROUND TRACK OF SATELLITE

Ground track consists of all points of the earth's surface overflown by the satellite. It is also the projection of a point S of the orbit of the satellite on the Earth's surface, the projection point is then expressed in latitude and Longitude geographical LS and λS (Fig.2), calculated

by [5]:

5 APPLICATION

The application provides the ability to represent main-ly a terrestrial reference ground track satellites after stud-ying their trajectories and calculate their positions over time and the possibility to calculate at a precise moment, the link budget between the satellite and a station (Fig. 3).

Satellites can be studied existing satellites or satellites

created by the user by introducing himself, in this case, the orbital parameters.

So this interface allows us to: Choose a satellite, Give the geometric coordinates of a station,

)Ecose(1ayxr 22

EsinB)eE(cosAz

EsinB)eE(cosAy

EsinB)eE(cosAx

ZZ

YY

XX

sinisinP

sincosicoscossinP

sinsinicoscoscosP

Z

Y

X

cosisinQ

coscosicossinsinQ

cossinicossincosQ

Z

Y

X

22

12

gg

gs

gg

gs

YX

Zarctan

XsgnX

YarctanL

Fig.2 Geometric coordinates of the satellite

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Start the simulation of the ground track of the satellite,

Stop or delete it at any time, Obtain the latitude, longitude and altitude of the

satellite (position), Start the calculation of link budget between the

satellite and the station on calling a second interface,

Access to assistance help.

By clicking on a satellite, it will load a TLE file (Two Lines Elements) and convert it to orbital parameters then displayed them on the window.

The Two-Line Elements or TLE is a standardized

representation of the orbital parameters. They can calculate the position of objects in orbit at all times as they follow the laws of Kepler and Newton [6].

Fig.3 Interface of trajectory

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6 SIMULATION RESULTS

Fig.5 Link budget between Alsat1 and the site of Arzew

Fig.4 Ground track of the satellite Alsat-1

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The track of Algerian satellite ALSAT-1 was simulated, its position is displayed for each trip with its altitude (Fig. 4). As ground station, we chose the station of Arzew (Algeria), was calculated link budget between the station and the satellite and this by clicking on the link budget button (Fig.5).

We checked the good functioning of our application

after a test validation and comparison of traces of satellites with those made by verified software from the Centre National d’Etudes Spatiales CNES (Fig 6 and Fig.7). Here is an example for the Russian satellite Molnya:

So we conclude that we have the same trace with our developped application and with the verified software of simulation (Solstice).

7 CONCLUSION

Our application allows the calculation of the orbits of satellites and their positions and then sees their ground tracks in a terrestrial planisphere.

So with this developed software, it was able to simulate the trajectory of any satellite and determine its position and analyze the puissance between it and any station that can tell us about the quality of the connection design .

REFERENCES

[1] Carrou J.P., " Le mouvement du véhicule spatial en orbite ", ISSN 0244-

8041, Centre National d’Etudes Spatiales, Toulouse, France, Juin1980.

[2] Zarrouati O., "Trajectoires Spatiales", Centre National d’Etudes Spa-

tiales, Edition Cepadues, Toulouse. France, 1987.

[3] Tarik Kaya, "Orbital mechanics’’, Carleton University, De-

partement of Mechanical and Aerospace Engi-neering.

[4] Lauren Rose Chung, " Orbit Determination Methods for Drag-

Free Controlled Laser Interferometry Missions”, University of

Maryland, College Park, 2006.

[5] Kristian Svartveit, "Attitude determination of the NCUBE satel-

lite’’,

[6] Felix R. Hoots, Ronald L. Roehrich, "Models for Propagation of

NORAD Element Sets", Package Com-piled by TS Kelso.

Fig.7 Ground track of the satellite Molnya

with Solstice.

Fig.6 Ground track of the satellite Molnya.