Int. J. Communications, Network and System Sciences, 2011, 4, 585-589
doi:10.4236/ijcns.2011.49070 Published Online September 2011 (http://www.SciRP.org/journal/ijcns)
The Range and Horizon Plane Simulation for Ground
Stations of Low Earth Orbiting (LEO) Satellites
Shkelzen Cakaj, Bexhet Kamo, Vladi Koliçi, Olimpjon Shurdi
Faculty of Information Technology, Polytechnic University of Tirana, Albania
[e-mail], [e-mail]
Received August 2, 2011; revised August 24, 2011; accepted September 5, 2011
Abstract
Communication via satellite begins when the satellite is positioned in the desired orbital position. Ground
stations can communicate with LEO (Low Earth Orbiting) satellites only when the satellite is in their visibil-
ity region. The ground station’s ideal horizon plane is in fact the visibility region under 0˚ of elevation angle.
Because of natural barriers or too high buildings in urban areas, practical (visible) horizon plane differs from
the ideal one. The duration of the visibility and so the communication duration varies for each LEO satellite
pass at the ground station, since LEO satellites move too fast over the Earth. The range between the ground
station and the LEO satellite depends on maximal elevation of satellite’s path above the ground station. The
dimension of the horizon plane depends on satellite’s orbital attitude. The range variations between the
ground station and the satellite, and then ground station horizon plane simulation for low Earth orbiting sat-
ellites as a function of orbital attitude is presented. The range impact and horizon plane variations on com-
munication duration between the ground station and LEO satellites are given.
Keywords: LEO, Satellite, Range, Horizon
1. Introduction
A typical satellite communication system comprises a
ground segment and a space segment. Basic parameters
of communication satellites are communication frequen-
cies and orbits. The orbit is the trajectory follow ed by th e
satellite. Different types of orbits are possible, each suit-
able for a specific application or mission. Generally, the
orbits of communication satellites are ellipses within the
orbital plane defined by orbital parameters [1-3]. Orbits
with zero eccentricity are known as circular orbits. Cir-
cular orbits are presented in Figure 1 and mainly catego-
rized as:
 GEO (Geosynchronous Earth Orbits)
 MEO (Medium Earth Orbits) and
 LEO (Low Earth Orbits)
Ground stations can communicate with LEO (Low
Earth Orbiting) satellites only when the satellite is seen
above the ground station’s horizon plane. Because of
natural barriers practical (visible) horizon is always
shorter than ideal one. Natural barriers above the ideal
horizon plane create horizon mask. In order to avoid such
a mask, by implementing also a safe margin, designers
determine the designed horizon plane. Horizon plane
determination enables accurate link budget calculations.
Typical cases of designed horizon plane on 5˚ of eleva-
tion are ground stations of LEO satellites dedicated for
search and rescue services [4]. Another example of
higher designed horizon plane is for ground station
dedicate for communication with LEO satellite for iono-
sphere monitoring [5].
Logical order of designed horizon plane determination
is proceed with an in advance ideal horizon plane and
respective horizon mask determinatio n. Within this paper
we are limited only on ideal horizon plane simulation.
A general concept of a horizon plane is presented at
second section. The satellite and ground statio n geometry
for LEO satellites is briefly described. The range and
ground station horizon plane simulation for LEO satel-
lites is finally given for different satellite attitudes under
different maximal elevation angles.
2. Horizon Plane
The horizon plane is considered a tangent plane to the
surface of the Earth at the observer’s position (ground

586 S. CAKAJ ET AL.
Figure 1. Satellite orbits.
station). The position of the satellite with in its orbit con-
sidered from the ground station point of view can be de-
fined by Azimuth and Elevation angles. The concept of
azimuth, elevation and horizon plane is presented in Fig-
ure 2.
The azimuth (Az) is the angle of the direction of the
satellite, measured in the horizon plane from geographi-
cal north in clockwise direction. The range of azimuth is
0˚ to 360˚. The elevation (El) is the angle between a sat-
ellite and the observ er’s (ground station ’s) horizon plane.
The range of elevation is 0˚ to 90˚. The ellip se in Figure
2 represents the ideal horizon plane seen from the ob-
server’s (ground station).
For tracking the satellite, Kepler elements (space or-
bital parameters [1-3]) are fed to orbit determination
software which calculates the actual position of the satel-
lite. A software process running at the ground station
uses these parameters to precisely determine the time
when the satellite will communicate with the ground
station and prepares the ground station’s antenna in ad-
vance to wait for the upcoming p ass of the satellite [4,6 ].
For LEO satellites the communicatio n is locked when th e
satellite shows up at the horizon plane. The respective
software provides real-time tracking information , usually
displayed in different modes (satellite view, radar map,
tabulated, etc.). The “radar map” mode includes accurate
satellite path with the ground station considered at the
center, as in Figure 3 presented [3,6].
The perimeter of the circle is the horizon plane, with
North on the top (Az = 0˚), then East (Az = 90˚), South
(Az = 180˚) and West (Az = 270˚). Three concentric cir-
cles represent different elevations: 0˚, 30˚ and 60˚. At the
center the elevation is El = 90˚. Most usual software pa-
rameters which define the movement of the satellite re-
lated to the ground station are: AOStime—Acquisition of
the satellite (time), LOStime—Loss of the satellite (time),
AOSA—Acquisition of the satellite (azimuth), AOSEl—
Acquisition of the satellite (elevation), LOSAz—Loss of
the satellite (azimuth), LOSEl—Loss of the satellite (ele-
vation), Ma xEl—Maximal Elevation. Looking at Figure
3 the line crossing circles is projection of the satellite’s
path on horizon plane. Considering the case of ideal ho-
rizon plane (), at Figure 3 the other
approximate values of satellite’s parameters are
0
El El
AOS LOS

Figure 2. Azimuth, elevation and hor izon plane.
Figure 3. Radar map display.
350
Az
AOS , and . 165
Az
LOS50MaxEl 
For LEO satellites, the maximal elevation is very im-
portant parameter which in fact determines the commu-
nication duration between LEO satellite and respective
ground station.
The plane at 0˚ elevation represent ideal horizon plane.
If it is cons idered the whol e horizo n in the az imuth range
of 0˚ - 360˚, in any direction of the horizon plane the
natural barriers will differ; consequently so will the ac-
quisition and loss elevation. The practical elevation val-
ues ranges from 1˚ - 4˚ [6]. Practical (visible) horizon is
always shorter than ideal one, reflecting on shorter
communication time between the satellite an d the ground
station. So, the communication time depends on the
maximal elevation, and on the practical horizon [7]. In
order to avoid the problem of natural barriers, designers
predetermine the lowest elevation of the horizon plane
which is applied during link budget calculations. Con-
sidering a safe margin, this elevation ranges from 5˚ - 30˚
[4-6]. The horizon plane with a predetermined minimal
elevation is considered the desi gned horizon pla ne [7].

S. CAKAJ ET AL.
587
3. Slant Range for LEO Satellites
The basic geometry between a LEO satellite and ground
station is depicted in Figure 4.
The two points indicate th e satellite (SAT) and ground
station (P), and then the third is the Earth’s center. The
subsatellite point is indicated by T (T is the point where
the joining line of the satellite and Earth’s center inter-
sect the Earth’s surface). Distance d represents slant
range between a satellite and ground station. This range
changes over time since the satellite flies too fast above
the ground station . In Figure 4, the radius r is:
E
rR H (1)
RE = 6378 km is Earth’s radius and H is LEO satellite’s
attitude. The lin e crossing point P ind icates tangent plan e
to Earth’s surface at point P, what by definition is in fact
ideal horizon plane. The angle formed between ideal
horizon plane and the slant range is elevation angle 0

.
The triangle from Figure 4 brought in plane lo oks like in
Figure 5 [8].
Two sides of this triangle are usually known (the dis-
tance from the ground station to the Earth’s center RE =
6378 km, and distance form the satellite to Earth’s cen-
ter-orbital radius). The angle under which the satellite
sees the ground station is called nadir angle. There are
four variables in this triangle: 0

—is elevation angle,
0

—is nadir angle, 0

—is central angle and d is slant
range. As soon as two quantities are known, the others
can be found with the following equations [8]:
000
90

  (2)
0
cos sindr
0

  (3)
0
sin sin
e
dR
0

  (4)
The most a ske d pa r am e ter is the s lant ra nge d (distance
from the ground station to the satellite). This parameter
will be used during the link budget calculation, and it is
expressed through elev ation angle 0

. Applying cosines
law for triangle at Figure 5 yields:

222 0
2cos 90
EE
rRd Rd


  (5)
Solving Equation (5) by d, yields:
2
20
cos sin
EE
r
dR R0














(6)
Substituting,
E
rHR at Equation (6) finally we
will get the slant range as function of el evation angle 0

:
2
20
cos sin
E
EE
HR
dR R
Figure 4. Ground station geometry.
Figure 5. Ground station geometry.
or elevation 0

expressed for known slant range d as:


2
0
2
sin 2
E
E
H
HR d
dR


 (8)
For )
2(2
E
dHHR yields out 00 sin 00

  ,
for dH

yields out sin .
00
The range under the lowest elevation angle represents
the worst link budget case, since that range represents the
maximal possible distance between the ground station
and the satellite. More power is required to overcome
larger distance. Thus a trade off should be applied, in
order to optimize the required transmit power and the
designed horizon plane.
1   90  
4. Horizon Plane Simulation for Ground
Stations of LEO Satellites
0



 











(7)
LEO satellites have very wide applications, from remote
sensing of oceans, through analyses on Earth’s climate
changes, Earth’s imagery with high resolution or astro-
nomical purposes [9]. LEOs are just above Earth’s at-
mosphere, where there is almost no air to cause drag on
the satellite and reduce its speed. Less energy is required
to launch a satellite into this type of orbit than into any
other orbit [2,3]. LEO altitudes range from 275 km up to
1400 km limited by Van Allen radiation effects (sensors,
integrated circuits and solar cells can be damage d by this
radiation) [10].
Goal of this simulation is to conclude about slant
range and horizon plane variations for a ground station

588 S. CAKAJ ET AL.
dedicated to communicate with LEO satellite. As input
simulation parameters (based on Equation (7)) are con-
sidered maximal elevation angle of the satellite’s path
above the respective ground station and LEO satellite’s
attitude. Considering Van Allen belt effect, for simula-
tion purposes are considered attitudes form 600 km up to
1200 km. Simulation expected output is slant range
variations.
For these attitudes applying Equation (7) it is calcu-
lated the range from a hypothetical ground station, pre-
sented at Table 1, and graphically in Figure 6. From
Figure 6 it is obvious that the shortest range occurs at
90˚ elevation, since the satellites appears perpendicularly
above the ground station [6]. At 90˚ elevation, the slant
range is the shortest and it equals with satellites attitude
H.
From Figure 6, the largest range is achieved under 0˚
elevation, representing the radius of the circle of an ideal
horizon plane seen from the ground station. Mathemati-
cally expressed, as:
0
max( 0)
dd


 (9)
This range increases as satellite’s attitude H increases.
The ideal horizon planes for different satellite attitudes,
considering max ranges from Table 1 or Figure 6 in
Figure 7 is presented.
d
Figure 7 confirms the expansion of horizon plane as
satellite attitude increases. For respectively, the lowest
and the highest cons idered satellite’s attitude o f H = 600
km and H = 1200 km the ranges are:

max 6002830 km H
d
Table 1. LEO satellite ranges.
Orbital
Attitude
[km]
H
600 H 700 H 800 H 900 H 1000 H 1100 H 1200
Max El
(0

) Range
[km] Range [km] Range [km] Range [km] Range [km] Range [km] Range [km]
0˚ 2830 3065 3289 3504 3708 39004088
10˚ 1942 2180 2372 2577 2770 29553136
20˚ 1386 1581 1765 1947 2120 22872453
30˚ 1070 1234 1392 1549 1701 18491996
40˚ 886 1027 1164 1302 1436 15671698
50˚ 758 883 1005 1128 1248 13661486
60˚ 680 794 905 1018 1129 12381348
70˚ 636 742 847 954 1058 11601266
80˚ 697 707 809 908 1012 11131214
90˚ 600 700 800 900 1000 11001200
Figure 6. Stellite range for LEO orbits.
Figure 7. Ideal horizon planes.

max 12004088 km H
d
The ideal horizon planes of ground stations dedicated
to communicate with LEO satellites of attitudes from
(600 - 1200) km may be considered as ideal flat circles
with diam et er from 5660 km to 8176 km.
Within these horizon planes the communication can be
locked between the LEO satellites and appropriate gr ou nd
stations. Communication duration will depend on maxi-
mal elevation of satellite’s path above the respective ho-
rizon plane.

S. CAKAJ ET AL.
589
Considering above analysis, the communication dura-
tion between LEO satellites and the appropriate ground
station usually takes (5 - 15) minutes, few times (6 - 8)
during the day. This too short communication time makes
necessity for horizon plane determination as a precondi-
tion of optimized communication (data download) be-
tween the LEO satellite and respective ground station.
5. Conclusions
The communication duration between the LEO satellite
and respective ground station depends on maximal ele-
vation of satellite’s path over the ground station and
largeness of the hor izon plane.
For ground stations dedicated to communicate with
LEO satellites the ideal horizon plane can be considered
as a flat circle with diameter ranging approximately from
6000 km to 8000 km. Because of natural barriers or too
high buildings in urban areas, practical horizon plane
always differs (smaller) from the ideal one.
Through simulation it is confirmed that the horizon
plan expands as satellite’s attitude increases, conse-
quently providing longer communication between satel-
lite and appropriate grou nd station.
Considering the ideal horizon plane and the respective
mask because of natural barriers, ground station design-
ers by applying a safe margin, successfully define the
designed horizon plane for the planned satellite ground
station to be installed.
6. References
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[2] M. Richharia, “Satellite Communication Systems,” McGraw
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