1

SATELLITE COMMUNICATION
AN INTRODUCTION
Contents
1.1 Introduction
1.2 Basics
1.3 Applications of Satellites
Weather Forecasting
Radio and TV Broadcast
Military
Navigation
Global Telephone
Connecting Remote Areas
Global Mobile Communication
1.4 Frequency Allocation of Satellites
1.5 Types of Orbits
GEO
LEO
MEO
Sun Synchronous Orbit
Hohmann Transfer Orbit
Prograde Orbit
Retrograde Orbit
Polar Orbits
1.6 Examples
INTELSAT
U.S. Domsats
Polar Orbiting Satellites
1.7 Summary
1.8 Exercise

1.1 INTRODUCTION

Satellites are specifically made for telecommunication

purpose. They are used for mobile applications such as
communication to ships, vehicles, planes, hand-held terminals
and for TV and radio broadcasting.
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They are responsible for providing these services to an

assigned region (area) on the earth. The power and bandwidth
of these satellites depend upon the preferred size of the
footprint, complexity of the traffic control protocol schemes
and the cost of ground stations.

A satellite works most efficiently when the transmissions are

focused with a desired area. When the area is focused, then

minimizing the interference to the other systems. This leads

more efficient spectrum usage.

Sate
be designed to best cover the designated geographical area
(which is generally irregular in shape). Satellites should be
designed by keeping in mind its usability for short and long
term effects throughout its life time.

The earth station should be in a position to control the satellite

if it drifts from its orbit it is subjected to any kind of drag from
the external forces.

1.2 BASICS

Satellites orbit around the earth. Depending on the application,

these orbits can be circular or elliptical. Satellites in circular

following a simple law:

The attractive force Fg of the earth due to gravity equals
m·g (R/r) 2
The centrifugal force Fc trying to pull the satellite away equals
m·r· 2
The variables have the following meaning:
m is the mass of the satellite;
R is the radius of earth with R = 6,370 km;
ri s the distance of the satellite to the centre of the earth;
g is the acceleration of gravity with g = 9.81 m/s2;
f, f is the frequency of
the rotation.

To keep the satellite in a stable circular orbit, the following equation

must hold:
Fg = Fc, i.e., both forces must be equal. Looking at this
equation the first thing to notice is that the mass m of a
satellite is irrelevant (it appears on both sides of the
equation).
Solving the equation for the distance r of the satellite to the
centre of the earth results in the following equation:
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The distance r = (g·R2 f)2)1/3

From the above equation it can be concluded that the distance

frequency.

Important parameters in satellite communication are the

inclination and elevation angles. The inclinatio
1.1) is defined between the equatorial plane and the plane
described by the satellite orbit. An inclination angle of 0
degrees means that the satellite is exactly above the equator. If
the satellite does not have a circular orbit, the closest point to
the earth is called the perigee.

Figure 1.1: Angle of Inclination

1.2) is defined between the centre

surface. A so called footprint can be defined as the area on

earth where the signals of the satellite can be received.

Figure 1.2: Angle of Elevation

1.3 APPLICATIONS OF SATELLITES

1.3.1) Weather Forecasting

Certain satellites are specifically designed to monitor the
climatic conditions of earth. They continuously monitor the assigned
areas of earth and predict the weather conditions of that region.
This is done by taking images of earth from the satellite. These
images are transferred using assigned radio frequency to the earth
st
used for relaying signals from satellites.) These satellites are
exceptionally useful in predicting disasters like hurricanes, and
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monitor the changes in the Earth's vegetation, sea state, ocean

color, and ice fields.

1.3.2) Radio and TV Broadcast

These dedicated satellites are responsible for making 100s
of channels across the globe available for everyone. They are also
responsible for broadcasting live matches, news, world-wide radio
services. These satellites require a 30-40 cm sized dish to make
these channels available globally.

1.3.3) Military Satellites

These satellites are often used for gathering intelligence, as
a communications satellite used for military purposes, or as a
military weapon. A satellite by itself is neither military nor civil. It is
the kind of payload it carries that enables one to arrive at a decision
regarding its military or civilian character.

1.3.4) Navigation Satellites

The system allows for precise localization world-wide, and
with some additional techniques, the precision is in the range of
some meters. Ships and aircraft rely on GPS as an addition to
traditional navigation systems. Many vehicles come with installed
GPS receivers. This system is also used, e.g., for fleet
management of trucks or for vehicle localization in case of theft.

1.3.5) Global Telephone

One of the first applications of satellites for communication
was the establishment of international telephone backbones.
Instead of using cables it was sometimes faster to launch a new
satellite. But, fiber optic cables are still replacing satellite
communication across long distance as in fiber optic cable, light is
used instead of radio frequency, hence making the communication
much faster (and of course, reducing the delay caused due to the
amount of distance a signal needs to travel before reaching the
destination.).

Using satellites, to typically reach a distance approximately

10,000 kms away, the signal needs to travel almost 72,000 kms,
that is, sending data from ground to satellite and (mostly) from

amount of delay and this delay becomes more prominent for users
during voice calls.

1.3.6) Connecting Remote Areas

Due to their geographical location many places all over the
world do not have direct wired connection to the telephone network
or the internet (e.g., researchers on Antarctica) or because of the
current state of the infrastructure of a country. Here the satellite
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provides a complete coverage and (generally) there is one satellite

always present across a horizon.

1.3.7) Global Mobile Communication

The basic purpose of satellites for mobile communication is
to extend the area of coverage. Cellular phone systems, such as
AMPS and GSM (and their successors) do not cover all parts of a
country. Areas that are not covered usually have low population
where it is too expensive to install a base station. With the
integration of satellite communication, however, the mobile phone
can switch to satellites offering world-wide connectivity to a
customer. Satellites cover a certain area on the earth. This area is

communication with that satellite is possible for mobile users.

These users communicate using a Mobile-User-Link (MUL). The
base-stations communicate with satellites using a Gateway-Link
(GWL). Sometimes it becomes necessary for satellite to create a
communication link between users belonging to two different
footprints. Here the satellites send signals to each other and this is
done using Inter-Satellite-Link (ISL).

1.4 FREQUENCY ALLOCATION FOR SATELLITE

Allocation of frequencies to satellite services s a complicated

process which requires international coordination and planning.
This is done as per the International Telecommunication Union
(ITU). To implement this frequency planning, the world is
divided into three regions:
Region1: Europe, Africa and Mongolia
Region 2: North and South America and Greenland
Region 3: Asia (excluding region 1 areas), Australia and
south-west Pacific.
Within these regions, he frequency bands are allocated to
various satellite services. Some of them are listed below.
Fixed satellite service: Provides Links for existing
Telephone Networks Used for transmitting television signals
to cable companies
Broadcasting satellite service: Provides Direct Broadcast
to homes. E.g. Live Cricket matches etc
Mobile satellite services: This includes services for:
Land Mobile
Maritime Mobile
Aeronautical mobile
Navigational satellite services : Include Global Positioning
systems
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Meteorological satellite services: They are often used to

perform Search and Rescue service
Below are the frequencies allocated to these satellites:
Frequency Band (GHZ) Designations:
VHF: 01-0.3
UHF: 0.3-1.0
L-band: 1.0-2.0
S-band: 2.0-4.0
C-band: 4.0-8.0
X-band: 8.0-12.0
Ku-band: 12.0-18.0 (Ku is Under K Band)
Ka-band: 18.0-27.0 (Ka is Above K Band)
V-band: 40.0-75.0
W-band: 75-110
Mm-band: 110-300
m-band: 300-3000
Based on the satellite service, following are the frequencies
allocated to the satellites:
Frequency Band (GHZ) Designations:
VHF: 01-0.3 ---Mobile & Navigational Satellite
Services
L-band: 1.0-2.0 --- Mobile & Navigational Satellite
Services
C-band: 4.0-8.0 --- Fixed Satellite Service
Ku-band: 12.0-18.0 --- Direct Broadcast Satellite
Services

1.5 TYPES OF SATELLITES (BASED ON ORBITS)

1.5.1) Geostationary or geosynchronous earth orbit (GEO)

GEO satellites are synchronous with respect to earth. Looking
from a fixed point from Earth, these satellites appear to be
stationary. These satellites are placed in the space in such a
way that only three satellites are sufficient to provide connection
throughout the surface of the Earth (that is; their footprint is
covering almost 1/3rd of the Earth). The orbit of these satellites
is circular.

There are three conditions which lead to geostationary

satellites. Lifetime expectancy of these satellites is 15 years.
1) The satellite should be placed 37,786 kms (approximated to
36,000 kms) above the surface of the earth.
2) These satellites must travel in the rotational speed of earth,
and in the direction of motion of earth, that is eastward.
3) The inclination of satellite with respect to earth must be 0 0.
Geostationary satellite in practical is termed as geosynchronous
as there are multiple factors which make these satellites shift
from the ideal geostationary condition.
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1) Gravitational pull of sun and moon makes these satellites

deviate from their orbit. Over the period of time, they go

these satellites due to their distance from the surface of the

Earth.)
2) These satellites experience the centrifugal force due to the
rotation of Earth, making them deviate from their orbit.
3) The non-circular shape of the earth leads to continuous
adjustment of speed of satellite from the earth station.

These satellites are used for TV and radio broadcast, weather

forecast and also, these satellites are operating as backbones
for the telephone networks.

Disadvantages of GEO: Northern or southern regions of the

Earth (poles) have more problems receiving these satellites due
to the low elevation above a latitude of 60°, i.e., larger antennas
are needed in this case. Shading of the signals is seen in cities
due to high buildings and the low elevation further away from
the equator limit transmission quality. The transmit power
needed is relatively high which causes problems for battery
powered devices. These satellites cannot be used for small
mobile phones. The biggest problem for voice and also data
communication is the high latency as without having any
handovers, the signal has to at least travel 72,000 kms. Due to
the large footprint, either frequencies cannot be reused or the
GEO satellite needs special antennas focusing on a smaller
footprint. Transferring a GEO into orbit is very expensive.

1.5.2) Low Earth Orbit (LEO) satellites:

These satellites are placed 500-1500 kms above the surface of
the earth. As LEOs circulate on a lower orbit, hence they exhibit
a much shorter period that is 95 to 120 minutes. LEO systems
try to ensure a high elevation for every spot on earth to provide
a high quality communication link. Each LEO satellite will only
be visible from the earth for around ten minutes.

Using advanced compression schemes, transmission rates of

about 2,400 bit/s can be enough for voice communication. LEOs
even provide this bandwidth for mobile terminals with Omni-
directional antennas using low transmit power in the range of
1W. The delay for packets delivered via a LEO is relatively low
(approx 10 ms). The delay is comparable to long-distance wired
connections (about 5 10 ms). Smaller footprints of LEOs allow
for better frequency reuse, similar to the concepts used for
cellular networks. LEOs can provide a much higher elevation in
Polar Regions and so better global coverage.
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These satellites are mainly used in remote sensing an providing

mobile communication services (due to lower latency).

Disadvantages: The biggest problem of the LEO concept is the

need for many satellites if global coverage is to be reached.
Several concepts involve 50 200 or even more satellites in
orbit. The short time of visibility with a high elevation requires
additional mechanisms for connection handover between
different satellites. The high number of satellites combined with
the fast movements resulting in a high complexity of the whole
satellite system. One general problem of LEOs is the short
lifetime of about five to eight years due to atmospheric drag and
radiation from the inner Van Allen belt1. Assuming 48 satellites
and a lifetime of eight years, a new satellite would be needed
every two months. The low latency via a single LEO is only half
of the story. Other factors are the need for routing of data
packets from satellite to if a user wants to communicate around
the world. Due to the large footprint, a GEO typically does not
need this type of routing, as senders and receivers are most
likely in the same footprint.

1.5.3) Medium Earth Orbit (MEO) satellites:

MEOs can be positioned somewhere between LEOs and GEOs,
both in terms of their orbit and due to their advantages and
disadvantages. Using orbits around 10,000 km, the system only
requires a dozen satellites which is more than a GEO system,
but much less than a LEO system. These satellites move more

design (satellite periods are about six hours). Depending on the

inclination, a MEO can cover larger populations, so requiring
fewer handovers.

Disadvantages: Again, due to the larger distance to the earth,

delay increases to about 70 80 ms. the satellites need higher
transmit power and special antennas for smaller footprints.

The above three are the major three categories of satellites,

apart from these, the satellites are also classified based on the
following types of orbits:

1.5.4) Sun- Synchronous Orbits satellites:

These satellites rise and set with the sun. Their orbit is defined
in such a way that they are always facing the sun and hence
they never go through an eclipse.
For these satellites, the surface illumination angle will be nearly
the same every time.
(Surface illumination angle: The illumination angle is
the angle between the inward surface normal and the direction
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of light. This means that the illumination angle of a certain point

of the Earth's surface is zero if the Sun is precisely overhead
and that it is 90 degrees at sunset and at sunrise.)

Special cases of the sun-synchronous orbit are

the noon/midnight orbit, where the local mean solar time of
passage for equatorial longitudes is around noon or midnight,
and the dawn/dusk orbit, where the local mean solar time of
passage for equatorial longitudes is around sunrise or sunset,
so that the satellite rides the terminator between day and night.

1.5.5) Hohmann Transfer Orbit:

This is an intermediate orbit having a highly elliptical shape.
It is used by GEO satellites to reach their final destination orbits.
This orbit is connected to the LEO orbit at the point of perigee
forming a tangent and is connected to the GEO orbit at the point of
apogee again forming a tangent.

1.5.6) Prograde orbit:

This orbit is with an inclination of less than 90°. Its direction
is the same as the direction as the rotation of the primary (planet).

1.5.7) Retrograde orbit:

This orbit is with an inclination of more than 90°. Its direction
is counter to the direction of rotation of the planet. Only few
satellites are launched into retrograde orbit because the quantity of
fuel required to launch them is much greater than for a prograde
orbit. This is because when the rocket starts out on the ground, it
already has an eastward component of velocity equal to the
rotational velocity of the planet at its launch latitude.

1.5.8) Polar Orbits

This orbit passes above or nearly above both poles (north
and south pole) of the planet on each of its revolutions. Therefore it
has an inclination of (or very close to) 90 degrees. These orbits are
highly inclined in shape.

1.6 EXAMPLES

1.6.1) INTELSAT
International Telecommunication Satellite:
Created in 1964
Over 140 member countries
More than 40 investing entities
Early Bird satellite in 1965
Six (6) evolutions of INTELSAT satellites between 1965-87
Geostationary orbit
Covers 3 regions:
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Atlantic Ocean Region (AOR),

Indian Ocean Region (IOR), and
Pacific Ocean Region (POR)

1.6.2) U.S DOMSATS

Domestic Satellite:
In geostationary orbit
Over 140 member countries
Direct-to-home TV service
Three (3) categories of U. S. DBS system: high power,
medium, and low power.
Measure in equivalent isotropic radiated power (EIRP).
The upper limit of EIRP:
High power (60 dBW),
Medium (48 dBW), and
Low power (37 dBW).

1.6.3) Polar Orbiting Satellites

These satellites follow the Polar Orbits. An infinite number of polar
orbits cover north and south polar regions.
Weather (ultraviolet sensor also measure ozone level)
satellites between 800 and 900 km
National Oceanic and Atmospheric Administration (NOAA)
operate a weather satellite system
Satellite period is 102 minutes and earth rotated 25 degree.
Estimate the sub-satellite point at the following times after
the equator 90 degree E North-South crossing:
a) 10 minutes, 87.5 degree E and 36 degree S;
b) 102 minutes, 65 degree E and equator;
c) 120 minutes, 60 degree E and 72 degree S.
The system uses both geostationary operational
environment satellite (GOES) and polar operational
environment satellite (POES)
Sun synchronous: they across the equator at the
same local time each day
The morning orbit, at an altitude of 830 km, crosses
the equator from south to north at 7:30 AM, and the
afternoon orbit, at an altitude of 870 km, at 1:40 PM.
Search and rescue (SAR) satellite: Cospas-Sarsat.

1.7 SUMMARY
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2
ORBITS AND LUNCHING METHODS
Contents

2.1 Introduction
2.2

2.3 Definitions
Orbital Elements
2.4 Orbital Perbutations
Effects of Non-Spherical Earth
Atmospheric Drag
2.5 Inclined Orbits
Calendars
Universal Time
Julian Date
Sidereal Time
2.6 Sun Synchronous Orbits
2.7 Summary
2.8 Exercise

2.1 INTRODUCTION

The mathematical basis o satellite orbit determination has

been known since the work of Newton and Kepler in the 17 th
Century. Since past half century some basic laws have been
applied to the man made satellites commonly known artificial
satellites in the Earth

2.2

Johann Kepler developed empirically three laws of planetary

motion, based on conclusions drawn from the extensive
observations of Mars by Tycho Brahe (taken around the year
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1600). While they were originally defined in terms of the motion of

the planets about the Sun, they apply equally to the motion of
natural or artificial satellites about the Earth
that the satellite follows an elliptical path in its orbit around the
Earth. The satellite does not necessarily have uniform velocity

satellite with the centre of the Earth sweeps out equal areas in

distance of the satellite from the Earth is proportional to the square

of its period.

2
The path followed be a satellite (in our case artificial satellite)
around the primary (a planet and in our case Earth) will be an
ellipse.

lipse with sun at one of the

An ellipse has two focal points. Let us consider F1 and F2. The
centre of mass of the two body system, known as the
barycentre as always cantered at one foci. Due to the great
difference between the masses of the planet (Earth) and the
satellite, centre of mass always coincides with the centre of
Earth and hence is always at one foci.
(Note: Ellipse: A regular oval shape, traced by a point moving in a
plane so that the sum of its distances from two other points (the
foci) is constant.
Foci: The center of interest and in our case centre of the ellipse.)
Parameters associated with the 1st law of Kepler:
Eccentricity (e): it defines how stretched out an ellipse is
from a perfect circle.

Semi-Major axis (a): It is the longest diameter, a line that

runs through the centre and both foci, its ends being at the
widest points of the shapes. This line joins the points of
apogee.

Semi-Minor axis (b): the line joining the points of perigee is

called the Semi-Minor axis.
2
b2) / a
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Figure 2.1: Foci F1 and F2, Semi-major axis a and semi-

minor axis b of an ellipse.

2 Second Law
ill sweep out equal areas

With respect to the laws governing the planetary motion around

the sun, tis

Figure 2.2: The areas A1 and A2 swept out in unit intervals

of time.

From figure 2.2 and considering the law stated above, if satellite
travels distances S1 and S2 meters in 1 second, then areas A1
and A2 will be equal.

The same area will be covered everyday regardless of where in

its orbit a satellite is. As the First Keplerian law states that the
satellite follows an elliptical orbit around the primary, then the
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satellite is at different distances from the planet at different parts

of the orbit. Hence the satellite has to move faster when it is
closer to the Earth so that it sweeps an equal area on the Earth.

This could be achieved if the speed of the satellite is adjusted

when it is closer to the surface of the Earth in order to make it
sweep out equal areas (footprints) of the surface of the Earth.

2 Third Law
The square of the periodic time of orbit is proportional to the
cube of the mean distance between the two bodies.

The square of the orbital period of a planet is directly

proportional to the cube of the semi-major axis of its orbit.

This law shows the relationship between the distances of

satellite from earth and their orbital period.

Example: suppose satellite Satellite-I is four times as far from

Earth as Satellite-II. Then I must traverse four times the
distance of II in each orbit. Now considering the speed of I and
II, suppose I travels at half the speed of II, then in order to
maintain equilibrium with the reduced gravitational force (as I is
four times away from Earth than what II is), then in all it will
require 4 x 2 = 8 times as long for I to travel an orbit in
agreement with the law which comes down to (82 = 43).

Symbolically: P2 3
(P2 is directly proportional to a3)
Where P is the orbital period; a is the semi-major axis
a3 = µ/n2

Where n is the mean motion of satellite in radians per second

and µ l constant.
µ = 3.986005 x 1014 m3/sec2

into account.
/n
Here, P is in seconds and n is in radians/ second

This law also confirms the fact that there is a fixed relation between
period and size.
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2.3 DEFINITIONS

Apogee: A point for a satellite farthest from the Earth. It is

denoted as ha.

Perigee: A point for a satellite closest from the Earth. It is

denoted as hp.

Line of Apsides: Line joining perigee and apogee through

centre of the Earth. It is the major axis of the orbit. One-half of
-major axis equivalents to
distance from the Earth.

Ascending Node: The point where the orbit crosses the

equatorial plane going from north to south.

Descending Node: The point where the orbit crosses the

equatorial plane going from south to north.

Inclination: the angle between the orbital plane and the

from the equator to the orbit, going from East to North. Also,
this angle is commonly denoted as i.

Line of Nodes: the line joining the ascending and descending

nodes through the centre of Earth.

Prograde Orbit: an orbit in which satellite moves in the same

direction as the . Its inclination is always
between 00 to 900
velocity makes it easier to lunch these satellites.

Retrograde Orbit: an orbit in which satellite moves in the

s rotation.

Argument of Perigee: An angle from the point of perigee

direction of the satellite motion.

Right ascension of ascending node: The definition of an

orbit in space, the position of ascending node is specified. But
as the Earth spins, the longitude of ascending node changes
and cannot be used for reference. Thus for practical
determination of an orbit, the longitude and time of crossing
the ascending node is used. For absolute measurement, a
fixed reference point in space is required. It could also be
right ascension of the ascending node; right
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ascension is the angular position measured eastward along

the celestial equator from the vernal equinox vector to the
hour circle of the object

Mean anamoly: It gives the average value to the angular

position of the satellite with reference to the perigee.

True anamoly: It is the angle from point of perigee to the

Figure 2.3: Apogee height ha, Perigee height hp,

Inclination i, line of apsides la

Figure 2.4: Prograde and Retrograde orbits

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Figure 2.5: Argument of Perigee and Right ascension of

ascending node

2.3.1) Orbital Elements

Following are the 6 elements of the Keplerian Element set
commonly known as orbital elements.
1. Semi-Major axis (a)
2. Eccentricity (e)
They
3. Mean anomaly (M0)
It denotes the position of a satellite in its orbit at a given
reference time.
4. Argument of Perigee

5. Inclination
6. Right ascension of ascending node

As the equatorial bulge causes a slow variation in argument

of perigee and right ascension of ascending node, and because
other perturbing forces may alter the orbital elements slightly, the
values are specified for the reference time or epoch.

2.4 ORBITAL PERBUTATIONS

Theoretically, an orbit described by Kepler is ideal as Earth is

considered to be a perfect sphere and the force acting around
the Earth is the centrifugal force. This force is supposed to
balance the gravitational pull of the earth.
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In reality, other forces also play an important role and affect the
motion of the satellite. These forces are the gravitational forces
of Sun and Moon along with the atmospheric drag.

Effect of Sun and Moon is more pronounced on geostationary

earth satellites where as the atmospheric drag effect is more
pronounced for low earth orbit satellites.

2.4.1) Effects of non-Spherical Earth

As the shape of Earth is not a perfect sphere, it causes some
variations in the path followed by the satellites around the
primary. As the Earth is bulging from the equatorial belt, and
keeping in mind that an orbit is not a physical entity, and it is
the forces resulting from an oblate Earth which act on the
satellite produce a change in the orbital parameters.

This causes the satellite to drift as a result of regression of the

nodes and the latitude of the point of perigee (point closest to
the Earth). This leads to rotation of the line of apsides. As the
orbit itself is moving with respect to the Earth, the resultant
changes are seen in the values of argument of perigee and
right ascension of ascending node.

Due to the non-spherical shape of Earth, one more effect called

-spherical shape
-5
leads to the small value of eccentricity (10 ) at the equatorial
plane. This causes a gravity gradient on GEO satellite and
makes them drift to one of the two stable points which coincide
with minor axis of the equatorial ellipse.

Working satellites are made to drift back to their position but

out-of-service satellites are eventually drifted to these points,
and making that point a Satellite Graveyard.

(Note: A graveyard orbit, also called a supersynchronous

orbit, junk orbit or disposal orbit, is an orbit significantly
above GEO where satellites are intentionally placed at the end
of theiroperational life. It is a measure performed in order to
lower the probability of collisions with operational spacecraft
and of the generation of additional space debris. The points
where the graveyard is made are separated by 1800 on the
equator and are set approximately on 750 E longitude and
1050 W longitude.)

2.4.2) Atmospheric Drag

For Low Earth orbiting satellites, the effect of atmospheric drag
is more pronounces. The impact of this drag is maximumat the
point of perigee. Drag (pull towards the Earth) has an effect on
velocity of Satellite (velocity reduces).
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This causes the satellite to not reach the apogee height

successive revolutions. This leads to a change in value of
semi-major axis and eccentricity. Satellites in service are
maneuvered by the earth station back to their original orbital
position.

2.5 INCLINED ORBITS

While considering an orbit of non- geostationary orbit satellite,

different parameters are referred at different reference frames.
The orbital elements are calculated with respect to the plane of
the orbit, which is fixed in space and the earth stations position
is given by geographic coordinates that rotate with the earth.

Other factors of consideration are azimuth and elevation

angles. Thus for calculation purpose, transformations between
coordinate system is required.

The following quantities and concepts are required

Orbital elements
Various measures of time
Perifocal coordinate system- based on orbital plane
Geocentric-equatorial plane coordinate system
equatorial plane
Topocentric horizon coordinate system-
horizon plane.

2.5.1) Calendars
Calendars are created with respect to the position of sun. As

year has 365.2422 days. It is generally taken as 365

(commonly known as civil year).

The extra 0.2422 is significant and for example after 100

years, there will be drift of 24 days between calendar year
and tropical year. Hence the concept of Leap year came into
existence.

By the year 1582, a discrepancy was once again observed.

The discrepancy existed between the civil and the tropical
years. To synchronize them, days between 5 th October
14th October 1582 were abolished.

Additional constraints were added that on years ending with

two zeros to be considered as leap years. The resulting
calendar is called as the Gregorian Calender; named after
Pope Gregory XIII.