UNIT I

COMMUNICATION SATELLITE ORBIT AND DESCRIPTION

HISTORY OF SATELLITE COMMUNICATION

In 1962, the world's first active communications satellite, Telstar 1, was launched. This

satellite was built by Telesat's predecessors at AT&T and Bell Laboratories. During its seven

months in operation, Telstar 1 dazzled the world with live images of sports, entertainment and

news. It was a simple single-transponder low-earth-orbit (LEO) satellite, but its technology of

receiving radio signals from the ground, and then amplifying and retransmitting them over a

large portion of the earth's surface, set the standard for all communications satellites that

followed.

During the 1960s and 1970s, advances in satellite performance came quickly and a global

industry began to develop. Satellites were mainly used at first for international and long-haul

telephone traffic and distribution of select television programming, both internationally and

domestically. In 1973 the Canadian Broadcasting Corporation began distributing its video

programming to Canadian customers using Telesat’s Anik A satellite. Then in 1975 HBO began

distributing its video programming to US customers by satellite. The commercial and technical

success of these ventures led to a greater use and acceptance of satellite broadcasting. By the

1990s, satellite communications would be the primary means of distributing TV programs

around the world.

A communications satellite is an artificial satellite that relays and

amplifies radio telecommunications signals via a transponder; it creates a communication

channel between a source transmitter and a receiver at different locations on Earth.

Communications satellites are used for television, telephone, radio, internet,

and military applications. There are about 2,000 communications satellites in Earth's orbit, used

by both private and government organizations. Many are in geostationary orbit 22,236 miles

(35,785 km) above the equator, so that the satellite appears stationary at the same point in the

sky, so the satellite dish antennas of ground stations can be aimed permanently at that spot and

do not have to move to track it.

The high frequency radio waves used for telecommunications links travel by line of sight and

so are obstructed by the curve of the Earth. The purpose of communications satellites is to relay

the signal around the curve of the Earth allowing communication between widely separated

geographical points. Communications satellites use a wide range of radio

and microwave frequencies. To avoid signal interference, international organizations have

regulations for which frequency ranges or "bands" certain organizations are allowed to use. This

allocation of bands minimizes the risk of signal interference

Communications Satellites are usually composed of the following subsystems:

Communication Payload, normally composed of transponders, antennas, and switching

systems

Engines used to bring the satellite to its desired orbit

A station keeping tracking and stabilization subsystem used to keep the satellite in the right

orbit, with its antennas pointed in the right direction, and its power system pointed towards

the sun

Power subsystem, used to power the Satellite systems, normally composed of solar cells, and

batteries that maintain power during solar eclipse

Command and Control subsystem, which maintains communications with ground control

stations. The ground control Earth stations monitor the satellite performance and control its

functionality during various phases of its life-cycle.

The bandwidth available from a satellite depends upon the number of transponders provided by

the satellite. Each service (TV, Voice, Internet, radio) requires a different amount of bandwidth

for transmission. This is typically known as link budgeting and a network simulator can be used

to arrive at the exact value.

Communications satellites support both "fixed applications" - so-called because the

terminals on the ground are in fixed locations, and "mobile applications" where the terminals can

be fixed, or in motion such as on a vehicle, a ship or even an airplane.

The worldwide market for fixed satellite services (FSS) is now over $10 billion annually and is

significantly larger than the worldwide market for mobile satellite services (MSS). Demand for

both FSS and MSS is growing rapidly and the distinction between the two is becoming blurred as

each is now serving the other's traditional markets. MSS can use several frequency bands, but

has historically relied on L-band and S-band frequencies which facilitate terminal designs. As

has happened with FSS, MSS applications are moving to higher frequencies such as Ka-band as

capacity demands increase.

Advantages of Satellites

Cost Effectiveness - Cost of satellite capacity does not increase with the number of users/receive

sites, or with the distance between communication points. Whether crossing continents or staying

local, satellite connection cost is distance insensitive.

Global Availability - Communications satellites cover all land masses and there is growing

capacity to serve maritime and even aeronautical markets. Customers in rural and remote regions

around the world who cannot obtain high speed Internet access from a terrestrial provider are

increasingly relying on satellite communications.

Superior Reliability - Satellite communications can operate independently from terrestrial

infrastructure. When terrestrial outages occur from man-made and natural events, satellite

connections remain operational.

Superior Performance - Satellite is unmatched for broadcast applications like television. For

two-way IP networks, the speed, uniformity and end-to-end control of today's advanced satellite

solutions are resulting in greater use of satellite by corporations, governments and consumers.

Immediacy and Scalability - Additional receive sites, or nodes on a network, can readily be

added, sometimes within hours. All it takes is ground-based equipment. Satellite has proven its

value as a provider of "instant infrastructure" for commercial, government and emergency relief

communications.

Versatility and More - Satellites effectively support on a global basis all forms of

communications ranging from simple point-of-sale validation to bandwidth intensive multimedia

applications. Satellite solutions are highly flexible and can operate independently or as part of a

larger network.

SATELLITE FREQUENCY BANDS

Allocating frequencies to satellite services is a complicated process which requires international

coordination and planning. This is carried out under the auspices of the International

Telecommunication Union (ITU). To facilitate frequency planning, the world is divided into

three regions: Region 1: Europe, Africa, what was formerly the Soviet Union, and Mongolia

Region 2: North and South America and Greenland Region 3: Asia (excluding region 1 areas),

Australia, and the southwest Pacific

Within these regions, frequency bands are allocated to various satellite services, although a given

service may be allocated different frequency bands in different regions. Some of the services

provided by satellites are:

Fixed satellite service (FSS)

Broadcasting satellite service (BSS)

Mobile-satellite service

Radio navigation-satellite service

Meteorological-satellite service

L-band (1-2 GHz)

C-band (4–8 GHz)

X-band (8–12 GHz)

Ku-band (12–18 GHz)

Ka-band (26–40 GHz)

L-band (1–2 GHz)

Global Positioning System (GPS) carriers and also satellite mobile phones, such as Iridium;

Inmarsat providing communications at sea, land and air; WorldSpace satellite radio.

S-band (2–4 GHz)

Weather radar, surface ship radar, and some communications satellites, especially those of

NASA for communication with ISS and Space Shuttle. In May 2009, Inmarsat and Solaris

mobile (a joint venture between Eutelsat and Astra) were awarded each a 2×15 MHz portion of

the S-band by the European

C-band (4–8 GHz)

Primarily used for satellite communications, for full-time satellite TV networks or raw satellite

feeds. Commonly used in areas that are subject to tropical rainfall, since it is less susceptible to

rainfade than Ku band (the original Telstar satellite had a transponder operating in this band,

used to relay the first live transatlantic TV signal in 1962).

X-band (8–12 GHz)

Primarily used by the military. Used in radar applications including continuous-wave, pulsed,

single-polarisation, dual- polarisation, synthetic aperture radar and phased arrays. X-band radar

frequency sub-bands are used in civil, military and government institutions for weather

monitoring, air traffic control, maritime vessel traffic control, defence tracking and vehicle speed

detection for law enforcement.

Ku-band (12–18 GHz)

Used for satellite communications. In Europe, Ku-band downlink is used from 10.7 GHz to

12.75 GHz for direct broadcast satellite services, such as Astra.

Ka-band (26–40 GHz)

Communications satellites, uplink in either the 27.5 GHz and 31 GHz bands, and high-

resolution, close-range targeting radars on military aircraft.

TYPES OF SATELLITE SYSTEMS

Satellites have been put in space for various purposes and their placement in space and orbiting

shapes have been determined as per their specific requirements.

Four different types of satellites orbits have been identified. These are:

GEO (Geostationary Earth Orbit) at about 36,000km above the earth's surface.

LEO (Low Earth Orbit) at about 500-1500km above the earth's surface.

MEO (Medium Earth Orbit) or ICO (Intermediate Circular Orbit) at about 6000-

20,000 km above the earth's surface.

HEO (Highly Elliptical Orbit)

1. GEO (Geostationary Earth Orbit)

If a satellite should appear in fixed in the sky, it requires a period of 24 hours. Using the

equation of distance earth and satellite, r = (g.r2 /2.r.f)2)1/3 and the period of 24 hours f =

1/24 h. the resulting distance is 35,786 km. the orbit must have an inclination of 0

degree.

Geostationary satellites have a distance of almost 36,000 km to the earth. Examples are

almost all TV and radio broadcast satellites, any weather satellites and satellites operating

as backbones for the telephone network.

Objects in GEO moves around the earth at the same speed as the earth rotates. This

means geostationary satellites remain in the same position relative to the surface of earth.

Advantages of GEO satellite

Three Geostationary satellites are enough for a complete coverage of almost any spot on

earth.

Receivers and senders can use fixed antenna positions, no adjusting is needed.

GEOs are ideal for TV and radio broadcasting.

Lifetime expectations for GEOs are rather high, at about 15 years.

Geostationary satellites have a 24 hour view of a particular area.

GEOs typically do not need handover due to the large footprints.

GEOs don't exhibit any Doppler shift because the relative movement is zero.

Disadvantages of GEO satellite

Northern or southern regions of the earth have more problems receiving these satellites

due to the low elevation above latitude of 60 degree, i.e. larger antennas are needed in

this case.

Shading of the signals in cities due to high buildings and the low elevation further away

from the equator limits transmission quality.

The transmit power needed is relatively high (about 10 W) which causes problems for

battery powered devices.

These satellites can't be used for small mobile phones.

The biggest problem for voice and also data communication is high latency of over 0.25s

one way-retransmission schemes which are known from fixed networks fail.

Transferring a GEO into orbit is very expensive.

2. LEO (Low Earth Orbit)

As LEOs circulate on a lower orbit, it is obvious that they exhibit a much shorter period

(the typical duration of LEO periods are 95 to 120 minutes). Additionally, 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 about ten minutes.

A further classification of LEOs into little LEOs with low bandwidth services (some 100

bit/s), big LEOs (some 1,000 bit/s) and broadband LEOs with plans reaching into the

Mbits/s range can be found in Comparetto (1997).

LEO satellites are much closer to earth than GEO satellites, ranging from 500 to 1,500

km above the surface. LEO satellites do not stay in fixed position relative to the surface,

and are only visible for 15 to 20 minutes each pass.

Advantages of LEO satellite

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 1 W.

A LEO satellite smaller area of coverage is less of a waste of bandwidth.

Using advanced compression schemes, transmission rates of about 2,400 bit/s can be

enough for voice communication.

A LEO satellite's proximity to earth compared to a Geostationary satellite gives it a better

signal strength and less of a time delay, which makes it better for point to point

communication.

Smaller footprints of LEOs allow for better frequency reuse, similar to the concepts used

for cellular networks.

Disadvantages of LEO satellite

The biggest problem of the LEO concept is the need for many satellites if global

coverage is to be reached.

The high number of satellites combined with the fast movement's results in a high

complexity of the whole satellite system.

The short time of visibility with a high elevation requires additional mechanism for

connection handover between different satellites.

One general problem of LEO is the short lifetime of about five to eight years due to

atmospheric drag and radiation from the inner Van Allen belt.

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 satellite (or several

times from base stations to satellites and back) if a user wants to communicate around the

world.

A GEO typically does not need this type of routing, as senders and receivers are most

likely in the same footprints.

3. MEO (Medium Earth Orbit)

A MEO satellite situates in orbit somewhere between 6,000 km to 20,000 km above the

earth's surface.

MEO satellites are similar to LEO satellites in the context of functionality.

MEO satellites are similar to LEO satellite in functionality.

Medium earth orbit satellites are visible for much longer periods of time than LEO

satellites usually between 2 to 8 hours.

MEO satellites have a larger coverage area than Low Earth Orbit satellites.

MEOs can be positioned somewhere between LEOs and GEOs, both in terms of their

orbit and due to their advantages and disadvantages.

Advantages of MEO

Using orbits around 10,000km, 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 slowly relative to the earth's rotation allowing a simpler

system design (satellite periods are about six hours).

Depending on the inclination, a MEO can cover larger populations, so requiring fewer

handovers.

A MEO satellite's longer duration of visibility and wider footprint means fewer satellites

are needed in a MEO network than a LEO network.

Disadvantages of MEO

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.

A MEO satellite's distance gives it a longer time delay and weaker signal than LEO

satellite.

4. HEO (High Earth Orbit)

The High Earth orbit satellite is the only non-circular orbit of the four types.

HEO satellite operates with an elliptical orbit, with a maximum altitude (apogee) similar

to GEO, and a minimum altitude (perigee) similar to the LEO.

The HEO satellites used for the special applications where coverage of high latitude

locations is required.

Once a contact has been established between a mobile system and a satellite using a LOS

beam, almost everyone in the world can be accessed, using the underlying hardware

backbone network on the surface of the earth.

The satellites are controlled by the base stations (BS) located at the surface of the earth,

which serves as a gateway.

Inter-satellite links can be used to relay information from one satellite to another, but they

are still controlled by the ground BS (also known as earth station or ES).

The illuminated area of a satellite beam, called a footprint, is the area within which a

mobile user can communicate with the satellite; many beams are used to cover a wide

area.

In addition, satellites are constantly rotating around the earth, and a beam may be

temporarily blocked either due to other flying objects or the terrain of the earth's surface.

Therefore, a redundancy concept, known as diversity, is used to transmit the same

message through more than one satellite, as shown in the above figure.

The basic idea behind path diversity is to provide a mechanism that can combine two or

more correlated information signals (primarily the same copy) traveling along different

paths and hence having uncorrected noise and/or fading characteristics. Such a

combination of two signals improves signal quality, which enables the receiver to have

flexibility in selecting a better quality signal.

The primary interest is with path diversity, though other forms of diversity such as

antenna, time, frequency, field, or code, are possible. Path diversity will depend on the

technology that is used to transmit and receive messages.

The use of diversity can be initiated by either the MS or the BS located on earth. The

diversity request from the BS (ES) enables the MS to locate and scan un-shadowed

satellite paging channels for unobstructed communication.

This kind of situation cannot be detected or determined by the BS, even though the MS's

location is known to the BS. The use of satellite path diversity may be primarily due to

the following conditions:

Elevation angle: Higher elevation angle decreases shadowing problems. One approach is

to initiate path diversity when the elevation angle becomes less than predefined threshold.

Signal quality: If the average signal level (in DB), quality (in BER), or fade duration

goes beyond some threshold, then path diversity can be used. Signal quality is a function

of parameters such as elevation angle, available capacity, current mobility pattern of the

MS, or anticipated future demand.

Stand-by option: A channel can be selected and reserved as a stand-by for diversity

whenever a threshold crossing is detected by the MS. Such a standby channel is used only

when the primary channel is obstructed. Since the use of diversity is considered a rare

event, several MSs can share the same standby channel.

Emergency handoff: Whenever a connection of a MS with a satellite is lost, the MS

with satellite is lost; the MS tries to have an emergency handoff.

APPLICATIONS

Vehicles

Many wireless communication systems and mobility aware applications are used for following

purpose:

Transmission of music, news, road conditions, weather reports, and other broadcast

information are received via digital audio broadcasting (DAB) with 1.5Mbit/s.

For personal communication, a universal mobile telecommunications system (UMTS)

phone might be available offering voice and data connectivity with 384kbit/s.

For remote areas, satellite communication can be used, while the current position of the

car is determined via the GPS (Global Positioning System).

A local ad-hoc network for the fast exchange of information (information such as

distance between two vehicles, traffic information, road conditions) in emergency

situations or to help each other keep a safe distance. Local ad-hoc network with vehicles

close by to prevent guidance system, accidents, redundancy.

Vehicle data from buses, trucks, trains and high speed train can be transmitted in advance

for maintenance.

In ad-hoc network, car can comprise personal digital assistants (PDA), laptops, or mobile

phones connected with each other using the Bluetooth technology.

Emergency

Following services can be provided during emergencies:

Video communication: Responders often need to share vital information. The

transmission of real time situations of video could be necessary. A typical scenario

includes the transmission of live video footage from a disaster area to the nearest fire

department, to the police station or to the near NGOs etc.

Push To Talk (PTT): PTT is a technology which allows half duplex communication

between two users where switching from voice reception mode to the transmit mode

takes place with the use of a dedicated momentary button. It is similar to walkie-talkie.

Audio/Voice Communication: This communication service provides full duplex audio

channels unlike PTT. Public safety communication requires novel full duplex speech

transmission services for emergency response.

Real Time Text Messaging (RTT): Text messaging (RTT) is an effective and quick

solution for sending alerts in case of emergencies. Types of text messaging can be email,

SMS and instant message.

Business

Travelling Salesman

Directly access to customer files stored in a central location.

Consistent databases for all agents

Mobile office

To enable the company to keep track of all the activities of their travelling employees.

In Office

Wi-Fi wireless technology saves businesses or companies a considerable amount of

money on installations costs.

There is no need to physically setup wires throughout an office building, warehouse or

store.

Bluetooth is also a wireless technology especially used for short range that acts as a

complement to Wi-Fi. It is used to transfer data between computers or cellphones.

Transportation Industries

In transportation industries, GPS technology is used to find efficient routes and tracking

vehicles.

Replacement of Wired Network

Wireless network can also be used to replace wired network. Due to economic reasons it

is often impossible to wire remote sensors for weather forecasts, earthquake detection, or

to provide environmental information, wireless connections via satellite, can help in this

situation.

Tradeshows need a highly dynamic infrastructure, since cabling takes a long time and

frequently proves to be too inflexible.

Many computers fairs use WLANs as a replacement for cabling.

Other cases for wireless networks are computers, sensors, or information displays in

historical buildings, where excess cabling may destroy valuable walls or floors.

Location dependent service

It is important for an application to know something about the location because the user might

need location information for further activities. Several services that might depend on the actual

location can be described below:

Follow-on Services:

Location aware services: To know about what services (e.g. fax, printer, server, phone,

printer etc.) exist in the local environment.

Privacy: We can set the privacy like who should get knowledge about the location.

Information Services: We can know about the special offers in the supermarket. Nearest

hotel, rooms, cabs etc.

Infotainment: (Entertainment and Education)

Wireless networks can provide information at any appropriate location.

Outdoor internet access.

You may choose a seat for movie, pay via electronic cash, and send this information to a

service provider.

Ad-hoc network is used for multiuser games and entertainment.

Mobile and Wireless devices

Even though many mobile and wireless devices are available, there will be many more devices in

the future. There is no precise classification of such devices, by sizes, shape, weight, or

computing power. The following list of given examples of mobile and wireless devices graded

by increasing performance (CPU, memory, display, input devices, etc.)

Sensor: Wireless device is represented by a sensor transmitting state information. 1 example

could be a switch, sensing the office door. If the door is closed, the switch transmits this

information to the mobile phone inside the office which will not accept incoming calls without

user interaction; the semantics of a closed door is applied to phone calls.

Embedded Controller: Many applications already contain a simple or sometimes more complex

controller. Keyboards, mouse, headsets, washing machines, coffee machines, hair dryers and TV

sets are just some examples.

Pager: As a very simple receiver, a pager can only display short text messages, has a tiny

display, and cannot send any messages.

Personal Digital Assistant: PDAs typically accompany a user and offer simple versions of

office software (calendar, notepad, mail). The typically input device is a pen, with built-in

character recognition translating handwriting into characters. Web browsers and many other

packages are available for these devices.

Pocket computer: The next steps towards full computers are pocket computers offering tiny

keyboards, color displays, and simple versions of programs found on desktop computers (text

processing, spreadsheets etc.)

Notebook/laptop: Laptops offer more or less the same performance as standard desktop

computers; they use the same software - the only technical difference being size, weight, and the

ability to run on a battery. If operated mainly via a sensitive display (touch sensitive or

electromagnetic), the device are also known as notepads or tablet PCs.

ORBITAL PERIOD AND VELOCITY

We know that the path of satellite revolving around the earth is known as orbit. This path can be

represented with mathematical notations. Orbital mechanics is the study of the motion of the

satellites that are present in orbits. So, we can easily understand the space operations with the

knowledge of orbital motion.

Orbital elements are the parameters, which are helpful for describing the orbital motion of

satellites. Following are the orbital elements.

Semi major axis

Eccentricity

Mean anomaly

Argument of perigee

Inclination

Right ascension of ascending node

The above six orbital elements define the orbit of earth satellites. Therefore, it is easy to

discriminate one satellite from other satellites based on the values of orbital elements.

Semi major axis

The length of Semi-major axis (a) defines the size of satellite’s orbit. It is half of the major

axis. This runs from the center through a focus to the edge of the ellipse. So, it is the radius of

an orbit at the orbit's two most distant points.

Both semi major axis and semi minor axis are represented in above figure. Length of

semi major axis (a) not only determines the size of satellite’s orbit, but also the time period of

revolution.

If circular orbit is considered as a special case, then the length of semi-major axis will be equal

to radius of that circular orbit.

Eccentricity

The value of Eccentricity (e) fixes the shape of satellite’s orbit. This parameter indicates the

deviation of the orbit’s shape from a perfect circle.

If the lengths of semi major axis and semi minor axis of an elliptical orbit are a & b, then the

mathematical expression for eccentricity (e) will be

e=a2−b2−−−−−−√ae=a2−b2a

The value of eccentricity of a circular orbit is zero, since both a & b are equal. Whereas, the

value of eccentricity of an elliptical orbit lies between zero and one.

The following figure shows the various satellite orbits for different eccentricity (e) values

In above figure, the satellite orbit corresponding to eccentricity (e) value of zero is a circular

orbit. And, the remaining three satellite orbits are of elliptical corresponding to the eccentricity

(e) values 0.5, 0.75 and 0.9.

Mean Anomaly

For a satellite, the point which is closest from the Earth is known as Perigee.  Mean

anomaly (M) gives the average value of the angular position of the satellite with reference to

perigee.

If the orbit is circular, then Mean anomaly gives the angular position of the satellite in the orbit.

But, if the orbit is elliptical, then calculation of exact position is very difficult. At that time,

Mean anomaly is used as an intermediate step.

Argument of Perigee

Satellite orbit cuts the equatorial plane at two points. First point is called as descending node,

where the satellite passes from the northern hemisphere to the southern hemisphere. Second

point is called as ascending node, where the satellite passes from the southern hemisphere to

the northern hemisphere.

Argument of perigee (ω) is the angle between ascending node and perigee. If both perigee and

ascending node are existing at same point, then the argument of perigee will be zero degrees

Argument of perigee is measured in the orbital plane at earth’s center in the direction of satellite

motion.

KEPLER’S LAW

In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion

of planets around the Sun, published by Johannes Kepler between 1609 and 1619. These

improved the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits with

epicycles with elliptical trajectories, and explaining how planetary velocities vary. The laws state

that:

The orbits are ellipses, with focal points F1 and F2 for the first planet and F1 and F3 for the second

planet. The Sun is placed in focal point F1.

The two shaded sectors A1 and A2 have the same surface area and the time for planet 1 to cover

segment A1 is equal to the time to cover segment A2.

The total orbit times for planet 1 and planet 2 have a ratio .

The orbit of a planet is an ellipse with the Sun at one of the two foci.

A line segment joining a planet and the Sun sweeps out equal areas during equal intervals

of time.

The square of the orbital period of a planet is directly proportional to the cube of

the semi-major axis of its orbit.

The elliptical orbits of planets were indicated by calculations of the orbit of Mars. From this,

Kepler inferred that other bodies in the Solar System, including those farther away from the Sun,

also have elliptical orbits. The second law helps to establish that when a planet is closer to the

Sun, it travels faster. The third law expresses that the farther a planet is from the Sun, the longer

its orbit, and vice versa.

First law of Kepler

The orbit of every planet is an ellipse with the Sun at one of the two foci.

Mathematically, an ellipse can be represented by the formula:

where P is the semi-latus rectum, ε is the eccentricity of the ellipse, r is the distance from the Sun

to the planet, and θ is the angle to the planet's current position from its closest approach, as seen

from the Sun. So (r, θ) are polar coordinates.

For an ellipse 0 < ε < 1 ; in the limiting case ε = 0, the orbit is a circle with the Sun at the centre

(i.e. where there is zero eccentricity).

At θ = 0°, perihelion, the distance is minimum

At θ = 90° and at θ = 270° the distance is equal to P.

At θ = 180°, aphelion, the distance is maximum (by definition, aphelion is – invariably –

perihelion plus 180°)

Kepler’s Second Law

Kepler’s Third Law:

where M is the mass of the Sun, m is the mass of the planet, and G is the gravitational

constant, T is the orbital period and ‘a’ is the elliptical semi-major axis.

EFFECTS OF ORBITAL INCLINATION

The angle between orbital plane and earth’s equatorial plane is known as inclination (i). It is

measured at the ascending node with direction being east to north. So, inclination defines the

orientation of the orbit by considering the equator of earth as reference.

There are four types of orbits based on the angle of inclination.

Equatorial orbit − Angle of inclination is either zero degrees or 180 degrees.

Polar orbit − Angle of inclination is 90 degrees.

Prograde orbit − Angle of inclination lies between zero and 90 degrees.

Retrograde orbit − Angle of inclination lies between 90 and 180 degrees.

Right Ascension of Ascending node

We know that ascending node is the point, where the satellite crosses the equatorial plane while

going from the southern hemisphere to the northern hemisphere.

Right Ascension of ascending node (Ω) is the angle between line of Aries and ascending node

towards east direction in equatorial plane. Aries is also called as vernal and equinox.

Satellite’s ground track is the path on the surface of the Earth, which lies exactly below its orbit.

The ground track of a satellite can take a number of different forms depending on the values of

the orbital elements.

Orbital Equations

In this section, let us discuss about the equations which are related to orbital motion.

Forces acting on Satellite

A satellite, when it revolves around the earth, it undergoes a pulling force from the earth due to

earth’s gravitational force. This force is known as Centripetal force (F1) because this force

tends the satellite towards it.

Mathematically, the Centripetal force (F1) acting on satellite due to earth can be written as

F1=GMm/R2

Where,

G is universal gravitational constant and it is equal to 6.673 x 10-11 N∙m2/kg2.

M is mass of the earth and it is equal to 5.98 x 1024 Kg.

m is mass of the satellite.

R is the distance from satellite to center of the Earth.

A satellite, when it revolves around the earth, it undergoes a pulling force from the sun and the

moon due to their gravitational forces. This force is known as Centrifugal force (F2) because

this force tends the satellite away from earth.

Mathematically, the Centrifugal force (F2) acting on satellite can be written as

F2=mv2/R

Where, v is the orbital velocity of satellite.

Orbital Velocity

Orbital velocity of satellite is the velocity at which, the satellite revolves around earth. Satellite

doesn’t deviate from its orbit and moves with certain velocity in that orbit, when both

Centripetal and Centrifugal forces are balance each other.

So, equate Centripetal force (F1) and Centrifugal force (F2).

Therefore, the orbital velocity of satellite is

Where,

G is gravitational constant and it is equal to 6.673 x 10-11 N∙m2/kg2.

M is mass of the earth and it is equal to 5.98 x 1024 Kg.

R is the distance from satellite to center of the Earth.

So, the orbital velocity mainly depends on the distance from satellite to center of the Earth (R),

since G & M are constants.

AZIMUTH AND ELEVATION

The following two angles of earth station antenna combined together are called as look angles.

Azimuth Angle

Elevation Angle

Generally, the values of these angles change for non-geostationary orbits. Whereas, the values

of these angles don’t change for geostationary orbits. Because, the satellites present in

geostationary orbits appear stationary with respect to earth.

These two angles are helpful in order to point at the satellite directly from the earth station

antenna. So, the maximum gain of the earth station antenna can be directed at satellite.

We can calculate the look angles of geostationary orbit by using longitude & latitude of earth

station and position of satellite orbit.

Azimuth Angle

The angle between local horizontal plane and the plane passing through earth station, satellite

and center of earth is called as azimuth angle.

The formula for Azimuth angle (α) is

Where,

L is Latitude of earth station antenna.

G is the difference between position of satellite orbit and earth station antenna.

The following figure illustrates the azimuth angle.

Measure the horizontal angle at earth station antenna to north pole as shown in figure. It

represents azimuth angle. It is used to track the satellite horizontally.

Elevation Angle

The angle between vertical plane and line pointing to satellite is known as Elevation angle.

Vertical plane is nothing but the plane, which is perpendicular to horizontal plane.

The formula for Elevation angle (β) is

We can calculate the elevation angle by using above formula. The following figure illustrates

the elevation angle.

Measure the vertical angle at earth station antenna from ground to satellite as shown in the

figure. It represents elevation angle.

COVERAGE ANGLE AND SLANT ANGLE

In radio electronics, especially radar terminology, slant range is the line-of-sight distance along

a slant direction between two points which are not at the same level relative to a specific datum.

An example of slant range is the distance to an aircraft flying at high altitude with respect to that

of the radar antenna. The slant range (1) is the hypotenuse of the triangle represented by the

altitude of the aircraft and the distance between the radar antenna and the aircraft's ground

track (point (3) on the earth directly below the aircraft). In the absence of altitude information,

for example from a height finder, the aircraft location would be plotted farther (2) from the

antenna than its actual ground track.

ECLIPSE

A satellite is said to be in eclipse when the earth or moon prevents sunlight from reaching

it.

If the earth’s equatorial plane coincides with the plane of earth’s orbit around sun, the

geostationary orbit will be eclipsed by the earth. This is called the earth eclipse of

satellite.

For a geostationary satellite, the solar eclipse due to earth occurs during two periods that

begin 23 days before equinox and ends 23 days after equinox. Because during equinox

(autumn and spring) the sun, earth and the satellite are in the same plane.

Solar eclipses are important as they affect the working of the satellite because during

eclipse satellite receives no power from its solar panels and it has to operate on its

onboard standby batteries which reduce satellite life.

Satellite failure is more at such times when satellite enters into eclipse (sudden switch to

no solar power region) and when it moves out of eclipse (suddenly large amount of solar

power is bombarded on satellite) as this creates thermal stress on satellite.

Eclipse caused by moon occurs when moon passes in front of sun but that is less

important as it takes place for short duration (twice in every 24 hours for an average of

few minutes).

Way to avoid eclipse during satellite lifetime:

Satellite longitudes which are west rather than east of the earth station are most desirable.

When satellite longitude is east of the earth station, the satellite enters eclipse during

daylight and early morning hours of the earth station. This can be undesirable if the

satellite has to operate on reduced battery power

When satellite longitude is west of the earth station, eclipse does not occur until the earth

station is in darkness when usage is likely to be low.

ORBITAL PERTURBATIONS

Following are the orbital perturbations due to gravitational and non-gravitational forces or

parameters.

Irregular gravitational force around the Earth due to non-uniform mass distribution.

Earth’s magnetic field too causes orbital perturbations.

Main external perturbations come from Sun and Moon. When a satellite is near to these

external bodies, it receives a stronger gravitational pull.

Low-orbit satellites get affected due to friction caused by collision with atoms and ions.

Solar radiation pressure affects large GEO satellites, which use large solar arrays.

Self-generated torques and pressures caused by RF radiation from the antenna.

Most satellites use a propulsion subsystem in order to maintain a proper spin axis direction

and control the altitude of the satellite against perturbation forces.

Satellites stay in space for most of their life time. We know that the environment of

weightlessness is present in the space. That’s why satellites don’t require additional strong

frames in space. But, those are required during launching process. Because in that process

satellite shakes violently, till the satellite has been placed in a proper orbit.

The design of satellites should be compatible with one or more launch vehicles in order to place

the satellite in an orbit.

We know that the period of revolution will be more for higher apogee altitude according

to Kepler’s second law. The period of geostationary transfer orbit is nearly equal to 16 hours.

If perigee is increased to GEO altitude (around 36,000 km), then the period of revolution will

increase to 24 hours.

PLACING SATELLITES INTO A GEO STATIONARY ORBIT

Satellite should be properly placed in the corresponding orbit after leaving it in the space. It

revolves in a particular way and serves its purpose for scientific, military or commercial. The

orbits, which are assigned to satellites with respect to earth are called as Earth Orbits. The

satellites present in those orbits are called as Earth Orbit Satellites.

We should choose an orbit properly for a satellite based on the requirement. For example, if the

satellite is placed in lower orbit, then it takes less time to travel around the earth and there will

be better resolution in an onboard camera. Similarly, if the satellite is placed in higher orbit,

then it takes more time to travel around the earth and it covers more earth’s surface at one time.

Following are the three important types of Earth Orbit satellites −

Geosynchronous Earth Orbit Satellites

Medium Earth Orbit Satellites

Low Earth Orbit Satellites

Geosynchronous Earth Orbit Satellites

A Geo-synchronous Earth Orbit (GEO) Satellite is one, which is placed at an altitude

of 22,300 miles above the Earth. This orbit is synchronized with a side real day (i.e., 23 hours

56 minutes). This orbit can have inclination and eccentricity.

It may not be circular. This orbit can be tilted at the poles of the earth. But, it appears stationary

when observed from the Earth. These satellites are used for satellite Television.

The same geo-synchronous orbit, if it is circular and in the plane of equator, then it is called

as Geostationary orbit. These Satellites are placed at 35,900kms (same as Geosynchronous)

above the Earth’s Equator and they keep on rotating with respect to earth’s direction (west to

east).

The satellites present in these orbits have the angular velocity same as that of earth. Hence,

these satellites are considered as stationary with respect to earth since, these are in synchronous

with the Earth’s rotation.

The advantage of Geostationary orbit is that no need to track the antennas in order to find the

position of satellites.

Geostationary Earth Orbit Satellites are used for weather forecasting, satellite TV, satellite radio

and other types of global communications.

The following figure shows the difference between Geo-synchronous and Geo-stationary orbits.

The axis of rotation indicates the movement of Earth.

Polar Orbiting Satellites

Due to the rotation of the Earth, it is possible to combine the advantages of low-altitude orbits

with global coverage, using near-polar orbiting satellites, which have an orbital plane crossing

the poles. These satellites, termed Polar Orbiting Environmental Satelliites (POES) are launched

into orbits at high inclinations* to the Earth's rotation (at low angles with longitude lines), such

that they pass across high latitudes near the poles. Most POES orbits are circular to slightly

elliptical at distances ranging from 700 to 1700 km (435 - 1056 mi) from the geoid. At different

altitudes they travel at different speeds.

*"High inclination" means that the subsatellite point moves north or south along the surface

projection of the earth's axis. If the orbit is designed correctly, the subsatellite point can be

largely in the day side (or night side) of the planet during the entire orbit. Such an orbit is termed

"sun-synchronous" and more details on that are given below. Obviously, in order for this to

happen, the orbital speed of the saltellite (and its orbital altitude) would have to be phased with

the rotation of the earth. The result is that the orbit of the satellite can be phased so that the

satellite maximizes its coverage of the the day side of the planet.

Example of a Near-Polar Orbit.

The ground track of the POES is displaced to the west after each orbital period, due to the

gravitaitonal effects and the rotation of the Earth. This displacement of longitude is a function of

the orbital period (often less than 2 hours for low altitude orbits). In essence, while the satellite

circles both poles, the portion of the earth at subsatellite point will be in sunlight or darkness

during that entire period. The balance between gravitational acceleration and centrifugal

acceleration for such satellites requires a low earth (h) orbit, contrasted to the h you calculated in

Homework 1 for the GOES.