Prof. Vilas Shamrao Patil

1. 1.5 : Satellite in Circular Orbit and Applications Satellite
in circular orbit : Satellites are launched from the earth so
as move round it. Once the satellite is positioned in the
desired orbit with the accurate speed for that orbit, it
continues to move in that orbit due to gravitational force
of attraction of the earth. The motion of the satellite is
similar to motion of the planets around the Sun so that
Kepler's laws of planetary motion are applicable to the
motion of satellite around the earth. The path of the
satellite around the earth is elliptical or circular. Moon is
the natural satellite of the earth with nearly circular orbit.
Many artificial satellites are launched for various practical
applications. The difference in the major and minor axis of
the orbit of the planet is not large; hence orbits can be
treated as circular.

2. Fig. 1.4 : Circular orbit of a satellite
Consider a satellite of mass m performing uniform circular
motion around the earth having mass M. Let R be the
radius of the earth. Let the satellite is orbiting with
velocity v at a height h from the earth surface as shown in
Fig. 1.1.
Satellite moves in the circular orbit of radius r = (R + h).
The centripetal force (F1) acting on the satellite will be
F1=
𝑚𝑣2
𝑟
This centripetal force is provided/ balanced by the
gravitational force (F2) of attraction by the earth on the
satellite. From Newton's law of gravitation
F2 =G
𝑀𝑚
𝑟2
For uniform circular motion F1 = F2
𝑚𝑣2
𝑟
= G
𝑀𝑚
𝑟2
𝑣2
=
G𝑀
𝑟

3. 𝑣 = √
G𝑀
𝑟2
It is seen that (i) velocity of satellite is independent of
mass of satellite and (ii) velocity decreases with increase
in height of the orbit. When satellite is very close to earth
surface i.e. h ≈0, hence r = R, its velocity is
𝑣2
=
G𝑀
𝑅
But for the satellite at the earth surface
i.e. Weight of the satellite = Gravitational force
mg =
G𝑀𝑚
𝑅2
g is acceleration due to gravity at the earth's surface.
g =
G𝑀
𝑅2
Hence equation (1.11) becomes
𝑣2
=
G𝑀
𝑅
=
G𝑀
𝑅
𝑥
𝑅
𝑅
=(
G𝑀
𝑅2 )𝑅 = 𝑔𝑅
𝑣2
= √𝑔𝑅
The velocity of the satellite in an orbit is called as orbital
velocity. The time taken by the satellite to complete one

4. revolution around the earth is called its period of
revolution T. Let the satellite move in a circular orbit of
radius (R + h). It covers the distance equal to
circumference of the circular orbit which is 2𝜋 (R + h) in
time T. Therefore time period of the satellite is
T =
Distance travelled by the satellite
its velocity
=
Circumference of the orbity
its velocity
T =
2𝜋𝑟
𝑣
Squaring both sides
T2
=
4𝜋2𝑟2
𝑣2
From above equation putting 𝑣2
=
G𝑀
𝑟
T2
=
4𝜋2
𝑟2
𝑟
G𝑀
T2
=
4𝜋2
𝑟3
G𝑀
as T2
=
4𝜋2
G𝑀
is constant T2
∝ 𝑟3
.

5. The square of the period of revolution of the satellite in
uniform circular motion is proportional to the cube of the
radius of the orbit. This is Kepler's law of periods.
From equation (1.15), period of the satellite is
T=2𝜋√
𝑟3
𝐺𝑀
= √
(𝑅+ℎ)3
𝐺𝑀
This is expression for periodic time of satellite. Period of
the satellite depends on radius of the earth, mass of the
earth and height of the satellite. It does not depend on
mass of the satellite. The periodic time of satellite
increases as height of the satellite from earth's surface is
increased.
1.6 : Applications of the Satellites
Satellites that are launched into the orbit by using the
rockets are called artificial satellites. Artificial satellites
revolve around the earth because of the gravitational
force of attraction between the earth and satellites.
Artificial satellites are used in various applications. The
various applications of artificial satellites include :
1.Weather forecasting : The satellites that are used to
predict the future of weather are called weather

6. satellites. Weather satellites continuously monitor the
climate and weather conditions of earth. They use
sensors called radiometers for measuring the heat
energy released from the earth surface. Weather
satellites also predict the most dangerous storms such
as cyclones.
2.Navigation : Generally, navigation refers to
determining the geographical
location of an object. The satellites that are used to
determine the geographic location of aircrafts, ships,
cars, trains, or any other object are called navigation
satellites. GPS (Global Positioning System) is an
example of navigation system. It allows the user to
determine their exact location at anywhere in the
world.
3. Satellite Phone : Satellite phone is a type of mobile
phone that uses satellites instead of cell towers for
transmitting the signal or information over long
distances. Mobile phones that use cell towers will
work only within the coverage area of a cell tower. If
we go beyond the coverage area of a cell tower or if
we reach the remote areas, it becomes difficult to

7. make a voice call or send text messages with the
mobile phones. Unlike the mobile mobiles, satellite
phones have global coverage. Satellite phones use
geostationary satellites and low earth orbit (LEO)
satellites for transmitting the information. When a
person makes a call from the satellite phone, the
signal is sent to the satellite. The satellite receives
that signal, processes it, and redirects the signal back
to the earth via a gateway. The gateway then send the
signal or call to the destination by using the regular
cellular and landline networks.
4. Satellite radio : Satellite radio is a wireless transmission
service that uses orbiting satellites to deliver the
information or radio signals to the consumers. It is
primarily used in the cars. When the ground station
transmit signal to the satellite that is revolving around the
earth, the satellite receives the signal, amplifies it, and
redirects the signal back to the earth (radio receivers in
the cars).
5. Television : Satellite television or satellite TV is a
wireless system that uses communication satellites to
deliver the television programs or television signals to the

8. users or viewers. TV or television mostly uses
geostationary satellites because they look stationary from
the earth. Hence, the signal is easily transmitted. When
the television signal is sends to the satellite, it receives the
signal, amplifies it, and retransmits it back to the earth.
6. Internet : Satellite internet is a wireless system that
uses satellites to deliver the internet signals to users. High-
speed internet is the main advantage of satellite internet.
Satellite internet does not use cable systems, buFinstead,
it uses satellites to transmit the information or signal.
7. Astronomy : Astronomytu is the study of celestial
objects such as stars, planets, galaxies, naral satellites me
, cots, etc. The satellites that are used to study or observe
the distant stars, galaxies, planets, etc. are called
astronomical satellites. They are mainly used to find the
new stars, planets, and galaxies. Hubble space telescope
is an example of astronomical satellite. It captures the
high-resolution images of the distant stars, galaxies,
planets etc.
8. Military : Military satellite is an artificial satellite used
by the army for various purposes such as spying on enemy
countries, military communication, and navigation.

9. Military satellites obtain the secret information from the
enemy countries. These satellites also detect the missiles
launched by the other countries in the space. The main
applications are the generation of maps, target
monitoring and detection, and digital elevation model
generation. Military satellites are used by armed forces to
communicate with each other. These satellites also used
to determine the exact location of an object.
9. Environment : Earth observation data offer powerful
solutions for environmental monitoring. The data can be
used mainly - Land Use / Land Cover maps, Hydrological /
Watershed map, Wildlife Habitat Maps, Land Unit Maps,
Soil Contamination Map, Surface Water Condition Maps,
Wetland Analyses, Quarries and Waste Identification,
Desertification analysis.