Prof. Vilas shamrao Patil

1. Mr. Vilas S. Patil,. Department of Physics , YCWM WARANANAGAR-B.Sc.I-Sem-I- Notes-
Gravitation-Pages -15
Page-1
1.7 : Geosynchronous Orbits :
The period of rotation of earth about its own axis (the line
joining the North Pole and the South Pole) is 24 hours. The
orbit of a satellite having period of revolution same as that
of the earth's period of rotation about its own axis is called
a geosynchronous orbit. Let the satellite is launched in an
orbit in the plane of the equator. The height of the satellite
is kept such that time period of the satellite is 24 hours
and it moves in the same sense as the earth. As seen from
the earth, this satellite will appear to be stationery. Such
satellite is called as geostationary satellite and orbit as
geostationary orbit. For geostationary satellite the orbital
angular velocity of the satellite and spin angular velocity
of earth are exactly equal. The period of revolution of the
satellite is
T2
=
4𝜋2𝑟3
GM
Here, T = 24 hours G = 6.667 x 10-11
Nm-2
kg-2
Mass of the earth M = 6 x 1024
kg and r = R + h = 4.2 x 104
km = radius of geostationary orbit.
But R = Radius of earth = 6400 km
Hence h = 3.6 x 104
km

2. Mr. Vilas S. Patil,. Department of Physics , YCWM WARANANAGAR-B.Sc.I-Sem-I- Notes-
Gravitation-Pages -15
Page-2
Therefore height of the geosynchronous satellite above
the surface of the earth is 3.6 x 104 km.
The satellite will always be overhead a particular place on
the equator. The geostationary satellites are used for
communication purposes, weather forecasting and other
applications.
1.8 : Weightlessness
The weight of the body is defined as the gravitational force
exerted by the earth on the body. It is directed towards
the centre of the earth. When a person stands on the
surface, the surface exerts normal reaction on him equal
to his weight. Because of this normal reaction, a person
feels his weight.
When an astronaut is at rest on the surface of the earth,
the weight of the astronaut acting downwards is called as
the action. The surface of the earth exerts equal and
opposite reaction on the astronaut. The feeling of the
weight is due to this reaction. Now consider an astronaut
in a satellite revolving around the earth under the action
of gravity. If M is the mass of the earth and r is the radius

3. Mr. Vilas S. Patil,. Department of Physics , YCWM WARANANAGAR-B.Sc.I-Sem-I- Notes-
Gravitation-Pages -15
Page-3
of the orbit of the satellite, then acceleration of the
satellite towards the centre of the earth is
a = G
𝑀
𝑟2 . If m is the mass r of the astronaut inside a
satellite moving round the earth. Then forces acting on
the astronaut are
(i) The gravitational force (pull) of the earth = G
𝑀𝑚
𝑟2 = mg
(ii) The force exerted by the surface on the astronaut = N
By Newton's law
G
𝑀𝑚
𝑟2 − 𝑁 = 𝑚(G
𝑀
𝑟2)
i.e. mg-N=ma or
i.e., N=mg-ma
But a= g, hence N = 0
Thus, the surface does not exert any force on the
astronaut and hence its apparent weight is zero. Hence he
feels weightlessness. Feeling of weightlessness arises
because of astronaut stays in rotating frame of reference.
One can observe phenomena in the space in a satellite,
where water will not fall down from the glass full of water

4. Mr. Vilas S. Patil,. Department of Physics , YCWM WARANANAGAR-B.Sc.I-Sem-I- Notes-
Gravitation-Pages -15
Page-4
even if it is inverted. If an astronaut drops a ball, it does
not fall. Weightlessness does not mean the absence of
gravity. It only means a situation where an astronaut feels
that he is not attracted by any gravitational force. The
weightlessness condition is also known as zero-gravity
condition.
Concept of weightlessness can be understood by
considering a man of mass m standing on the weighing
machine in a lift (elevator). When a lift moves down with
an acceleration a, the apparent weight shown by the
weighing machine is (mg — ma). If the supporting rope of
the lift is cut off,
1.9 : Basic Idea of Global Positioning System (GPS) :The
Global Positioning System (GPS) is "space based satellite
navigation system" that can show your exact position on
or near the Earth surface, anytime, anywhere, in any
weather condition, no matter where you are ? It provides
location and time information on or near the earth where
there is clear line of sight to four or more GPS satellites.
The GPS system provides critical abilities to military, civil
and commercial users around the world. The GPS
technology has tremendous amount of applications in GIS

5. Mr. Vilas S. Patil,. Department of Physics , YCWM WARANANAGAR-B.Sc.I-Sem-I- Notes-
Gravitation-Pages -15
Page-5
(Geographic Information System) and remote sensing
data collection, surveying and mapping. The technology
seems to be beneficial to the GPS user community in
terms of obtaining accurate data up to about 100 m for
navigation, metre-level for mapping and down to
millimeter level for geodetic positing. In simple words it
can be said that if one has a small GPS receiver, he can get
his position anywhere in the land, sea, air, desert or forest
in terms of any co-ordinate system.GPS receivers are
included in many commercial products, such as
automobiles, smart phones, exercise watches, and GIS
devices.
The GPS system includes 24 satellites deployed in space
about 12,000 miles (19,300 kilometers) above the earth's
surface. They orbit the earth once every 12 hours at an
extremely fast pace of roughly 7,000 miles per hour
(11,200 kilometers per hour). The satellites are evenly
spread out so that four satellites are accessible via direct
line-of-sight from anywhere on the earth. Each GPS
satellite broadcasts a message that includes the satellite's
current position, orbit, and exact time. A GPS receiver
combines the broadcasts from multiple satellites to

6. Mr. Vilas S. Patil,. Department of Physics , YCWM WARANANAGAR-B.Sc.I-Sem-I- Notes-
Gravitation-Pages -15
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calculate its exact position using a process called
triangulation. Three satellites are required in order to
determine a receiver's location, though a connection to
four satellites is ideal since it provides greater accuracy. In
order for a GPS device to work correctly, it must first
establish a connection to the required number of
satellites. This process can take anywhere from a few
seconds to a few minutes, depending on the strength of
the receiver. For example, a car's GPS unit will typically
establish a GPS connection faster than the receiver in a
watch or smartphone. Most GPS devices also use some
type of location catching to speed up GPS detection. By
memorizing its previous location, a GPS device can quickly
determine what satellites will be available the next time it
scans for a GPS signal.
Here are some other interesting facts about the GPS
satellites:
• The official USDOD (United States Department of
Defense) name for GPS is NAVSTAR( Navigation Signal
Timing And Ranging)
• The first GPS satellite was launched in 1978. • A full
constellation of 24 satellites was achieved in 1994.

7. Mr. Vilas S. Patil,. Department of Physics , YCWM WARANANAGAR-B.Sc.I-Sem-I- Notes-
Gravitation-Pages -15
Page-7
• Each satellite is built to last about 10 years.
Replacements are constantly being built and launched
into orbit.
• A GPS satellite weighs approximately 2,000 pounds and
is about 17 feet across with the solar panels extended.
• GPS satellites are powered by solar energy, but they
have backup batteries onboard, in case of a solar eclipse.
Following are some of the applications of GPS
1. Industry
2. Agriculture, mapping and GIS data collection, Public
safety, surveying, telecommunication.
3. Military
4. Intelligence and target location, navigation, weapon
aiming and guidance
5. Transportation -
6. Aviation, fleet tracking and marine.
7.Archeology, atmospheric science, environment,
8. Geophysics and geology,

8. Mr. Vilas S. Patil,. Department of Physics , YCWM WARANANAGAR-B.Sc.I-Sem-I- Notes-
Gravitation-Pages -15
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9. Oceanography
10. Wildlife