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### Satellite motion.

posted Oct 24, 2016, 7:19 PM by Upali Salpadoru   [ updated Oct 25, 2016, 12:27 PM ]
Courtesey : U  tube. Fig. 1. It was Arthur C. Clerk , the British astronomer who lived in Sri Lanka that predicted the possibility of using artificial satellites for communication.

 What exactly is a satellite? A satellite is a body that circles a planet or a star. Moon is a satellite of the earth while earth is a satellite of the sun.

 2. Why does the moon go round and round without getting attracted to the earth? It is actually in a state of falling. It is due to the attraction of the earth that the moon goes round the earth without moving into space.Yet as it has a high velocity , the amount of turn given by gravity is not sufficient to land on earth.

Artificial satellites.

This is an object sent by man to orbit a celestial body. Fig.2 Rockets reaching the 'escape velocity' may not come back?

This diagram explains how and why they work. If NASA sends a small rocket at a particular angle it will go some distance and land it somewhere as shown by the no.1 line. If the rocket had a greater speed it will go further as in no.2. No.3 , thick line shows a projectile with a greater speed, such as an inter continental ballistic missile. If it is launched at a much higher velocity it can be sent to an orbit as shown by no.4. Fig.3. First ever man made satellite, was launched on 4/10/57.

Mass of 83.6kg.

Average altitude of 700 km.

Newton explained the “The Law of Universal Gravity”.

1. Force of Gravity is directly proportional to the product of the masses concerned.      F ∝ Mx m.

2. Force is inversely proportional to square of the distance.

F ∝  1/ r2.

Converting this to an equation we get:

F = k  xM x m  /  r2

This constant has been named as Gravitational constant and is denoted by “G”.

It was Henry Cavendish that first calculated the value of this. It is an exceedingly a small number.

It is now taken as :  Fig.4.Sri Lankan elephant with a mahout.

Why won’t the elephant attract the man?

Let us do a calculation.

Mass of the elephant=1200kg.

Mass of man………=60 kg.

Distance …………= 2 m.

Is the force = 1200 x60 ÷ 4                = 72000 ÷ 4

=18000 Nkg-1...X.?

In order to get the correct answer we have to use the Gravitational constant.

That is   18000x 6.67 x10-11.

That is             =  1.2x10-6 Nkg-1.

This force is just a very small fraction of a newton which cannot be noticed.

Orbital Motion.

When there is circular motion the force is directed toward the centre. This is called centripetal force.

It is given by the equation    Fc  =  mass x velocity 2 ÷  radius.

When a satellite is in motion Fc = Fg.

That is   MV2         =   G xMxm

r                r

V2    = GxMxm     =    V2 = G M /  r

mr

Fg = G x Mxm ÷ r 2

Let us take an example.

A satellite, had a mass of 80kg. and was orbiting the earth at an average altitude of 700 km.

Fg = G x Mxm ÷ r 2

Fg = 6.673 x10-11 x 6 ×1024 x 80

(700+ 6,370) x 103)2

=    3.2 x10 16         =   3.2 x10 16

7070000 2                   5x10 13

Fg       =  64o N.

V2 = G M /  r

V2=   6.673 x10-11  x 6x10 24      =     4 x10 14

7070000                       7070x 103

V2 = 56577086   = 7521 ms-1