Idea of launching the satellite & Factors affecting orbital velocity of a satellite

Importance of satellites

The satellite is considered as a very high tower that can be used in transmitting and receiving the wireless waves , Satellites can be classified according to their applications into Astronomical satellites which are huge telescope floating in the space and they can photograph the space accurately .

Communication satellites , They are used in TV transmission , Radio transmission , phone calls , Internet , Locating sites through GPS , Monitor regions using Google Earth .

Remote sensing satellites , They are used to study and monitor the emigrant birds , They are used to determine the mineral resources and their distribution underground , They are used to look out the agricultural yields to protect them against weather dangers and they are used to study the formation of hurricanes .

Explanatory and spying satellites : They abound the information needed by military and political leaders to make decisions and war administration .

Satellites

Man has dreamt for centuries to explore the space , He continued developing probes and rockets that launch space ships to orbit the Earth or reach further to another planet like Mars .

That dream has come true on the 4th of October 1957 when the first satellite ( Sputnik ) has sent into space , That was followed by sending other satellites and stepping onto the Moon , Still space exploration continues successfully .

Idea of launching the satellite

A satellite in its orbit is considered as an object falls freely towards the Earth’s surface ( because it is under the effect of Earth’s gravity ) , In spite of this it never reaches the surface , Isaac Newton explained this as follows :

When projecting a cannon projectile from the top of a mountain in a horizontal direction ( neglecting the air resistance ) , the projectile moves through a certain distance before falling to ground , By increasing the velocity of projection , the horizontal distance moved by the projectile before falling to ground increases .

At a certain projecting velocity , the projectile falls freely along a curved path at a constant distance away from the Earth’s surface , The projectile orbits the Earth in a roughly circular path , It becomes a follower of the Earth and named a satellite .

A satellite is an object projected at a certain velocity to rotate in a roughly circular path at a constant distance from the Earth’s surface .

The orbital velocity of a satellite is the velocity that makes the satellite orbit Earth in the roughly circular path at the constant distance from the Earth’s surface .

Finding the orbital velocity of a satellite ( v )

The attractive gravitational force between the satellite and the Earth is the centripetal force itself .

F = G m M / r² = m v² / r

G M / r = v²

v =( G M / r )^½

Where ( m ) is the satellite mass , ( M ) is mass of the Earth , ( r ) is the orbit radius and ( G ) is the gravitational constant , If the height of the satellite above the surface is ( h ) : r = R + h , Where ( R ) is the radius of the Earth .

If the satellite stopped and its velocity became zero , it would move in a straight line under the gravity of Earth towards the Earth and fall down onto it .

If the gravitational force between the Earth and the satellite vanished , the satellite moves in a straight line tangent to the circular path away from the Earth .

To calculate the time taken by the satellite to complete one revolution around the Earth ( the periodic time T ) :

T = Circumference / Speed = 2 π r / v

The velocity of satellite does not depend on its mass but depends on other factors .

Factors affecting the orbital velocity of a satellite

The planet mass : The orbital velocity of a satellite is directly proportional to square root of the mass of the planet at constant radius of the orbit .

The orbit radius : Orbital velocity of a satellite is inversely proportional to the square root of the orbit radius .

v² = G M / r

As the mass of the satellite increases , a rocket of greater thrust is required to launch it into space and acquire the required velocity to orbit the Earth .