Time Period And Energy Of A Satellite - Practice Questions & MCQ

 The time period of satellite-

  It is the time taken by satellite to go once around the earth.         

And the time period (T) of the satellite is given by 

                

 Where  

 radius of orbit

 Time period

 Mass of planet

• If the satellite is very close to the earth’s surface,

            i.e., h<<<R,

             then 
               or

• The time period of a satellite in terms of density

    

 Density of planet

 Time period

 Gravitational constant

 for earth

• For a satellite, the time interval between the two consecutive appearances overhead

    If a satellite in the equilateral planes moves from west to east Angular velocity of the satellite  with respect to an observer on earth will be 

            

            Satellite angular velocity

             earth angular velocity

           So   

if     

means satellite will appear stationary relative to earth.

 Height of Satellite-

Putting the value of time period in the above formula we can calculate the height of the satellite from the surface of the earth. 

 The energy of Satellite-

When a satellite revolves around a planet in its orbit, it possesses both kinetic energy (due to orbital motion) and potential energy (due to its position against the gravitational pull of earth).

And these energies are given by 

Where 

   And 

•     Energy Graph of satellite

Where

• Energy distribution in an elliptical orbit

     

In this Total Energy

Where   

•     Binding Energy (B.E.)-

The minimum energy required to remove the satellite from its orbit to infinity is called Binding Energy.

And It is given by 

where 

• Work done in changing the orbit-

When the satellite is transferred to a higher orbit   i.e    as shown in the figure.

Where