The orbit of geo-stationary satellite is circular, the time period of satellite depends on - (i) mass of the satellite (ii) mass of the earth (iii) radius of the orbit (iv) height of the satellite from the surface of earth Which of the following is correct?
- (i) only
- (i) and (ii)
- (i), (ii) and (iii)
- (ii), (iii) and (iv)
The Correct Option is D
Solution and Explanation
$T \frac{1}{M^{1 /2}}$ where $M$ is mass of earth
$\propto (R + h)^{3/2}$ where $R$ is radius of the orbit, $h$ is the height of satellite from the earth's surface.
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Concepts Used:
Gravitational Potential Energy
The work which a body needs to do, against the force of gravity, in order to bring that body into a particular space is called Gravitational potential energy. The stored is the result of the gravitational attraction of the Earth for the object. The GPE of the massive ball of a demolition machine depends on two variables - the mass of the ball and the height to which it is raised. There is a direct relation between GPE and the mass of an object. More massive objects have greater GPE. Also, there is a direct relation between GPE and the height of an object. The higher that an object is elevated, the greater the GPE. The relationship is expressed in the following manner:
PEgrav = mass x g x height
PEgrav = m x g x h
Where,
m is the mass of the object,
h is the height of the object
g is the gravitational field strength (9.8 N/kg on Earth) - sometimes referred to as the acceleration of gravity.
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