# Geostationary Satellites

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Geostationary Satellites : : Gravitational Motion Physics

• Geostationary satellites are stationary with respect to an observer on the earth.
• Their time period is 24 h and they move with a velocity 3.08 kms. Their height above the surface of earth is 36,000 km.
• They are always in equatorial plane and their orbits are circular. They are also called parking orbits.
• Value of orbital velocity does not depend on the mass of the satellite but it depends on the mass and radius of the planet around which the rotation is taking place.
• Greater the height of the satellite smaller is the orbital velocity.

Facts Based on Binding Energy of a Satellite :

• When the satellite is orbiting in its orbit, no energy is required to keep it in its orbit.
• When the energy of the satellite is negative, it moves in either a circular or an elliptical orbit.
• When the energy of a satellite is zero, it escapes away from its orbit and path becomes parabolical.
• When the energy of a satellite is positive, it escapes from the orbit following a hyperbolic path.
• When the velocity of the satellite is increased, its energy increases and it starts moving in a circular path of smaller radius.
• When the height of the satellite is increased, its PE increases and KE decreases.
• The potential energy of a satellite orbiting in circular orbit is always more than its KE.

Facts Based on Escape Velocity :

• The value of escape velocity does not depend upon the mass of the projected body; instead it depends on the mass and radius of the planet from which it is being projected.
• The value of escape velocity does not depend on the angle and direction of projection.
• The minimum energy needed to escape is GMm / R.
• If the velocity of a satellite orbiting the earth is increased by 41.4%, then it will escape away from the gravitational field of the earth.
• If a body falls freely from infinite height, then it will reach the surface of earth with a velocity of 11.2 kms.

In an artificial satellite reaction of a person is zero; therefore the person does not experience any weight. This state is known as the state of weightlessness. The root mean square velocity of all gases on moon is more than the value of root mean square velocity on earth; hence there is no atmosphere on moon. The root mean square velocity of hydrogen is more than that of the escape velocity of earth; therefore hydrogen is not found in earth’s lower atmosphere.

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