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If the kinetic energy of a satellite orbiting around the earth is doubled then -
- a)The satellite will escape into the space.
- b)The satellite will fall down on the earth
- c)Radius of its orbit will be doubled
- d)Radius of its orbit will become half.
Correct answer is option 'A'. Can you explain this answer?
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If the kinetic energy of a satellite orbiting around the earth is doub...
Explanation:
When the kinetic energy of a satellite orbiting around the earth is doubled, it means that the satellite's speed has increased. According to Kepler's laws of planetary motion, when a body moves around another body in an elliptical orbit, the total energy of the system remains constant. This means that any increase in kinetic energy must be balanced by a decrease in potential energy.
Escape velocity:
The satellite's escape velocity is the minimum speed required for an object to escape the gravitational pull of the earth. It is given by the formula ve = √(2GM/R). Where G is the gravitational constant, M is the mass of the earth, and R is the radius of the earth.
The kinetic energy of a satellite in orbit around the earth is given by the formula KE = (1/2)mv^2. Where m is the mass of the satellite and v is its velocity.
Increasing the kinetic energy of a satellite in orbit requires an increase in its velocity. If the velocity of the satellite is increased to a point where its kinetic energy is doubled, it means that the satellite has acquired enough energy to escape the gravitational pull of the earth.
Therefore, the correct answer is option 'A': The satellite will escape into space.
Conclusion:
The increase in kinetic energy leads to an increase in velocity and potential energy. For the satellite to escape the gravitational pull of the earth, it must reach the escape velocity, which is dependent on the mass of the earth and the radius of its orbit.
When the kinetic energy of a satellite orbiting around the earth is doubled, it means that the satellite's speed has increased. According to Kepler's laws of planetary motion, when a body moves around another body in an elliptical orbit, the total energy of the system remains constant. This means that any increase in kinetic energy must be balanced by a decrease in potential energy.
Escape velocity:
The satellite's escape velocity is the minimum speed required for an object to escape the gravitational pull of the earth. It is given by the formula ve = √(2GM/R). Where G is the gravitational constant, M is the mass of the earth, and R is the radius of the earth.
The kinetic energy of a satellite in orbit around the earth is given by the formula KE = (1/2)mv^2. Where m is the mass of the satellite and v is its velocity.
Increasing the kinetic energy of a satellite in orbit requires an increase in its velocity. If the velocity of the satellite is increased to a point where its kinetic energy is doubled, it means that the satellite has acquired enough energy to escape the gravitational pull of the earth.
Therefore, the correct answer is option 'A': The satellite will escape into space.
Conclusion:
The increase in kinetic energy leads to an increase in velocity and potential energy. For the satellite to escape the gravitational pull of the earth, it must reach the escape velocity, which is dependent on the mass of the earth and the radius of its orbit.
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If the kinetic energy of a satellite orbiting around the earth is doubled then -a)The satellite will escape into the space.b)The satellite will fall down on the earthc)Radius of its orbit will be doubledd)Radius of its orbit will become half.Correct answer is option 'A'. Can you explain this answer?
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