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A satellite of mass m is orbiting around the earth in a circular orbit with a velocity v. What will be its total energy? [1991]
- a)(3/4) mv2
- b)(1/2) mv2
- c)mv2
- d)– (1/2)m v2
Correct answer is option 'D'. Can you explain this answer?
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A satellite of mass m is orbiting around the earth in a circular orbit...
Total energy = 
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A satellite of mass m is orbiting around the earth in a circular orbit...
Total Energy of a Satellite in Circular Orbit
To determine the total energy of a satellite in a circular orbit around the earth, we need to consider both its kinetic and potential energy.
Kinetic Energy
- The kinetic energy of the satellite is given by (1/2)mv^2, where m is the mass of the satellite and v is its velocity.
Potential Energy
- The potential energy of the satellite in a circular orbit is given by -GMm/r, where M is the mass of the earth, G is the gravitational constant, m is the mass of the satellite, and r is the radius of the orbit.
Total Energy
- The total energy of the satellite is the sum of its kinetic and potential energy.
- Total Energy = Kinetic Energy + Potential Energy
- Total Energy = (1/2)mv^2 - GMm/r
- Total Energy = (1/2)mv^2 - GMm/(R+h) [assuming the satellite is at a height h above the earth's surface]
Conclusion
- From the above expression, we can see that the total energy of the satellite in a circular orbit is given by (1/2)mv^2 - GMm/(R+h).
- Therefore, the correct option is d) - (1/2)mv^2.
To determine the total energy of a satellite in a circular orbit around the earth, we need to consider both its kinetic and potential energy.
Kinetic Energy
- The kinetic energy of the satellite is given by (1/2)mv^2, where m is the mass of the satellite and v is its velocity.
Potential Energy
- The potential energy of the satellite in a circular orbit is given by -GMm/r, where M is the mass of the earth, G is the gravitational constant, m is the mass of the satellite, and r is the radius of the orbit.
Total Energy
- The total energy of the satellite is the sum of its kinetic and potential energy.
- Total Energy = Kinetic Energy + Potential Energy
- Total Energy = (1/2)mv^2 - GMm/r
- Total Energy = (1/2)mv^2 - GMm/(R+h) [assuming the satellite is at a height h above the earth's surface]
Conclusion
- From the above expression, we can see that the total energy of the satellite in a circular orbit is given by (1/2)mv^2 - GMm/(R+h).
- Therefore, the correct option is d) - (1/2)mv^2.
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A satellite of mass m is orbiting around the earth in a circular orbit with a velocity v. What will be its total energy? [1991]a)(3/4) mv2b)(1/2) mv2c)mv2d)– (1/2)m v2Correct answer is option 'D'. Can you explain this answer?
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