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A sattelite of mass 1000kg moves in circular orbit of radius 7000km around earth calculate total energy required to place sattelite in orbit from earth's surface?
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A sattelite of mass 1000kg moves in circular orbit of radius 7000km ar...
Total Energy required to place a satellite in orbit from Earth's surface
Given:
- Mass of the satellite (m) = 1000 kg
- Radius of the orbit (r) = 7000 km = 7,000,000 meters
- Mass of the Earth (M) = 5.972 × 10^24 kg
- Gravitational constant (G) = 6.674 × 10^-11 Nm^2/kg^2
Explanation:
Step 1: Calculate the gravitational force between the satellite and the Earth
The gravitational force between two objects can be calculated using the formula:
F = (G * M * m) / r^2
Where:
- F is the gravitational force
- G is the gravitational constant
- M is the mass of the Earth
- m is the mass of the satellite
- r is the distance between the centers of the Earth and the satellite
Plugging in the values, we get:
F = (6.674 × 10^-11 Nm^2/kg^2 * 5.972 × 10^24 kg * 1000 kg) / (7,000,000 meters)^2
Simplifying the equation, we get:
F = 8.974 × 10^15 N
Step 2: Calculate the work done to move the satellite to the orbit
The work done to move an object against a force is given by the formula:
Work = Force * Distance
In this case, the force is the gravitational force calculated in the previous step and the distance is the radius of the orbit.
Work = 8.974 × 10^15 N * 7,000,000 meters
Simplifying the equation, we get:
Work = 6.282 × 10^22 J
Step 3: Calculate the kinetic energy of the satellite in orbit
The kinetic energy of an object in orbit can be calculated using the formula:
Kinetic Energy = (1/2) * m * v^2
In this case, since the satellite is in a circular orbit, the velocity can be calculated using the formula:
v = √(G * M / r)
Plugging in the values, we get:
v = √(6.674 × 10^-11 Nm^2/kg^2 * 5.972 × 10^24 kg / 7,000,000 meters)
Simplifying the equation, we get:
v = 7456.35 m/s
Plugging the velocity into the kinetic energy formula, we get:
Kinetic Energy = (1/2) * 1000 kg * (7456.35 m/s)^2
Simplifying the equation, we get:
Kinetic Energy = 2.778 × 10^10 J
Step 4: Calculate the total energy required
The total energy required to place the satellite in orbit from Earth's surface is the sum of the work done and the kinetic energy:
Total Energy = Work + Kinetic Energy
Plugging in the values, we get:
Total Energy = 6.282 × 10^22 J + 2.778 × 10^10 J
Simplifying the equation, we get:
Total Energy =
Given:
- Mass of the satellite (m) = 1000 kg
- Radius of the orbit (r) = 7000 km = 7,000,000 meters
- Mass of the Earth (M) = 5.972 × 10^24 kg
- Gravitational constant (G) = 6.674 × 10^-11 Nm^2/kg^2
Explanation:
Step 1: Calculate the gravitational force between the satellite and the Earth
The gravitational force between two objects can be calculated using the formula:
F = (G * M * m) / r^2
Where:
- F is the gravitational force
- G is the gravitational constant
- M is the mass of the Earth
- m is the mass of the satellite
- r is the distance between the centers of the Earth and the satellite
Plugging in the values, we get:
F = (6.674 × 10^-11 Nm^2/kg^2 * 5.972 × 10^24 kg * 1000 kg) / (7,000,000 meters)^2
Simplifying the equation, we get:
F = 8.974 × 10^15 N
Step 2: Calculate the work done to move the satellite to the orbit
The work done to move an object against a force is given by the formula:
Work = Force * Distance
In this case, the force is the gravitational force calculated in the previous step and the distance is the radius of the orbit.
Work = 8.974 × 10^15 N * 7,000,000 meters
Simplifying the equation, we get:
Work = 6.282 × 10^22 J
Step 3: Calculate the kinetic energy of the satellite in orbit
The kinetic energy of an object in orbit can be calculated using the formula:
Kinetic Energy = (1/2) * m * v^2
In this case, since the satellite is in a circular orbit, the velocity can be calculated using the formula:
v = √(G * M / r)
Plugging in the values, we get:
v = √(6.674 × 10^-11 Nm^2/kg^2 * 5.972 × 10^24 kg / 7,000,000 meters)
Simplifying the equation, we get:
v = 7456.35 m/s
Plugging the velocity into the kinetic energy formula, we get:
Kinetic Energy = (1/2) * 1000 kg * (7456.35 m/s)^2
Simplifying the equation, we get:
Kinetic Energy = 2.778 × 10^10 J
Step 4: Calculate the total energy required
The total energy required to place the satellite in orbit from Earth's surface is the sum of the work done and the kinetic energy:
Total Energy = Work + Kinetic Energy
Plugging in the values, we get:
Total Energy = 6.282 × 10^22 J + 2.778 × 10^10 J
Simplifying the equation, we get:
Total Energy =
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A sattelite of mass 1000kg moves in circular orbit of radius 7000km around earth calculate total energy required to place sattelite in orbit from earth's surface?
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A sattelite of mass 1000kg moves in circular orbit of radius 7000km around earth calculate total energy required to place sattelite in orbit from earth's surface? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A sattelite of mass 1000kg moves in circular orbit of radius 7000km around earth calculate total energy required to place sattelite in orbit from earth's surface? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A sattelite of mass 1000kg moves in circular orbit of radius 7000km around earth calculate total energy required to place sattelite in orbit from earth's surface?.
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