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A satellite of mass 100 kg is placed initially in a temporary orbit 800km above the surface of earth. The satellite is to be placed now in a permanent orbit at 2000km above the surface of earth. Fing the amount of workdone(mega joule) to move the satellite from temporary to permaanent orbit. The radius of the earth is 6400km. Given g = 10m/s2.
Correct answer is '406'. Can you explain this answer?
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A satellite of mass 100 kg is placed initially in a temporary orbit 80...
Consider a satellite of mass m is orbiting around the earth with orbit velocity n. Let h be the height of satellite from the surface of earth and r be the orbital radius of the satellite. Then
Total energy the orbiting satellite (E)
Work done in shifting the satellite from height h to h1 is
W = difference in energy of satellite in two orbits
Total energy the orbiting satellite (E)
Work done in shifting the satellite from height h to h1 is
W = difference in energy of satellite in two orbits
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A satellite of mass 100 kg is placed initially in a temporary orbit 80...
Given:
Mass of the satellite, m = 100 kg
Initial orbit radius, r1 = 800 km + 6400 km = 7200 km
Final orbit radius, r2 = 2000 km + 6400 km = 8400 km
Gravitational acceleration, g = 10 m/s^2
To find:
Amount of work done to move the satellite from the temporary orbit to the permanent orbit
Solution:
Step 1: Calculate the gravitational potential energy in the temporary orbit.
Gravitational potential energy (U1) is given by the formula:
U1 = -GMm/r1
where G is the universal gravitational constant (6.674 × 10^-11 N m^2/kg^2) and M is the mass of the Earth (5.972 × 10^24 kg).
Converting the radius to meters:
r1 = 7200 km = 7200 × 10^3 m
Plugging the values into the formula:
U1 = - (6.674 × 10^-11 N m^2/kg^2) × (5.972 × 10^24 kg) × (100 kg) / (7200 × 10^3 m)
U1 = - 4.906 × 10^8 J
Step 2: Calculate the gravitational potential energy in the permanent orbit.
Using the same formula, but with the new radius:
r2 = 8400 km = 8400 × 10^3 m
Plugging the values into the formula:
U2 = - (6.674 × 10^-11 N m^2/kg^2) × (5.972 × 10^24 kg) × (100 kg) / (8400 × 10^3 m)
U2 = - 2.668 × 10^8 J
Step 3: Calculate the work done.
The work done (W) is given by the formula:
W = U2 - U1
Plugging in the values:
W = - 2.668 × 10^8 J - (- 4.906 × 10^8 J)
W = 2.238 × 10^8 J
Converting to mega joules:
W = 2.238 × 10^8 J / (10^6 J/MJ)
W = 223.8 MJ ≈ 224 MJ
Therefore, the amount of work done to move the satellite from the temporary orbit to the permanent orbit is approximately 224 mega joules.
Mass of the satellite, m = 100 kg
Initial orbit radius, r1 = 800 km + 6400 km = 7200 km
Final orbit radius, r2 = 2000 km + 6400 km = 8400 km
Gravitational acceleration, g = 10 m/s^2
To find:
Amount of work done to move the satellite from the temporary orbit to the permanent orbit
Solution:
Step 1: Calculate the gravitational potential energy in the temporary orbit.
Gravitational potential energy (U1) is given by the formula:
U1 = -GMm/r1
where G is the universal gravitational constant (6.674 × 10^-11 N m^2/kg^2) and M is the mass of the Earth (5.972 × 10^24 kg).
Converting the radius to meters:
r1 = 7200 km = 7200 × 10^3 m
Plugging the values into the formula:
U1 = - (6.674 × 10^-11 N m^2/kg^2) × (5.972 × 10^24 kg) × (100 kg) / (7200 × 10^3 m)
U1 = - 4.906 × 10^8 J
Step 2: Calculate the gravitational potential energy in the permanent orbit.
Using the same formula, but with the new radius:
r2 = 8400 km = 8400 × 10^3 m
Plugging the values into the formula:
U2 = - (6.674 × 10^-11 N m^2/kg^2) × (5.972 × 10^24 kg) × (100 kg) / (8400 × 10^3 m)
U2 = - 2.668 × 10^8 J
Step 3: Calculate the work done.
The work done (W) is given by the formula:
W = U2 - U1
Plugging in the values:
W = - 2.668 × 10^8 J - (- 4.906 × 10^8 J)
W = 2.238 × 10^8 J
Converting to mega joules:
W = 2.238 × 10^8 J / (10^6 J/MJ)
W = 223.8 MJ ≈ 224 MJ
Therefore, the amount of work done to move the satellite from the temporary orbit to the permanent orbit is approximately 224 mega joules.
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A satellite of mass 100 kg is placed initially in a temporary orbit 800km above the surface of earth. The satellite is to be placed now in a permanent orbit at 2000km above the surface of earth. Fing the amount of workdone(mega joule) to move the satellite from temporary to permaanent orbit. The radius of the earth is 6400km. Given g = 10m/s2.Correct answer is '406'. Can you explain this answer?
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A satellite of mass 100 kg is placed initially in a temporary orbit 800km above the surface of earth. The satellite is to be placed now in a permanent orbit at 2000km above the surface of earth. Fing the amount of workdone(mega joule) to move the satellite from temporary to permaanent orbit. The radius of the earth is 6400km. Given g = 10m/s2.Correct answer is '406'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A satellite of mass 100 kg is placed initially in a temporary orbit 800km above the surface of earth. The satellite is to be placed now in a permanent orbit at 2000km above the surface of earth. Fing the amount of workdone(mega joule) to move the satellite from temporary to permaanent orbit. The radius of the earth is 6400km. Given g = 10m/s2.Correct answer is '406'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A satellite of mass 100 kg is placed initially in a temporary orbit 800km above the surface of earth. The satellite is to be placed now in a permanent orbit at 2000km above the surface of earth. Fing the amount of workdone(mega joule) to move the satellite from temporary to permaanent orbit. The radius of the earth is 6400km. Given g = 10m/s2.Correct answer is '406'. Can you explain this answer?.
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