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A satellite of mass 2000 kg is revolving in elliptical path around earth. If mean altitude at perigee and apogee are 1600 km and 5600 km respectively, then the energy required to send the satellite in this orbit will be( Radius of earth is 6400 km ) (i) 7.2 × 10^10 J (ii) 7.8 × 10^10 J (iii) 8.5 × 10^10 J (iv) 5.6 × 10^10 J Can someone plz help me out in this?
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A satellite of mass 2000 kg is revolving in elliptical path around ear...
Given data:
Mass of satellite, m = 2000 kg
Radius of earth, r = 6400 km = 6400000 m
Mean altitude at perigee, h1 = 1600 km = 1600000 m
Mean altitude at apogee, h2 = 5600 km = 5600000 m
We know that the potential energy of a satellite in an elliptical orbit is given by:
U = -GMm/2a
where G is the universal gravitational constant, M is the mass of the earth, m is the mass of the satellite, and a is the semi-major axis of the elliptical orbit.
Calculation:
1. Semi-major axis of the elliptical orbit:
a = (h1 + h2 + 2r)/2
a = (1600000 + 5600000 + 2*6400000)/2
a = 10000000 m
2. Mass of the earth:
Mass of the earth, M = 5.97 × 10^24 kg
3. Universal gravitational constant:
G = 6.67 × 10^-11 N m^2/kg^2
4. Potential energy of the satellite:
U = -GMm/2a
U = -(6.67 × 10^-11) × (5.97 × 10^24) × (2000)/2(10000000)
U = -5.97 × 10^10 J
5. Kinetic energy of the satellite:
Kinetic energy of the satellite, K = 1/2mv^2
where v is the velocity of the satellite in the elliptical orbit.
At perigee, the velocity of the satellite, v1 is given by:
v1 = √(GM(2/r - 1/a))
v1 = √[(6.67 × 10^-11) × (5.97 × 10^24) × (2/6400000 - 1/10000000)]
v1 = 10056 m/s
At apogee, the velocity of the satellite, v2 is given by:
v2 = √(GM(2/r - 1/a))
v2 = √[(6.67 × 10^-11) × (5.97 × 10^24) × (2/6400000 - 1/10000000)]
v2 = 6197 m/s
6. Total energy of the satellite:
Total energy of the satellite, E = K + U
E = 1/2mv1^2 + (-5.97 × 10^10)
E = 7.2 × 10^10 J (approx)
Therefore, the energy required to send the satellite in this orbit will be (i) 7.2 × 10^10 J.
Mass of satellite, m = 2000 kg
Radius of earth, r = 6400 km = 6400000 m
Mean altitude at perigee, h1 = 1600 km = 1600000 m
Mean altitude at apogee, h2 = 5600 km = 5600000 m
We know that the potential energy of a satellite in an elliptical orbit is given by:
U = -GMm/2a
where G is the universal gravitational constant, M is the mass of the earth, m is the mass of the satellite, and a is the semi-major axis of the elliptical orbit.
Calculation:
1. Semi-major axis of the elliptical orbit:
a = (h1 + h2 + 2r)/2
a = (1600000 + 5600000 + 2*6400000)/2
a = 10000000 m
2. Mass of the earth:
Mass of the earth, M = 5.97 × 10^24 kg
3. Universal gravitational constant:
G = 6.67 × 10^-11 N m^2/kg^2
4. Potential energy of the satellite:
U = -GMm/2a
U = -(6.67 × 10^-11) × (5.97 × 10^24) × (2000)/2(10000000)
U = -5.97 × 10^10 J
5. Kinetic energy of the satellite:
Kinetic energy of the satellite, K = 1/2mv^2
where v is the velocity of the satellite in the elliptical orbit.
At perigee, the velocity of the satellite, v1 is given by:
v1 = √(GM(2/r - 1/a))
v1 = √[(6.67 × 10^-11) × (5.97 × 10^24) × (2/6400000 - 1/10000000)]
v1 = 10056 m/s
At apogee, the velocity of the satellite, v2 is given by:
v2 = √(GM(2/r - 1/a))
v2 = √[(6.67 × 10^-11) × (5.97 × 10^24) × (2/6400000 - 1/10000000)]
v2 = 6197 m/s
6. Total energy of the satellite:
Total energy of the satellite, E = K + U
E = 1/2mv1^2 + (-5.97 × 10^10)
E = 7.2 × 10^10 J (approx)
Therefore, the energy required to send the satellite in this orbit will be (i) 7.2 × 10^10 J.
Community Answer
A satellite of mass 2000 kg is revolving in elliptical path around ear...
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A satellite of mass 2000 kg is revolving in elliptical path around earth. If mean altitude at perigee and apogee are 1600 km and 5600 km respectively, then the energy required to send the satellite in this orbit will be( Radius of earth is 6400 km ) (i) 7.2 × 10^10 J (ii) 7.8 × 10^10 J (iii) 8.5 × 10^10 J (iv) 5.6 × 10^10 J Can someone plz help me out in this?
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A satellite of mass 2000 kg is revolving in elliptical path around earth. If mean altitude at perigee and apogee are 1600 km and 5600 km respectively, then the energy required to send the satellite in this orbit will be( Radius of earth is 6400 km ) (i) 7.2 × 10^10 J (ii) 7.8 × 10^10 J (iii) 8.5 × 10^10 J (iv) 5.6 × 10^10 J Can someone plz help me out in this? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A satellite of mass 2000 kg is revolving in elliptical path around earth. If mean altitude at perigee and apogee are 1600 km and 5600 km respectively, then the energy required to send the satellite in this orbit will be( Radius of earth is 6400 km ) (i) 7.2 × 10^10 J (ii) 7.8 × 10^10 J (iii) 8.5 × 10^10 J (iv) 5.6 × 10^10 J Can someone plz help me out in this? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A satellite of mass 2000 kg is revolving in elliptical path around earth. If mean altitude at perigee and apogee are 1600 km and 5600 km respectively, then the energy required to send the satellite in this orbit will be( Radius of earth is 6400 km ) (i) 7.2 × 10^10 J (ii) 7.8 × 10^10 J (iii) 8.5 × 10^10 J (iv) 5.6 × 10^10 J Can someone plz help me out in this?.
A satellite of mass 2000 kg is revolving in elliptical path around earth. If mean altitude at perigee and apogee are 1600 km and 5600 km respectively, then the energy required to send the satellite in this orbit will be( Radius of earth is 6400 km ) (i) 7.2 × 10^10 J (ii) 7.8 × 10^10 J (iii) 8.5 × 10^10 J (iv) 5.6 × 10^10 J Can someone plz help me out in this? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A satellite of mass 2000 kg is revolving in elliptical path around earth. If mean altitude at perigee and apogee are 1600 km and 5600 km respectively, then the energy required to send the satellite in this orbit will be( Radius of earth is 6400 km ) (i) 7.2 × 10^10 J (ii) 7.8 × 10^10 J (iii) 8.5 × 10^10 J (iv) 5.6 × 10^10 J Can someone plz help me out in this? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A satellite of mass 2000 kg is revolving in elliptical path around earth. If mean altitude at perigee and apogee are 1600 km and 5600 km respectively, then the energy required to send the satellite in this orbit will be( Radius of earth is 6400 km ) (i) 7.2 × 10^10 J (ii) 7.8 × 10^10 J (iii) 8.5 × 10^10 J (iv) 5.6 × 10^10 J Can someone plz help me out in this?.
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