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A satellite is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of second satellite is longer than the first one (approximately) by A) 1.5% B) 0.5% C) 3% D) 1% If you give me answer please explain it.?
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A satellite is launched in a circular orbit of radius R around the ear...
Calculation of Period of Satellite
The period of a satellite in a circular orbit can be calculated as:
T = 2π√(r^3/GM)
Where,
T = period of satellite
r = radius of orbit
G = gravitational constant
M = mass of the earth
Calculation of Period Difference
Now, let's calculate the period difference between the two satellites:
For the first satellite in circular orbit of radius R,
T1 = 2π√(R^3/GM)
For the second satellite in circular orbit of radius 1.01R,
T2 = 2π√((1.01R)^3/GM)
The difference in periods can be calculated as:
ΔT = T2 - T1
ΔT = 2π√((1.01R)^3/GM) - 2π√(R^3/GM)
ΔT = 2π(√((1.01R)^3/GM) - √(R^3/GM))
ΔT = 2π(√(1.01^3R^3/GM) - √(R^3/GM))
ΔT = 2π(√(1.030301R^3/GM) - √(R^3/GM))
Approximating ΔT
Now, let's approximate the value of ΔT:
ΔT = 2π(√(1.030301R^3/GM) - √(R^3/GM))
ΔT = 2π(1.015 - 1)
ΔT = 0.030π
ΔT ≈ 0.094
The percentage difference in periods can be calculated as:
% difference = (ΔT/T1) x 100
% difference = (0.094/6.28) x 100
% difference ≈ 1.5%
Therefore, the correct answer is A) 1.5%.
The period of a satellite in a circular orbit can be calculated as:
T = 2π√(r^3/GM)
Where,
T = period of satellite
r = radius of orbit
G = gravitational constant
M = mass of the earth
Calculation of Period Difference
Now, let's calculate the period difference between the two satellites:
For the first satellite in circular orbit of radius R,
T1 = 2π√(R^3/GM)
For the second satellite in circular orbit of radius 1.01R,
T2 = 2π√((1.01R)^3/GM)
The difference in periods can be calculated as:
ΔT = T2 - T1
ΔT = 2π√((1.01R)^3/GM) - 2π√(R^3/GM)
ΔT = 2π(√((1.01R)^3/GM) - √(R^3/GM))
ΔT = 2π(√(1.01^3R^3/GM) - √(R^3/GM))
ΔT = 2π(√(1.030301R^3/GM) - √(R^3/GM))
Approximating ΔT
Now, let's approximate the value of ΔT:
ΔT = 2π(√(1.030301R^3/GM) - √(R^3/GM))
ΔT = 2π(1.015 - 1)
ΔT = 0.030π
ΔT ≈ 0.094
The percentage difference in periods can be calculated as:
% difference = (ΔT/T1) x 100
% difference = (0.094/6.28) x 100
% difference ≈ 1.5%
Therefore, the correct answer is A) 1.5%.
Community Answer
A satellite is launched in a circular orbit of radius R around the ear...
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A satellite is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of second satellite is longer than the first one (approximately) by A) 1.5% B) 0.5% C) 3% D) 1% If you give me answer please explain it.?
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A satellite is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of second satellite is longer than the first one (approximately) by A) 1.5% B) 0.5% C) 3% D) 1% If you give me answer please explain it.? 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 is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of second satellite is longer than the first one (approximately) by A) 1.5% B) 0.5% C) 3% D) 1% If you give me answer please explain it.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A satellite is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of second satellite is longer than the first one (approximately) by A) 1.5% B) 0.5% C) 3% D) 1% If you give me answer please explain it.?.
A satellite is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of second satellite is longer than the first one (approximately) by A) 1.5% B) 0.5% C) 3% D) 1% If you give me answer please explain it.? 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 is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of second satellite is longer than the first one (approximately) by A) 1.5% B) 0.5% C) 3% D) 1% If you give me answer please explain it.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A satellite is launched in a circular orbit of radius R around the earth. A second satellite is launched into an orbit of radius 1.01R. The period of second satellite is longer than the first one (approximately) by A) 1.5% B) 0.5% C) 3% D) 1% If you give me answer please explain it.?.
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