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What is the solid angle subtended by the moon at any point of earth given the diameter of the moon is 3474 km and it's distance from the earth 3.84 × 10 to the power 8 m?
Verified Answer
What is the solid angle subtended by the moon at any point of earth gi...
Diameter of moon = 3474 km.
Therefore, radius is 1737 km. The area will be,
A_m = x pi r^2 = (3.14)(1737)^2 = 9.473 x times 10^6 m^2
The distance from the Earth is given as,
= 3.84 x 10^8 m
Squaring this value,
r^2 = (3.84 x 10^8)^2 = 14.74 x10^{16} \ m^2
Now the solid angle in steradians is,
And that should be the answer.
And that should be the answer.
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What is the solid angle subtended by the moon at any point of earth gi...
Calculating the Solid Angle Subtended by the Moon
The solid angle subtended by an object at a point is a measure of how large that object appears from that point. In this case, we are interested in finding the solid angle subtended by the Moon at any point on Earth.
Given Data:
- Diameter of the Moon = 3474 km
- Distance from the Earth to the Moon = 3.84 × 10^8 m
Calculations:
1. First, we need to convert the diameter of the Moon to meters: 3474 km = 3.474 × 10^6 m
2. Now, we can calculate the radius of the Moon:
Radius = Diameter / 2 = 3.474 × 10^6 m / 2 = 1.737 × 10^6 m
3. Next, we can calculate the angular size of the Moon as seen from Earth:
Angular size = 2 * arctan(radius / distance) = 2 * arctan(1.737 × 10^6 m / 3.84 × 10^8 m)
4. Finally, we can calculate the solid angle subtended by the Moon using the formula:
Solid Angle = 2π * (1 - cos(angular size))
Final Result:
By performing the calculations above, we can determine the solid angle subtended by the Moon at any point on Earth.
The solid angle subtended by an object at a point is a measure of how large that object appears from that point. In this case, we are interested in finding the solid angle subtended by the Moon at any point on Earth.
Given Data:
- Diameter of the Moon = 3474 km
- Distance from the Earth to the Moon = 3.84 × 10^8 m
Calculations:
1. First, we need to convert the diameter of the Moon to meters: 3474 km = 3.474 × 10^6 m
2. Now, we can calculate the radius of the Moon:
Radius = Diameter / 2 = 3.474 × 10^6 m / 2 = 1.737 × 10^6 m
3. Next, we can calculate the angular size of the Moon as seen from Earth:
Angular size = 2 * arctan(radius / distance) = 2 * arctan(1.737 × 10^6 m / 3.84 × 10^8 m)
4. Finally, we can calculate the solid angle subtended by the Moon using the formula:
Solid Angle = 2π * (1 - cos(angular size))
Final Result:
By performing the calculations above, we can determine the solid angle subtended by the Moon at any point on Earth.
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What is the solid angle subtended by the moon at any point of earth given the diameter of the moon is 3474 km and it's distance from the earth 3.84 × 10 to the power 8 m?
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What is the solid angle subtended by the moon at any point of earth given the diameter of the moon is 3474 km and it's distance from the earth 3.84 × 10 to the power 8 m? 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 What is the solid angle subtended by the moon at any point of earth given the diameter of the moon is 3474 km and it's distance from the earth 3.84 × 10 to the power 8 m? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the solid angle subtended by the moon at any point of earth given the diameter of the moon is 3474 km and it's distance from the earth 3.84 × 10 to the power 8 m?.
What is the solid angle subtended by the moon at any point of earth given the diameter of the moon is 3474 km and it's distance from the earth 3.84 × 10 to the power 8 m? 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 What is the solid angle subtended by the moon at any point of earth given the diameter of the moon is 3474 km and it's distance from the earth 3.84 × 10 to the power 8 m? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the solid angle subtended by the moon at any point of earth given the diameter of the moon is 3474 km and it's distance from the earth 3.84 × 10 to the power 8 m?.
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