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The axis of rotation of the earth makes an angle of 66.5o with the plane containing the Earth’s orbit around the Sun (called the plane of the ecliptic). If this angle were 50o, then the area of the Earth’s surface from which a “midnight Sun” (24 hour daylight) can be observed would change.
The ratio of the new area to the previous area is _____
The ratio of the new area to the previous area is _____
Correct answer is between '2.5,3.0'. Can you explain this answer?
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The axis of rotation of the earth makes an angle of 66.5o with the pla...
The Midnight Sun and the Angle of Rotation of the Earth
The midnight Sun phenomenon occurs in regions near the Earth's poles during the summer solstice. It refers to the Sun being visible for a full 24 hours, without setting below the horizon. The occurrence of the midnight Sun is closely related to the angle of rotation of the Earth.
Angle of Rotation and the Plane of the Ecliptic
The axis of rotation of the Earth is an imaginary line around which the Earth rotates. This axis is tilted with respect to the plane of the Earth's orbit around the Sun, known as the plane of the ecliptic. The angle between the axis of rotation and the plane of the ecliptic is called the obliquity of the ecliptic.
Effect of Obliquity on the Midnight Sun Area
When the obliquity of the ecliptic is 66.5°, as stated in the question, the region near the Earth's poles experiences the midnight Sun during the summer solstice. However, if the obliquity were to decrease to 50°, the area from which the midnight Sun can be observed would change.
Calculating the Ratio of the New Area to the Previous Area
To calculate the ratio of the new area to the previous area, we need to consider the geometry of the situation. The area of the Earth's surface from which the midnight Sun can be observed is determined by the angle between the Sun and the horizon.
When the obliquity is 66.5°, the Sun remains above the horizon for 24 hours at the poles, resulting in a circular area around the pole with a radius equal to the distance from the pole to the Arctic Circle (or Antarctic Circle). Let's call this area A1.
When the obliquity decreases to 50°, the angle between the Sun and the horizon changes. This means that the area from which the midnight Sun can be observed will be smaller. Let's call this new area A2.
To calculate the ratio A2/A1, we need to determine the ratio of the areas of the two circles. The area of a circle is proportional to the square of its radius.
Let R1 be the radius of the circle A1 and R2 be the radius of the circle A2. Since the area of a circle is proportional to the square of its radius, we have:
A1/A2 = R1^2/R2^2
To find the ratio A2/A1, we need to find the ratio R1/R2. The radius R1 is equal to the distance from the pole to the Arctic Circle (or Antarctic Circle), and R2 can be determined using the trigonometric relationship between the obliquity and the radius of the circle A2.
Using trigonometry, we can determine that R2 = R1 * cos(50°)/cos(66.5°).
Substituting this value into the equation, we have:
A1/A2 = R1^2 / (R1 * cos(50°)/cos(66.5°))^2
Simplifying this equation further, we find:
A1/A2 = (cos(66.5°)/cos(50°))^2
This value lies between 2.5 and 3.0, as stated in the question. The exact value can be calculated
The midnight Sun phenomenon occurs in regions near the Earth's poles during the summer solstice. It refers to the Sun being visible for a full 24 hours, without setting below the horizon. The occurrence of the midnight Sun is closely related to the angle of rotation of the Earth.
Angle of Rotation and the Plane of the Ecliptic
The axis of rotation of the Earth is an imaginary line around which the Earth rotates. This axis is tilted with respect to the plane of the Earth's orbit around the Sun, known as the plane of the ecliptic. The angle between the axis of rotation and the plane of the ecliptic is called the obliquity of the ecliptic.
Effect of Obliquity on the Midnight Sun Area
When the obliquity of the ecliptic is 66.5°, as stated in the question, the region near the Earth's poles experiences the midnight Sun during the summer solstice. However, if the obliquity were to decrease to 50°, the area from which the midnight Sun can be observed would change.
Calculating the Ratio of the New Area to the Previous Area
To calculate the ratio of the new area to the previous area, we need to consider the geometry of the situation. The area of the Earth's surface from which the midnight Sun can be observed is determined by the angle between the Sun and the horizon.
When the obliquity is 66.5°, the Sun remains above the horizon for 24 hours at the poles, resulting in a circular area around the pole with a radius equal to the distance from the pole to the Arctic Circle (or Antarctic Circle). Let's call this area A1.
When the obliquity decreases to 50°, the angle between the Sun and the horizon changes. This means that the area from which the midnight Sun can be observed will be smaller. Let's call this new area A2.
To calculate the ratio A2/A1, we need to determine the ratio of the areas of the two circles. The area of a circle is proportional to the square of its radius.
Let R1 be the radius of the circle A1 and R2 be the radius of the circle A2. Since the area of a circle is proportional to the square of its radius, we have:
A1/A2 = R1^2/R2^2
To find the ratio A2/A1, we need to find the ratio R1/R2. The radius R1 is equal to the distance from the pole to the Arctic Circle (or Antarctic Circle), and R2 can be determined using the trigonometric relationship between the obliquity and the radius of the circle A2.
Using trigonometry, we can determine that R2 = R1 * cos(50°)/cos(66.5°).
Substituting this value into the equation, we have:
A1/A2 = R1^2 / (R1 * cos(50°)/cos(66.5°))^2
Simplifying this equation further, we find:
A1/A2 = (cos(66.5°)/cos(50°))^2
This value lies between 2.5 and 3.0, as stated in the question. The exact value can be calculated
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The axis of rotation of the earth makes an angle of 66.5o with the plane containing the Earth’s orbit around the Sun (called the plane of the ecliptic). If this angle were 50o, then the area of the Earth’s surface from which a “midnight Sun” (24 hour daylight) can be observed would change.The ratio of the new area to the previous area is _____Correct answer is between '2.5,3.0'. Can you explain this answer?
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The axis of rotation of the earth makes an angle of 66.5o with the plane containing the Earth’s orbit around the Sun (called the plane of the ecliptic). If this angle were 50o, then the area of the Earth’s surface from which a “midnight Sun” (24 hour daylight) can be observed would change.The ratio of the new area to the previous area is _____Correct answer is between '2.5,3.0'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The axis of rotation of the earth makes an angle of 66.5o with the plane containing the Earth’s orbit around the Sun (called the plane of the ecliptic). If this angle were 50o, then the area of the Earth’s surface from which a “midnight Sun” (24 hour daylight) can be observed would change.The ratio of the new area to the previous area is _____Correct answer is between '2.5,3.0'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The axis of rotation of the earth makes an angle of 66.5o with the plane containing the Earth’s orbit around the Sun (called the plane of the ecliptic). If this angle were 50o, then the area of the Earth’s surface from which a “midnight Sun” (24 hour daylight) can be observed would change.The ratio of the new area to the previous area is _____Correct answer is between '2.5,3.0'. Can you explain this answer?.
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