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CGP EDU Academic Team
Published on: September 12, 2026
If the radius of earth is R and height of a satellite above earth's surface is R then find the minimum co-latitude (in degree) which can directly receive a signal from satellite. (Satellite is in equatorial plane)
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Let\'s define the parameters. The radius of the Earth is R and the height of the satellite above the Earth\'s surface is also R. Hence the total distance of the satellite from the center of the Earth is \(R + R = 2R\).
Step 2: The angle of co-latitude (denoted by \(\theta\)) is defined as the complement of the latitude and helps in determining how high one must be on the globe to receive the signal from the satellite. To find \(\theta\), we can use right triangle properties.
Step 3: In the right triangle formed by the Earth\'s radius and the line connecting the satellite to the point on the surface (forming the angle of view with the center of the Earth), we have the following:
- The height of the satellite above the Earth's surface is R.
- The total distance from the satellite to the Earth's surface at that point is equal to the Earth's radius (R) + satellite height (R) = 2R.
The angle of depression from the satellite to the Earth's surface can be found using the cosine formula:
\[ \cos(\theta) = \frac{R}{2R} = \frac{1}{2} \]
Step 4: Solving this gives us:
\[ \theta = \cos^{-1}(\frac{1}{2}) = 60^{\circ} \]
Thus, the minimum co-latitude that can directly receive a signal from the satellite is \(60^{\circ}\). Therefore, The correct answer is 60 degrees.
Step 2: The angle of co-latitude (denoted by \(\theta\)) is defined as the complement of the latitude and helps in determining how high one must be on the globe to receive the signal from the satellite. To find \(\theta\), we can use right triangle properties.
Step 3: In the right triangle formed by the Earth\'s radius and the line connecting the satellite to the point on the surface (forming the angle of view with the center of the Earth), we have the following:
- The height of the satellite above the Earth's surface is R.
- The total distance from the satellite to the Earth's surface at that point is equal to the Earth's radius (R) + satellite height (R) = 2R.
The angle of depression from the satellite to the Earth's surface can be found using the cosine formula:
\[ \cos(\theta) = \frac{R}{2R} = \frac{1}{2} \]
Step 4: Solving this gives us:
\[ \theta = \cos^{-1}(\frac{1}{2}) = 60^{\circ} \]
Thus, the minimum co-latitude that can directly receive a signal from the satellite is \(60^{\circ}\). Therefore, The correct answer is 60 degrees.
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