Diffraction - central spot covers moon

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The discussion revolves around calculating the diameter of a radar antenna needed to cover the Moon's central diffraction spot. The formula used is D=(2.44*λ*L)/(diameter of the moon), where λ is the radar wavelength and L is the distance to the Moon. An initial calculation resulted in an antenna diameter of 50.325 meters, which was questioned for accuracy. Participants sought clarification on the origin of the constant 2.44, which is related to diffraction patterns. Ultimately, the inquirer resolved their confusion independently.
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Homework Statement


The Moon is about 4x10^8 m from the Earth and has a diameter of about 3.2x10^6 m. You want a radar which just covers the Moon with the central spot of its diffraction pattern. If the radar has a wavelength of 16.5cm , what is the diameter of the radar antenna?

Homework Equations


Circular Aperture D=(2.44*λ*L)/(diameter of the moon)
D=diameter of the radar

The Attempt at a Solution


plugging in the values I found D=(2.44*(16.5*10^-2)*(4x10^8))/(3.2x10^6) and D=50.325m, which is incorrect. Am I making any incorrect assumptions, or is it the incorrect formula to be using for this type of problem.

Thanks
 
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Can you tell me where the 2.44 comes from? Maybe a URL?
 
no worries figured it out
 

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