Diffraction - central spot covers moon

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SUMMARY

The discussion focuses on calculating the diameter of a radar antenna required to cover the Moon's central diffraction spot using the formula D=(2.44*λ*L)/(diameter of the moon). The values provided include a wavelength (λ) of 16.5 cm and a distance (L) of approximately 4x10^8 m. The initial calculation yielded a diameter (D) of 50.325 m, which was later questioned for accuracy. The participant also sought clarification on the origin of the constant 2.44 used in the formula.

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Ducks_in_OR
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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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