Diffraction - central spot covers moon

[Ducks_in_OR]

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

 

[haruspex]

Can you tell me where the 2.44 comes from? Maybe a URL?

 

[Ducks_in_OR]

no worries figured it out