Why is the lunar landing site not visible through a telescope?

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The human flight to the moon was the greatest achievement of human scientific and engineering thought. However, many people have a question: why the traces left by the Americans on the moon cannot be seen through a telescope? In this article, I will analyze this issue in detail.

Alas, the best and largest telescopes that we use today are not able to «see» such small details. This is not because telescopes are poorly designed — in a sense, they are close to perfect. The problem is more fundamental.

Resolution

The resolution of each telescope is limited firstly by the wavelength of visible light, and secondly by the diameter of the telescope lens, or as they say it

The larger the telescope aperture, the more light waves emitted or reflected by the object have a chance to be distinguished from those from neighboring points. The relationship between light wavelength, maximum resolution angle and telescope aperture is described by the formula:

Visible light has a wavelength of approximately 0.5 micrometers. The largest telescope on Earth has an aperture of just over 10 meters (which is 4 times the aperture of the Hubble telescope in orbit).

This means that the best resolution angle that can be obtained with this telescope is approximately 0.00000006 radians, or approximately 0.01 arc seconds. And we do not even take into account the scattering of light in the atmosphere.

The lunar module has a diameter (when viewed from above) about 4 meters and is located at a distance of 384,403,000 meters. This means that its angular size (as viewed from Earth) is 0.002 arc seconds. It will be easy to make sure that the minimum size of the telescope aperture required to obtain a distinguishable image of the lunar module will be 200 meters.

In this case, the size of the lunar module in the image will be one pixel. If we want to get a clearer image, then we will need to build a several times larger telescope.

Actually, the answer to the question why the traces on the moon are not visible through a telescope is very simple: because the moon is very far away, the trails are too small and we do not have telescopes with the required resolution to distinguish them.

This is also the answer to questions sometimes sounding from supporters of the lunar conspiracy theory like:

Well, in fact, Hubble was sent to the moon many times and there are many photographs of the moon taken with this telescope, but looking for traces on the moon with the help of Hubble is a little more than completely meaningless activity, this is obvious to anyone familiar with the laws of optics at the 8th grade level of high school …