The Moon received the last human being in 1972 and since then it has been the great forgotten of the solar system, from 1969 to 1972 a total of six lunar missions arrived to the moon and due to its geography they left traces, marks and routes of a total of 12 people, all these missions had to abandon numerous instruments and bulky equipment.

No one has photographed this equipment, which is located in very specific locations, from the ground, and the question that many ask themselves is how is it that today, with the new telescopes and the advancement of technology, we have not focused on those traces, those teams, those tours and to resolve once and for all the controversy of some people about whether man really did reach the moon (I'm not one of them)

We can solve this by resorting to mathematics, a current planetary equipment, like the one we can buy in specialized stores, has a specific resolution and can be calculated with the Dawes formula, if we divide 116 by the aperture of the telescope we obtain the limit resolution of the equipment in arc seconds, in the case of a good home telescope we divide 116/150mm = 0.773 arc seconds of resolution.

We know that on the moon 1 arc second is equivalent to 1.86 kilometers on its surface, I have it very simple, it is a relationship, I simply have to make a rule of three (1.86 km/arcSx0.773arcS=1.43 km) , according to these calculations the smallest details that a telescope would allow me to see and photographs on the lunar surface would be about 1.5 to 2.0 kilometers in size, but it would be like absolutely perfect collimation or conditions and a completely stable atmosphere. that are impossible to reproduce.

Therefore, we could say that the maximum resolution that a lunar observation and photography team can allow me in practice would be in details of around two or three kilometers approximately and it already seems outrageous considering that we are photographing an object which is the average distance of 384,000 kilometers.

But now we go further, there are much larger telescopes like the only one in my country called Llano del Hato which is at 3600 meters above sea level and I had the opportunity to visit several times, the Dawes formula is as follows: 116/650mm = 0.178 arc seconds of resolution, we make the corresponding calculations (1.86 km/arcSx0.178 arcS=0.331 km), we see that with this telescope we can see details in the environment of 400 meters but once again this would be in conditions Impossible to reproduce this telescope in practice, it would give us a resolution in lunar details in the environment of 400 or 500 meters, it is still a lower resolution than what we need to get to see the objects of the lunar missions and even more a trace .

But the Llano del Hato telescope is quite old and it is still a small telescope, so we are going big, we are going with the largest telescope in the world (El Gran Telescopio CANARIAS), with its 10.4 meter aperture and its focal length of 169 meters, yes we can see more, then 116/10400mm = 0.0111 arc seconds of resolution, and this means that with it we could get to see details on the lunar surface in the environment of 20 meters (1.86 km/arcSx0.011 arcS=0.021 km), but in practice and with an atmosphere above it, we would stay around 50 or 100 meters.

It is still insufficient to be able to see the remains of the lunar missions and even more so a footprint, and we have done all this for telescopes that are inside our planet, so the atmosphere does not allow us to reach the maximum resolution that it could give its optics, but outside the planet we also have a telescope like Hubble.

The calculations for the Hubbe are 116/2400mm = 0.0482 arc seconds of resolution, according to the calculations the Hubbe is from outside the earth and as a primary mirror of 24 meters we can get to resolve details on the lunar surface in the environment of the 90 meters (1.86 km/arcSx0.0482 arcS = 0.0899 km) and in this case it is an exact resolution because Hubble does not have an atmosphere above it to get in the way.

If we take into account that the largest object that all the lunar missions left on the lunar surface is the lander that measures around 10 meters, it is still not enough to be able to photograph an object of this size on the lunar surface. we would need to use a 25 meter aperture telescope in Space (0.010 km/1.86 km/arcS = 0.054 arcS) and (116 / 0.054 arcS = 2148 mm) we are talking about maximum resolution, and this means that this object would be shown in images like a dot, a pixel we could not see any type of detail and distinction that truly tells us I know that what we are seeing is the landing module.

So it is impossible to photograph any object that has landed on the Moon, but I thank all those people who worked and gave their lives for many years so that the missions and the conquest of space are carried out. And to you readers who came this far.

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