Did the man ever go to the Moon? It depends on what we call "the Moon"
If we accept the Moon as this piece of rock that is 384,000 km distant from Earth, then it's perfectly possible to go there on a spaceship, the point is that there will be nothing interesting there.
Apart from the concept of multiple universes, the Vedas describe our universe as a multidimensional space, and this is a detail that makes the descriptions quite hard to understand at times since it frequently describes higher levels of reality we don't have access to. Different beings with different types of bodies and different sets of senses experience the universe in ways different from the way we do. THe way we perceive reality is quite different from a demigod, just as the concept of reality of an ant is very different from us, even tough humans and ants share the same three-dimensional reality. We can easily study and understand ants, but ants can't understand us. The difference between the perception of human beings and demigods is even more dramatic, since we live is separate dimensions.
One simple way to understand the concepts of dimensions is to imagine that our tridimensional reality can be represented on a two-dimensional piece of paper in the form of a map. In a map, a building can be represented in the form of a square, and a bridge in the form of a line that goes over another line that represents a road. The building is not a square, nor a cube, but when we represent it in a two-dimensional map it is represented like that. Similarly, a bridge is a tridimensional structure: there is something under the bridge and there is something over it, but when we put it into a map it looks just like a flat line. Similarly, when the gigantic structure of Bhu-mandala described in the Vedas is represented in our plane, it appears as our earthly globe, while the celestial moon, which is described as bigger than the sun and the abode of an extraordinarily opulent civilization is represented as the rocky moon we have access to. Because most of the beings of the universe live in higher dimensions, to which we don't have access, the universe appears to be uninhabited to us.
The Vedas describe that our universe is divided into 14 planetary systems. Each planetary system is composed of innumerable planets, stars, and other structures. We live somewhere in Bhu-Mandala, the 8th planetary system, but because we live in Kali-yuga, the last of the sequence of four eras when human beings degrade into a base level of consciousness, we have access to only part of it, in the form of the gross dimension we live in. The Vedas explain that in the past human beings had access to other parts of Bhu-Mandala and some could even visit the higher planetary systems of Bhuvarloka, Svargaloka, Maharloka, and even Brahmaloka, which is currently impossible for us.
The Puranas call the Milky Way, the giant path of stars we see when we look to the sky Śiśumāra, which includes the planetary system of Svargaloka and extends all the way close to Dhruvaloka, the Polestar. It's described that Yogis can follow this path after abandoning their mortal bodies to attain the higher planetary systems. Above Dhruvaloka there are the planetary systems of Maharloka, Janaloka, Tapoloka, and Satyaloka, each one exponentially more distant than the previous. After these higher planetary systems, there are the coverings of the universe, which also include different structures composed of elemental matter. The first cover is ten times larger than the universe itself, and each of the other six coverings is ten times larger than the previous. The universe described in the Puranas is thus practically unlimited, and that's just one amongst trillions of universes that form the cosmic manifestation.
Nowadays there is great interest in space exploration, but according to the Vedas, this is not a very effective way to travel. A small crew may be able to make a dangerous and uncomfortable trip to the moon or Mars at an exorbitant cost, but it will be ultimately unfruitful. Without access to higher dimensions, they will just find sand and rocks anywhere they go. Worse still is that these excursions will be restricted to the vicinity of our planet since any trip outside of the confinements of our solar system would take much longer than a human life. Even if it would be somehow attempted, it would be useless from our point of view, because we would not be there to see the results.
Instead, the Vedas explain that the process of having access to the other planetary systems is by purifying our consciousness and transferring ourselves to an appropriate body at the planetary system of our choice at the time of death. In this way, not only does it become possible to reach higher planetary systems beyond the confinements of our galaxy, but allows us to receive an appropriate body in which we can comfortably live and interact with the inhabitants there.
Without this, but even if one is able to visit other planets through some mechanical arrangement, he will find only rocks, dust, poisonous gasses, and extremes of temperature, without the possibility of interacting with the local inhabitants, who will be living in a different dimension.
For example, according to our tridimensional view of reality, measured by experimental methods, the moon is situated at about 384,000 km from earth, and one can reach it in about three days in a space probe. Unfortunately, if one goes there he will find only dust and rocks. The Puranas, however, state that the moon is in reality a celestial planet, with a standard of living much superior to our planet. There, people live for 10,000 celestial years, drinking soma-rasa in the company of celestial ladies. The question is that to access it one has to develop a very subtle consciousness, similar to the superior beings who live there. Then, reaching the moon through the rays of the sun after leaving his gross body, one can take birth there, assuming an appropriate body to enjoy the subtle reality there. Without this change in consciousness, one may visit this piece of rock orbiting our planet that we call the Moon, but he will see only rocks. The celestial moon where Indra lives will however remain inaccessible.
The Vedas offer two separate descriptions of our planet. One description is very similar to what is offered by modern astronomy, the Earth is a spherical planet, with a circumference of about 25,000 miles, seven continents, and so on. This description describes the distance to the moon, the orbits of the sun, the planets, and so on.
The distances mentioned in the Vedas are calculated according to a unit called yojana. There is some discussion about the correct length of the yojana, and it appears that different books use different lengths for the yojana. It is largely accepted that the Srimad Bhagavatam uses a yojana of 8 miles, while experimental evidence suggests that the Surya Siddhanta uses a yojana of 5 miles.
The Surya Siddhanta gives the circumference of the Earth as 4,967 yojanas. If we accept the probable measurement of 5 miles per yojana, we get 24,835 miles, which is remarkably close to the 24,901 miles given by modern studies. Similarly, the Surya Siddhanta gives values for the distances of the planets of the solar system that are similar to what is found in modern studies. Therefore, the model studied in modern cosmology was very well known to the sages who wrote the Vedas. Even without any modern equipment, they had access to precise data connected to it.
However, there is another model, completely different that is described in the Puranas. In this model, the Earth is part of a gigantic planetary system called Bhu-Mandala, that extends for two billion miles, including dozens of planets and other structures, which are all interconnected. Inhabitants of each planet (called a dwipa) can thus freely move from one to the other through cosmic passages. In both the Puranas and the Mahabharata there are descriptions of both human beings visiting other planets, as well as inhabitants of other planets vising our world.
How can these two views of the universe be reconciled? This can be explained with a simple example. Suppose you want to visit an office on the 82nd floor of a building in Manhattan. You may take a taxi and go to the front of the building. This would bring you close to the office in the horizontal dimension. However, to finally reach it you would need to also travel in the vertical dimension, taking a lift or the stairs, going up until you reach the right floor. If somehow your credentials would not allow you to enter the building, you would be stuck in the street, which would not be as luxurious as the inside. Similarly, when a human being tries to go to the moon without the proper consciousness he will not be able to travel in the subtle vertical dimension and will thus be stuck in the gross dimension, where there is only dust and rocks. Our universe is composed of different dimensions and we can synchronize in each one according to the particular set of senses we have, which is in turn determined by our level of consciousness.
Concluding, many discuss if man really went to the moon or not. It actually depends on what one calls "the Moon". If we accept the Moon as this piece of rock that is 384,000 km distant from Earth, then it's perfectly possible to go there on a spaceship, the point is that there will be nothing interesting to observe there. However, if we accept the Moon as the celestial planet where Indra lives, then it's possible to attain it only by mystical means.
The Puranas state that the celestial moon is actually very far from Earth in the subtle vertical dimension, even further away than the sun. To reach there, one has to radically change his level of consciousness. A space probe will not help. The process to access the celestial moon involves not only changing one’s consciousness and thus traveling in the subtle vertical dimension but also acquiring a particular set of senses and a suitable body to live there. In the past, this was an art understood by yogis, who were able to travel through the Universe by elevating their consciousness and thus transferring themselves to the desired planet. Nowadays we try to do the same using probes and space suits, but the results are not the same.