Ancient people could understand the world around them much better than the flat earth that was the centre if the universe, as we suggest for them. If we take a look at Greek mythology we can see a lot of knowledge hidden behind some myths. Some movements of known stars are saved on this form. As example we can see the myth of Kronos that eat his children until Zeus comes and changes the situation
Mars (the God of war) had two followers: Fovos and Deimos, they have been found recently as two small satellites of planet Mars, invisible with simple telescopes! There is also a strange related report at "the Gulliver's travels" from Jonathan Swift. He reports also the amazing detail that one of the two satellites moves with the double speed of the other. Swift described that 150 years before the 'scientific' finding of these satellites.
A lot of indications forces us to conclude that at the religious ceremonies of the ancient times, known as Mysteries to Greece, there were given a lot of knowledge about astronomy and cosmogony. This knowledge was only for the few chosen people and was forbidden by the penalty of stop to talk about this knowledge on other people. This could be done only with symbolic level of myths that could be safe and useful for anyone.
Ipparhus reports that he was using geodesy methods able to determine every place on earth. If we check the accuracy on placing some ancient monuments in exact distances from others, this seems to be true. The result that this measuring method was giving is directly comparable to the methods that we use today! Only with the help of our artificial satellites we can get better results.
Many ancient Greeks knew the fact that the earth has a spherical shape. They not only knew the correct shape but hey had also calculated the periphery around the earth. Eratosthenes proved with experiment the statement of Aristotle about the spherical shape of earth with the next way: During the summer solstice at the Aswan and at Alexandria of Egypt, at the same time he measured the shadow of two sticks vertically placed on earth. At Aswan there was no shadow but at Alexandria the shadow has a length equal to the 1/5 of the stick. Knowing the two sides of the right angle triangle and the angle of 7 1/5 degrees, he calculated that is the 1/50 of the 3600. So, if we multiply the distance Aswan - Alexandria 50 times we get the perimeter of earth. This gives us 25.000 miles. Now we are able to find that this measure is off by 50 miles!
The sun central planetary system seems that was part of the ancient religious Mysteries of Elefsis and other places. When Aristarhos the student of Pythagoras taught that, Kleanthis said that the Greeks had to call him to apologize and convict him for blasphemy against the Gods. Some people believe that this was also the real reason that sent Socrates to stop . The report of forbidden knowledge to not 'chosen' insider people.
Map making was something very important for the ancient Greeks. But as a prime meridian they were not using the one passing Greenwich (and why should they?) but the one that passes from Giza and the big pyramid of Egypt. And why this, you can ask. It is the meridian that passes through the bigger part of earth if you have not observed it yet. It is also the only meridian that divides equally the sea and the earth!
Herodotus reports the side height of the great pyramid was a stadium, the 1/600 of a degree of geographical latitude. Agatharhidis from Knidos wrote at the 2nd century B.C. that the length of one side of the great pyramid was the 1/8 of one degree of geographical latitude. Both of them seem to know the dimension of earth.
Pythagoras concluded that earth has a spherical shape, observing the shape of the shadow that earth drops on the moon.
On many ancient monuments we can observe that they are on straight line with some stars or to the equinoxes. This means that some people could measure and build much better than we learned to believe for these time periods. We have a lot of such temples or monuments from south America, Egyptian pyramids, French megalithic tombs, Stonehenge, other north American observatory remains etc.
Stonehenge by itself could have material for an entire site. Built on latitude of 51o17' is located to the best place for observations of sun and moon.
Great pyramid of Egypt also has many strange hi den knowledge. The four sides are four triangles exactly equilateral. The total length of the sides divided by two times it's height gives the number pi=3,1416. It's height multiplied to 10 million gives the distance from earth to sun. Doubling the length of the sum of the 4 sides we get the length of 1 degree at the equator as 1842,92 meters (today our moderns calculations gives us 1842,78). The weight of the pyramid (600.000 tons) multiplied to one billion gives the weight of earth.
Another strange source of unexpected knowledge can be found at the people of the central African known as Dogon. They have a lot of symbolic knowledge about the star Sirius and it's movement. Many of them confirmed just recently from modern scientists! These people sustain that they came from Serius. It seems strange but this star can be found in the traditions of many peoples as Greeks Egyptians etc. In every people it has a different tradition but it seems to represent something important for all.
At the famous Nazka value of Peru except of the known shapes of animals, birds etc. there are also a lot of straight lines indicating astronomical directions. Maybe this is the most ancient book of astronomy. These shapes can't be seen from the ground level but they are made following much smaller designs. What was the purpose for these lines and shapes nobody knows yet?
Mayas knew the existence of the most distant planets in our solar system, Uranus and Neptune many centuries before our civilization finds them again at 1781 and 1846.