Hi,
The Inca at Machu Picchu didn't "study" the Sun in the same way we do. The Sun to them was a God and their ruler, "The Inca", was the embodiment of the Sun on Earth and as such, was the head of their religion. The Inca led many religious ceremonies, among them, the Inti Raymi festival at the time of the winter solstice (June in the southern hemisphere). At Machu Picchu, is a building called Torreon (semicircular temple) in which a window is aligned with the rising of the Pleiades just before the Sun on or around June 21. The Pleiades were called Collca by the Inca, because to them that star pattern represented a storehouse (for food) in the sky. On the opposite side of the sky another Collca, marked by the tail of the Scorpion, would be setting on the June solstice; there was always a storehouse in the sky. In this way, the Inca people hoped they would never go hungry. But I digress. At the time of the winter solstice, the Inca would have observed the Pleiades rising, then the Sun, and would have worshipped the Sun all day with singing and merry-making. I have three images of the Torreon and the alignment on this website:
http://solarscience.msfc....suntime/slshow10.stm
Now you asked about the evidence that exists. How do we know what the Inca did in the Torreon? In the case of the Inca, who had no written language, we must rely heavily on the writings of the Spanish from the time of their arrival in Peru (about the mid-1500s). In addition, we use the current knowledge of the Inca descendants, and combine all this with the physical evidence of the structures that exist. The physical evidence is obtained by making careful measurements of the sites, as you can see in more detail if you access this work by Drs. David Dearborn and Raymond White, Sr., Title: The "Torreon" of Machu Picchu as an Observatory,
Authors: Dearborn, D. S. P. & White, R. E.
Journal: Journal for the History of Astronomy, Archaeoastronomy Supplement, Vol. 14, p.S37. You can find the article online here:
http://articles.adsabs.ha.../1983JHAS...14...37D