Aztec Astronomy and Observation of Nature
The sun's rays shining between the shrines of Tlaloc and Hutzilopochtli atop the Templo Mayor into the Temple of Quetzalcoatl, occured at sunrise on March 21, the equinox. It is said that the Templo Mayor was reconstructed, at Moctezuma's behest, as the alignment was slightly twisted. It can be seen from the temple ruins that it is skewed so that it is pointed nearly 7 degrees south of true east to match the sun's path. 
The Aztecs were observers of nature in all its cycles: the stars, the passing of the seasons , and the birth and death of plant and animal life. These observations informed many aspects of life-from the creation of the calendars, to the integration of time cycles with the stories of the gods and creation, to structuring of rituals in their proper time and place. (More unpredictable astronomical events were linked to omens and portents. For example, the comet seen by Moctezuma prior to the Spaniards' arrival was seen as a forewarning of an impending crisis.)
The Aztec Calendars
There were two calendar systems used by the Aztecs. The first was the solar year, or the 365 day cycle, which was divided up into 18 months of 20 days each, with 5 leftover days (called "nemontemi" which were deemed to be bad luck. The second calendar was a 260 day cycle made up of 20 day signs (named mostly after aspects of nature), and 13 numbers. These two cycles can be represented schematically as two intermeshing "gears". 
The smaller gear represents the 13 numbers, and the one on the right the 20 day signs.
And on a larger scale, the two calendrical systems can be visualized in a similar schematic-after the "gears" of the 260 and 365 day cycles have gone completely around, 52 years-the equivalent of our century-will have passed.
Astronomically, this 52 year cycle was begun when the "Pleiades crossed the fifth cardinal point or the zenith of heaven at midnight".  The ritual that marked this new cycle was called the "New Fire Ceremony", which was probably a once in a lifetime event for most Aztec people. On this evening, priests and a warrior chosen by the king began their 20 kilometer procession to the Hill of the Star. At the proper moment of alignment in the heavens, wood bundles representing the past 52 year cycle were lit, the heart sacrifice of the warrior was enacted, and the "new fire" built on his chest. Watching from afar, the citizens also cut and bled themselves and celebrated as the fire was brought back to the Great Temple at Tenochtitlan. Priests and emissaries from outlying towns came to Tenochtitlan to fetch the fire to bring back to their people, so that all could share in the marking of the time as well as symbolically renewing ties with the capital. [4 ]
On a larger scale still is the illustration of the universal time scale, as embodied in one of the most famous of Aztec relics, the Calendar Stone (or Sunstone). This huge object (4 feet thick, 12 feet in diameter, and weighing over 24 tons) was found in Mexico City's main square, or Zocalo, in 1790. Scholars believe that the stone was meant to portray the five ages or cycles of creation. At the time of the arrival of Cortes, the Aztecs were in the fifth and final age, which had started 535 years earlier. In the center of the stone is the face of the Sun God, Tonatiuh, Surrounding him are square areas representing the four previous ages which had been destroyed by hurricanes, jaguars, fires, and rains. Doomsday is marked by the pointing triangular area at the top of the stone.
Here is a very simple schematic of the Calendar Stone. In the center of the stone is the face of the Sun God, Tonatiuh, Surrounding him are square areas representing the four previous ages which had been destroyed by hurricanes, jaguars, fires, and rains. Doomsday is marked by the pointing triangular area at the top of the stone. The light colored circular area surrounding the central carving contains the 20 day signs.
These brief examples show a glimpse into the importance of the observation of nature, of the sun and the stars. For the Aztecs this provided a framework for marking temporal events in calendars, and also served to help order the time and place of the rituals that were so important to their society.