Astronomy
The Maya were quite accomplished astronomers. Their primary interest, in contrast to "western" astronomers, were Zenial Passages when the Sun crossed over the Maya latitudes. On an annual basis the sun travels to its summer solstice point, or the latitude of 23-1/3 degrees north.
Most of the Maya cities were located south of this latitude, meaning that they could observe the sun directly overhead during the time that the sun was passing over their latitude. This happened twice a year, evenly spaced around the day of solstice.
The Maya could easily determine these dates, because at local noon, they cast no shadow. Zenial passage observations are possible only in the Tropics and were quite unknown to the Spanish conquistadors who descended upon the Yucatan peninsula in the 16th century. The Maya had a god to represented this position of the Sun called the Diving God.
The Sun
The Maya evidently thought quite a bit about the Sun and they watched it trace out a path along the ecliptic. They followed it the whole year round, presumably following its path along the horizon as well.
At Chichen Itza, during sunset a sun serpent rises up the side of the stairway of the pyramid called El Castillo on the day of Spring and Autumn Equinox. It tells us that the Maya noted, not only the extremes of the Sun at the Solstices, but also the Equinoxes when the Sun appeared to rise due East or due West.
In addition to the Zenial Passages mentioned earlier, ecliptic observations must have been a major portion of Maya solar observing.
The Moon
The Maya had a lunar component to their calendric inscriptions. After giving the pertinent information on the date according to the Maya calendar the typical Maya inscriptions contain a lunar reckoning. The lunar count was counted as 29 or 30 days, alternating. The lunar synodic period is close to 29.5 days, so by alternating their count between these two numbers the moon was carefully meshed into the calendric sequence as well. Their lunar knowledge was impressive for they also made eclipse predictions, an almanac for predicting them is contained in the Dresden Codex.
Venus
Venus was the astronomical object of greatest interest. I think it possible that the Maya knew it better than any civilization outside Mesoamerica. They thought it was more important than the Sun. They watched it carefully as it moved through its stations--it takes 584 days for Venus and the Earth to line up in their previous position as compared to the Sun. It takes about 2922 days for the Earth, Venus, the Sun, and the stars to agree.
The pattern of Venus is usually reckoned at Inferior Conjunction, that time when Venus passes between the Sun and the Earth. A diagram of this situation can be seen on the left.
During this period, Venus cannot be seen from Earth. It disappears for a short period that averages 8 days. When it first rises after inferior conjunction, that is when it was first spotted in the morning sky, called heliacal rising because it is rising with the sun, was the most important position of Venus.
After rising, Venus will reach its greatest brilliancy then it greatest elongation west, moving quickly (in retrograde motion) away from the Sun.
After that it will remain visible for about 260 days in the morning sky until it reaches superior conjunction. At this point Venus is on the opposite side of the Sun as we view it from Earth. It becomes dim, until it dips back under the horizon, only to appear on the opposite side of the sun an average of 50 days later. It then rises as a evening star and remain in the night sky about 260 days until it goes through its eastern elongation point and greatest brilliancy before arriving at Inferior Conjunction again.
The Maya made daytime observations of Venus. Venus had a psychological effect upon the Maya and other Mesoamerican cultures, it has been shown that the Maya were timing some of their wars based on the stationary points of Venus and Jupiter. Humans were sacrificed on first appearance after Superior Conjunction when Venus was at its dimmest magnitude but they most feared the first Heliacal Rising after Inferior Conjunction.
In the Dresden Codex, the Maya had an almanac that displayed the full cycle of Venus. They counted five sets of 584 days, that is 2,920 days is approximately 8 years or 5 repetitions of the Venus cycle.
The Milky Way
The Milky Way itself was much venerated by the Maya. They called it the World Tree, which was represented by a tall and majestic flowering tree, the Ceiba. The Milky Way was also called the Wakah Chan. Wak means "Six" or "Erect". Chan or K'an means "Four", "Serpent" or "Sky". The World Tree was erect when Sagittarius was well over the horizon. At this time the Milky Way rose up from the horizon and climbed overhead into the North. The star clouds that form the Milky Way were seen as the tree of life where all life came from. Near Sagittarius, the center of our galaxy, where the World Tree meets the Ecliptic was given special attention by the Maya. A major element of the World Tree include the Kawak Monster, a giant head with a kin in its forehead. This monster was also a mountain or witz monster. A sacrificial bowl on its head contains a flint blade representing sacrifice, and the Kimi glyph that represents death. The Ecliptic is sometimes represented as a bar crossing the major axis of the world tree, making a form that is similar to the Christian Cross. On top of the World Tree we find a bird that has been called, the Principal Bird deity, or Itzam Ye. There is also evidence that shows the Sun on the World Tree as it appeared to the Maya at Winter Solstice.
During the months of winter, when the so-called "Winter" Milky Way dominates the sky, it was called the "White Boned Serpent." This part of the Milky Way passed overhead at night during the dry season. It is not brilliant like the star clouds that dominate the sky North of the equator during the months of Summer, but observers at dark locations will easily see the glow. Here the Ecliptic crosses the Milky Way again, near the constellation of Gemini which was the approximate location of the Sun during Summer Solstice. It is possible that the jaws of the White-Boned Serpent were represented by the Kawak monster head.
The Ecliptic
The Maya portrayed the Ecliptic in their artwork as a Double-Headed Serpent. The ecliptic is the path of the sun in the sky which is marked by the constellations of fixed stars. Here the moon and the planets can be found because they are bound, like the Earth, to the sun. The constellations on the ecliptic are also called the zodiac. We don't know exactly how many fixed constellations on the ecliptic were seen by the Maya, but we have some idea of the order in some parts of the sky. We know there is a scorpion, which we equate with our own constellation of Scorpius.
It has also been found that Gemini appeared to the Maya as a pig or peccary, (a nocturnal animal in the pig family.) Some other constellations on the ecliptic are identified as a jaguar, at least one serpent, a bat, a turtle, a xoc monster -that is, shark, or a sea monster. The Pleiades were seen as the tail of the rattlesnake and is called "Tz'ab."