How did early astronomers use observations of the Sun and Moon to create calendars?

Early astronomers developed calendars by observing the predictable cycles of the Sun and Moon to track the passage of time, though they faced challenges due to the incommensurability of these cycles.1

Lunar Observations

The month was primarily determined by the Moon’s cycle of phases, known as the synodic month, which lasts approximately 29.53 days. Early societies, such as the Sumerians, tracked these phases to establish months, often alternating between 29 and 30 days. Because 12 lunar months are shorter than a solar year, civilizations eventually used intercalation—the periodic addition of days or months—to keep their calendars aligned with the seasons.12

Solar Observations

To track the year and seasons, astronomers observed the Sun’s apparent motion. Because the Sun obscures the stars, they used indirect methods:
* Heliacal Risings: In tropical regions, astronomers observed stars rising just before sunrise to determine the Sun's position among the constellations.1
* Horizon Markers: In temperate regions, cultures built structures like Stonehenge to align with the Sun’s extreme northern and southern positions, known as solstices.13

These observations allowed ancient peoples to calculate the tropical year and regulate agricultural activities.1