Astronomy is often used to generally mark the passage of time and has been, in the past, used to time the planting and harvesting of crops. You can accurately predict many astronomical events, which are periodic in nature, using Wolfram|Alpha. From the rising and setting of the Sun to the arrival of autumn and spring to when the next full moon will happen, the number and type of astronomical events ranges far and wide.
Determine eclipse events, which occur when the Sun or Moon is blocked, typically from the point of view of an Earth observer.
Calculate the time of sunrise and sunset, which varies throughout the year, from one location to the next.
Plan the observation of meteor showers, which are annual events that have various activity rates.
Predict the longest and shortest days of the year, which happen during the summer and winter solstices, and observe that on the spring and autumnal equinoxes, the Sun rises and sets due east and west, respectively.
Witness the growing and shrinking phases of the Moon throughout the month as the amount of illumination from the Sun, as observed from Earth, changes.