Question

What are examples of astronomical cycles

Answer 1

One example would be that of an Eclipse. It is an astronomical event that occurs when an astronomical object is temporarily obscured, either by passing into the shadow of another body or by having another body pass between it and the viewer. ( Like when the moon's shadow crosses the earth's surface you get a solar eclipse.)
Another example would be a year. A year is the orbital period of the Earth moving in its orbit around the Sun.