According to what pattern do sunrises, sunsets, moonrises and moonsets change?

The movements of bodies in the central gravitational field are described by Kepler's laws, of which only law 3 has the form of a formula. Isaac Newton used Kepler's laws to formulate (his) law of gravity. For the calculation, we can use Newton's law of gravity, thanks to which we can find out important information — the distance between the Earth and the Moon and the distance between the Earth and the Sun.

Or we will simplify the situation and consider the movements of the Earth-Sun and the Moon-Earth as movements along a circle (which is not far from the truth) and then we only solve a simple arithmetical problem with the position of a point on a circle, when we know how long it takes the given object to make one revolution.

If we want the result to be more accurate, we have to also take into account the tilt of the Earth's axis relative to the Sun (which is roughly 23°). Thanks to the tilt of the Earth's axis, the seasons change on the Earth.