Why do the days get shorter and longer?

The very alternation of day and night is caused by the rotation of the Earth around its axis. But that's not the only movement the Earth makes, it also orbits the Sun. Orbiting around the Sun alone would not affect the length of the day, but the Earth's axis is tilted (about 23°) relative to the Sun. If this inclination was zero, the days and nights would still be the same — the Sun would always shine at the Earth at the same angle. However, because the Earth is tilted, part of the orbit (roughly half) of the northern hemisphere is tilted towards the Sun (therefore, the sun's rays fall on it longer) but the southern one is tilted away and the time when it is exposed to the sun's rays is shorter. It's good to realize that the tilted part of the Earth actually shadows the part that is not tilted, I think it's nicely explained in this video: https://www.youtube.com/…

Just as a matter of interest — the inclination of Uranus' axis of rotation is almost 90°, so its northern hemisphere is actually always in the shadow of the southern one — therefore it is always night in the north, while it is always day in the south. To be exact, I will add that the speed of the Earth's rotation around the Sun is not constant, therefore, in our hemisphere the days get longer faster in the winter than when they get shorter in the summer.