Why is the moons orbit slightly irregular?
It’s not so much “irregular” as just “complicated”. The moon’s orbit is affected by the sun’s gravity as well as the earth’s. The earth’s orbit round the sun is elliptical not circular. So is the moon’s orbit round the earth. The moon’s orbit is tilted at an angle to the plane of the earth-sun orbit. So the effect of the sun on the moon’s orbit changes during each earth year. The orbital period if the moon isn’t an exact multiple of a year, so the perturbations caused by the sun are slightly different each year. Actually the earth-moon-sun positions repeat almost exactly every 19 years. This is called the Metonic cycle, named after the Greek astronomer (Meton) who discovered it about 2500 years ago. As well as the sun’s gravity there are other effects, like the fact that the earth and the moon are not perfect spheres, the ocean tides on earth are slowly converting the kinetic energy of the moon’s orbit into heat, etc.
