Why is the Earth-Moon distance not the same at each perigee/apogee? I wonder why the Earth-Moon distance is not the same at each perigee/apogee. Isn't the Moon's orbit a fixed ellipse with Earth at one of the foci? If it is so, shouldn't the distance at perigee/apogee be a fixed value?
Isn't the Moon's orbit a fixed ellipse with Earth at one of the foci?


No, it's not. This isn't even true for the planets' orbits about the Sun. Each planet perturbs the orbits of the other planets, making Kepler's ellipses approximately correct rather than exact. The Moon's orbit is strongly perturbed by the Sun in a number of ways. The Moon's orbit deviates from being a fixed ellipse in a number of ways. One result of these solar perturbations (and to a much lesser extent, perturbations from Venus and Jupiter, and to an even lesser extent, from the other planets) is that the Moon's orbit precesses in a number of ways.

One such precession is the apsidal precession. The line from the Earth to the point at which the Moon reaches perigee does not point to a fixed position in space. It instead precesses with a period of about 8.85 years. This is what results in the so-called supermoons, which occur when the Moon's orbit is close to perigee when the Moon is full.

Another such precession is the nodal precession. The line of nodes (where the Moon crosses from above to below the ecliptic, and vice versa), also precesses, but with a period of about 18.6 years. We only get eclipses when the Moon is very close to a node at a syzygy (either a full Moon, resulting in a lunar eclipse, or a new Moon, resulting in a solar eclipse).