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If the phases of the moon and the moon's perigee are just dependent on the point that the moon is in through it's orbit, why can perigee happen at different phases of the moon?

My thinking is this:

  • The phases of the moon take one lunar orbit to complete
  • A lunar perigee will occur at the same point throughout the lunar orbit (the point where it is closest to earth)
  • Therefore, a lunar perigee will always coincide with the same phase of the moon.

However, I know that this conclusion is not true, so I am not understanding something properly.

Thanks

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The orbit of the Moon is not exactly simple. First, it’s an ellipse, as you probably know already. The Earth is at one focus of the ellipse; this is why sometimes the Moon is closer, sometimes it’s farther.

This ellipse is tilted with respect to the ecliptic, not the Earth’s equator (it’s one of the few planetary satellites in that situation), by about 5.15° (it’s slightly variable). If you imagine the lunar orbit ellipse and the ecliptic as two planes, then a line is formed by their junction. It’s called the nodal line, as it joins the nodes of the Moon’s orbit: the ascending node when the Moon goes from south of the ecliptic to north of it; the descending node when it goes from north to south.

Now, imagine another line, joining the apses of the Moon’s orbit—the apogee and the perigee. This is the apsidal node.

Let’s make that move, now.

First, the Moon travels on its orbit in about 27.322 days with respect to the stars—in other words, that’s the time it takes to align with the same star again. Because the Earth travels around the Sun during that time, it takes a little more than 2 more days (total ≈ 29.530 days) to align again with the Sun, hence returning from, e.g., a new moon to another new moon.

Now, the fun begins…

The nodal line rotates around the Earth in the opposite direction of the Moon, in about 18.6 years (this rate is variable). This means the nodes are not always in line with the Sun from one revolution of the Moon to the next.

The apsidal line also rotates around the Earth, in the same direction as the Moon, in about 8.85 Earth years. This means the apses (apogee and perigee) don’t necessarily align with the Sun at each of the Moon’s revolution around the Earth.

Finally, the size of the Moon’s orbit varies with time as well, so one perigee can be closer than another one—hence the “supermoon” phenomenon that happens only a few times a year at most.

All this combines to make the Moon sometimes closer, sometimes further; sometimes more to the north, sometimes more to the south; and sometimes going north to south, sometimes going south to north, at any particular point of the celestial equator (the projection of the Earth’s equator on the celestial sphere).

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  • $\begingroup$ .. and even if the mechanic were much simpler (no rotation of nodal/apsidal lines) and perigee happened at full moon now, it would happen at new moon in half a year $\endgroup$ Oct 3, 2022 at 13:08
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    $\begingroup$ This answer deserves some qualifiers. The moon's orbit is only roughly elliptical, its accurate description has been started from either of two quite different approximations. One, a Keplerian ellipse with eccentricity ~0.0549, dominates the eccentric character of the motion, the other, the 'variational orbit', dominates the amount of orbital flattening and is nearly elliptical but the earth is near the center. The mean orbital size hardly varies. For more, see astronomy.stackexchange.com/questions/24677/… $\endgroup$
    – terry-s
    Oct 3, 2022 at 21:56
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While the Moon orbits the Earth, the Earth orbits the Sun. So, by the time the Moon completes one orbit around the Earth, the Earth will have completed about 1/13th of its orbit around the Sun. This means the Earth-Moon-Sun angle will be different from one apogee to another, so the phase will be different.

Put another way, the orbit of the Moon around the Earth does not change relative to the distant stars as the Earth orbits the Sun. For example, if a line drawn from the center of the Earth through the center of the Moon at apogee, out to infinity, would point to Orion, that line will always point to Orion for every orbit of the moon, regardless of the Earth's position in its orbit around the Sun.

Additionally, the Moon's orbit undergoes apsidal precession, which means that apogee and perigee don't really always line up as in the previous paragraph. Instead, the nodes precess slightly over the course of about 9 years.

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  • $\begingroup$ Actually, no: The Moon’s orbit does change with respect to the stars; see my answer and en.wikipedia.org/wiki/Orbit_of_the_Moon. Besides, your third paragraph contradicts the second one… $\endgroup$ Oct 3, 2022 at 5:02
  • $\begingroup$ @PierrePaquette, yes, the second paragraph is a deliberate simplification, and the third paragraph completes the explanation. $\endgroup$ Oct 3, 2022 at 5:05

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