As you already know by this point (we hope), the book takes planets and zodiac signs pretty seriously and uses them to symbolize and draw attention to certain aspects of the characters and their actions/relationships. For example, when a chapter is titled "Mercury in Sagittarius," you know that the important action is going to involve Walter Moody and Tom Balfour.
Similarly, having Anna and Emery associated with the sun and the moon draws attention to their close interdependent relationship, which Lydia Wells makes explicit later when, after meeting Emery, she realizes that Anna "may have an astral soul-mate" (IV.9.41). They do turn out to be incredibly bonded (and smitten with each other), and the novel's little graphs and chapter titles suggesting Emery and Anna's association with the "luminaries" drives home their connection early and often—and long before we actually ever get a scene with them in a room together, actually.
The zodiac and planetary motif also highlights the novel's overall emphasis on the idea that even minor changes in the positions/relationships of the characters can make the future a whole new ballgame—kind of like how the movement of heavenly bodies across the sky and their positions create the potential for new things as the year goes on, if you're astrology minded.
Suggesting that a lot has changed for the characters in the month that elapses between Part I and Part I, Catton likens the shifting gears of life in Hokitika to the machinery of the heavens:
For the planets have changed places against the wheeling canvas of the stars. The Sun has advanced one-twelfth along the tilted wheel of her ecliptic path, and with that motion comes a new world order, a new perspective on the whole. With the Sun in Capricorn we were reserved, exacting, and lofty in our distance. When we looked upon Man, we sought to fix him: we mourned his failures and measured his gifts. We could not imagine what he might have been, had he been tempted to betray his very nature—or had he betrayed himself without temptation, better still. But there is no truth except truth in relation, and heavenly relation is composed of wheels in motion, tilting axes, turning dials; it is a clockwork orchestration that alters every minute, never repeating, never still. (II.1.2)
Put differently, the "truth" of a situation is never a totally absolute thing—it depends on who and where you are when you're looking at what's happening. Catton's novel insists that you not get too hung up on "What really happened" and think more about how the characters are relating to each other in a particular situation and what "truth" they know and are acting on. For example, Anna firmly believes that Emery Staines is talking to her telepathically at one point—which no one else seems to believe, but that belief definitely influences her actions.
So, the point is that, when it comes to sussing out what's really important in the book, to paraphrase James Carville, "It's the relationships, stupid."