The original use of syzygys was in predicting ecllipses. An eclipse can only happen at a syzygy of the Sun, Moon, and Earth, so predicting eclipses boils down to predicting syzygys plus the side conditions that specialize some syszygys into eclipse confinguration. Briefly the orbits of the Erth and Moon about the Sun are tilted with respect to each other, but syzygy only concerns movement in what astronomers call longitude, and the reason every new moon is not an eclipse of the Sun is that when the three orbs are aligned in two dimensions, they can miss alignment in the third.
Another important fact about syszygys is that when you have one, you can conclude from Earthly observations valid facts about the kinematics of the other two bodies relative to each other. Thus Ptolemy and Copernicus using three oppositions of Mars (syzygys of Earth, Mars, and the Sun) and a geometric assumption ("bisection of the equant") could compute the position of the equant or point of equal angular velocity for Mars, within their hypothesis that the planets, even if they don't move with constant angular velocity relative to th center of their orbits (which is contradicted by observation) do so with respect to SOME point, the desired equant.
Then Kepler was led to throw out the equant when he saw that with FOUR oppositions he could find the equant without assuming the bisection hypothesis. But when he did this with two different sets of four oppositions (giving thanks to Tycho Brahe for all those wonderfully accurate observations) he found the position of the equant depended on which oppositions (syzygys) you used to compute it. So it wasn't a real thing, and Kepler went looking for an alternative to constant angular velocity and found his area rule (Kepler's Second Law).
"Ancient astronomers" had no concept of the galaxy as a collection of stars. Even Aristarchus, who conceived the motion of the Earth around the Sun, thought of the stars as little lights on a fixed sphere, and the galaxy (Latin via galactica; Milky Way) was just a spill of brightness across the sky which the naked eye was unable to resolve into stars. When somebody today tells you the ancient people had knowledge which there is no way they could have learned, you can be confident they're feeding you bunk.
