Mecha Talk

Gundam is a franchise that chooses aesthetics over making sense.

Otherwise, you wouldn't have 'windows' on a bridge, and all ships would essentially be more like giant rockets.

Only the most hand-wavy justifications can be made.

How is that supposed to work? Shooting down colonies when there's a planet and its moon in between you and the target...?

One could use a guided weapon, of course, but that's one of the basic reasons why the story is rigged so guided weapons don't generally work in Gundam. (and it's fair to assume Zeon would have ample opportunity to spot and confront the dangerous missile as it makes its days-long journey to the far side of the Earth-Moon system)

You could also fire an unguided shot and rely on orbital mechanics to hit your target: but you're talking about hitting a target with a 256km^2 cross-section from, effectively, over 12 million km away. (It could be farther than that - I don't know exactly what kind of orbit would be needed to get from L3 to L2.) If your shot is 4km too high or low (that is, your shot winds up not coming within 4km of the colony's center axis), you've missed the target entirely. These targets are also by no means "stationary" - the whole Earth-Moon system is orbiting, of course but additionally colonies aren't at Lagrange points, but rather orbit them.

Additionally, the first three Lagrange points are "unstable": meaning that if you're close to one, but not on it, gravity will not help you to converge on that point. If your shot at L2 (Side 3) strays too close to the Moon, the Moon (and Earth) will pull the shot closer, away from L2. If your shot goes too far from the Moon, the gravity of Earth and Moon won't correct the shot and pull it into L2. That, combined with the extreme distance of the shot (and the fact that, most likely, Zeon isn't going to be to accommodating of any recon units you put out there to adjust your shots, or comm relays to get intel back to Luna 2) makes it extremely unlikely that an unguided shot would reach the intended target.

They could launch a massive barrage from Luna 2 - and simply hope they hit something - but the amount of energy needed to launch projectiles on a path to the far side of the Earth-Moon system is not insignificant.

Would you say that energy is more or less than the energy required to launch dozens (even hundreds) of 300-meter long starships out of Earth's gravity well? And then send them to Lunar orbit?

You've already explained how it is possible to do what I suggested. Sure, only the L4 and L5 points are "stable" and even there the colonies are in halo orbits. I'm not saying they hit a colony on the first try, or even with every shot. The Federation would only need to get lucky a few times, but Zeon would need to be lucky every time. And think of how energy-draining the potential evasive maneuvers would be for the Zeons, to say nothing of the potential for causing political turmoil within Side 3.

The simplest reason for the Federation not taking pot shots at Side 3 has already been put forward: There's no dramatic tension in truly effective tactics that keep our plucky magical teenagers from saving the day.

Secondly, it's just too barbaric a thing for the OYW-era Federation to do. The Titans wouldn't have hesitated to do it, though, and it's a wonder the Federation didn't resort to such slimy tactics out of desperation after Zeon's gas-happy, nuke-slinging massacres. Maybe the old guard of the Federation wanted to win the war the "right" way.

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Well, there were a small handful of officers that would probably do so (like Ryer), but compared to the whole of the Federation at the time under Revil, they'd pretty much be signing their own death warrants for further war crimes and such.

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"I'll show you that a superior mobile suit has its limits when it goes up against a superior pilot!" - Char Aznable, The Red Comet