I'm sorry if this is not the place to discuss this, but I wasn't really sure where else to go (I was doing some Google searching on orbital mechanics and this forum popped up). I've written a certain amount of fanfiction (yeah, yeah, I know), most of which takes place in the Gundam franchise, and as such involves space combat. As I'm a science major, I like to try and apply as much real science to the stories as I can, but as I'm a biology major, I'm not so great when it comes to certain aspects of physics. I've been able to fill in a lot of the gaps courtesy of Nyrath's Atomic Rockets website and other online sources, but I've hit one or two questions that I just can't find an answer for, which brings me here. In one of my stories, a hostile military fleet departs their base on the Moon and heads for the space colonies at Lagrange point 5. I want to know how long it would take them to get there. Given that the Lagrange points are on the Moon's orbital path around the Earth, I'd thought the fleet could simply accelerate and then fly along the Mon's orbit until they reached L5, but it turns out that if they did that it would boost them into a higher orbit. I looked up how a co-orbital rendezvous works and learned about how it's done by NASA (dropping into a phasing orbit and exiting it when your target loops back around and catches up to you). The problem is that using that method would take over three weeks (about 23 days). It occurred to me, however, that the phasing orbit method may just be the rendezvous method that uses the least DeltaV, and that there might be other ways that are faster but have a higher DeltaV cost (sort of like how a brachistochrone orbit is faster than a Hohmann transfer orbit, but uses much more DeltaV). Does anyone know of this hypothetical faster method? Again, I'm sorry if I've brought this to the wrong place; I know this is more for people who play the KSP game. I just figured it couldn't hurt to ask.
