I'm bored, so here's a thread. Does there have to be a war with Earth?
Anyways, first, some assumptions and founding thoughts:
Manpower/Population: Vasudan homeworld has been eliminated with massive loss of life, and the remaining settled areas of the GTVA are essentially the colonial remnants of the PVN and GTA. Capella, a "densely populated" system, has a population of 250 million. Sol's population might equal or even exceed that of the GTVA.
Industrial capacity: It's taken for granted that the Earth has been stripped of industrially-useful resources (not an unfair assumption, look at the poor thing now). The remainder of the system, however, is likely highly developed and extremely productive. Gas giants to mine, planets to colonize and build-up, and hundreds of moons to exploit.
Technological development: It all started when the better half of the Lucifer floated sheepishly in front of the Earth ("damn, almost"). There's the potential for Earth to have had developed beam weaponry/etc parallel to the GTVA. Even if not enough useful bits of the Lucifer made it to Sol, development of beam technology is still highly probable. Earth was the industrial core of the GTA...the Avenger prototype traveled to Earth from Antares, and the shield prototypes from distant Beta Cygni! If work was started on beam weapons prior to the destruction of the Lucifer, then it is probable that important materials were already at Sol.
First conclusion is obvious and has been explored by every campaign featuring a return to Sol: Earth is very powerful, and would make a credible opponent in battle with the GTVA; but, perhaps it is more likely that reunion results in a subtle subversion of the GTVA political system over time, with the terran blocs (I've always assumed that the GTVA "General Assembly" was representatives from each bloc) aligning to Earth.