This appears to be the same issue as this:
http://forum.micdoodle8.com/index.php?threads/parachest-causing-server-crash.4058/
There, Moose identified the cause as being an incompatibility with OreSpawn. But, it doesn't look like you have OreSpawn in your modpack.
You do have a large modpack though, so I am wondering if this a more general issue like Minecraft "running out" of entities. Minecraft does have a hard limit of 256 entity IDs.
Normally I would advise, make a new world for testing, then take half your mods out of the /mods folder, see if the crash happens, if it still happens take out half of what is left (or if the crash didn't happen, put back in half of what you took out) - etc. - until you have identified which mod is incompatible. You should try that.
But I am also wondering if you will actually find that if you take
either half of the mods out of the /mods folder then things will start to work, because taking either half of the mods out will ease the problem of Minecraft running out of entities. If it is that, then you will have to cut down your modpack so that there are not more than 256 entities - so think about which mods add the most entities to Minecraft, and which you can live with out. "Entities" in Minecraft are things which can move by themselves - the main examples would be new kinds of mob, and vehicles which you can ride. Galacticraft adds around 20 entities, that's 9 new mobs, 6 types of rideable vehicle, parachests, flags, meteors and a new type of arrow - so Galacticraft is a big hog of entities. You could maybe improve that a little by taking GalacticraftPlanets out of the modpack.
One more thing, I notice from the log that you have DragonAPI, but it
looks like DragonAPI is no longer clashing with Galacticraft. You might want to try pulling that out of the modpack for testing, just in case it's that.