The F3 screen shows the problem here. You haven't given Minecraft enough memory for playing with mods, especially a large mod like Galacticraft. 1000MB is not enough on a 64-bit PC like yours!! You can see at top-right the Java is already at 99% of available memory even just standing still. That's not going to work. The lag is being caused by the Java "garbage collector" desperately running all the time, trying to free up slightly more memory.
To fix this, in the Minecraft launcher, change your JVM settings to give Minecraft more memory.
-Xmx2G should be enough for Galacticraft. If you want to add more mods in future, you might want to push that up to a higher number. This is documented on our
installation guide.
For an alternative solution you can also try downloading a mod named
FoamFix, it works really well to reduce Minecraft's memory requirements.