First off, powering them up is purely arbitrary in the amount required and doesn't even make sense. Why they are not handled in a similar manner as the core baffles me. It's simple, each gate is opened with the planet or moon's primary resource, secondary resource and astronium. The core remains as is i guess and provide at least some use for the astronium.
There is no real backstory, so at least having to utilize resources of the planet to unlock the gates would be more logical.