Life support techs and modules increase ship range.

The Hyperion resuply centre has a very very small potential to be useful. It is for the most part an over expensive unimportant insignificant luxury that you would hardly miss in most games. You can build it when your planets are getting bored and have nothing better to do. But at least it is not as useless as that wonder that allows all ships to survey.... see i cannot even remember it's name it is so useless! (because all the anomalies are gone by the time you can build it)

What the heck is this spam in reply 6 above? Never seen garbage like this before, Kryo could you please delete?

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Anyway in regard to the OP's question here's a little trick that I learned from Evil Druid that's really quite slick. It doesn't answer the question directly but is a real good method to quickly colonize as far out as you want. It's called the leap frog method.

What you do is you have your basic colony ship as cheap as possible, cargo hull, colony module and as much engine as you can cram in. Then you send the ship out and colonize a planet. You immediately rush buy a Starport (only 156 bc) and rush buy another colony ship at the planet (price varies but generally around 1000 bc). The next turn you load all the colonists except one (million) and continue onward and outward. Repeat this twice per colony ship and you'll find you'll have no problem with range even without wasting space on life support on any of your ships.

The key to be able to do this is to research the 1st Sensor Tech to get Survey module, put out a few cargo hull survey ships and start collecting those cash anomalies early. You end up with a very quick start with a wide perimeter where most of your early pop and stronger colonies will be. The closer in colonies can be filled in with pop bussed in on a colony ship from your home planet. It's one way to get out there quickly and beat the AI in the colony rush.

And for your informwation, all starbases add to your range, not just the influence ones.

That is the strategy i sometimes use, however cash anomalies seem to have a way of being either fairly common or extremely rare,,,, so typically for me, that strategy will often stall because my servey ships will be too busy pulling in all manner of anomaly 'except' cash ones!