Seems that you can only purchase online tickets for the same day as you intend to use them.
Interesting, not sure if it matters. When we were in Gatlinburg a few weeks ago, we were walking by the aquarium on our way to meet friends for dinner and decided to stop and ask a question. There was no one in line, so we asked if we could purchase our tickets and then use them the next day. The lady at the counter said that would not be a problem. We arrived the next day and used the tickets purchased from the prior day. I really don't think it matters... however a quick phone call may clear it up. Good luck and you will enjoy the aquarium, it is a great experience.
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