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Hi, all you should have to to is double click on it... can you tell me more about the problems you are having?
Yes I read your question, but this is what was presented to me: "how do you open google earth exe file". That's it. There was nothing about Debian or Ubuntu. Since the question involves Linux and there are other Pros who are far more versed in it than I, I will opt out and leave you in their very capable hands.
Have you installed it as in the link above