The phrase "shoot for the moon" is likely attributed to Norman Vincent Peale, an American preacher and self-help author in the 1950s. Peale is known for popularizing the concept of positive thinking. The full saying is "Shoot for the moon. Even if you miss, you'll land among the stars".
The phrase means to try to achieve something that is very difficult. For example, "an ambitious businessman who is always shooting for the moon".
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I burst out laughing first when I saw this short phrase yesterday: stars are further off from us than the moon, if one can't reach the moon, how can one reach the stars? Then thought about it again: yes you can! There is only one moon, but at least 200 billion trillion stars ;-), so go for it as long as one has enough power supply ;-)
Back down to earth, I almost forgot the Mid-Autumn Festival (俗称:月饼节:-)which is today! Due to travelling (landed in Monterey CA 37 hours ago), I don't have the gears making mooncakes, so a couple BIG grapefruits picked from neighbour's tree (with permission;-) and a couple interesting small stones found on Cannery Row beach, with a beautiful song by Teresa Teng, for you all to enjoy.