What would a baseball game look like on the moon? With the moon's light gravity – only 1/6th of the Earth's – and the airless environment of the surface, it's easy to imagine a ball flying for hundreds and even thousands of feet off the bat of a Barry Bonds or Mark McGwire. Just picture Alan Shepard hitting that golf ball for "miles and miles" during Apollo 14. Of course, that image of Shepard also brings up some other details, like men in giant spacesuits who can't even bend at the waist or slow-moving, exhausting treks across even the shortest distances. The moon is a harsh, harsh environment.

Alas, with everything we know today, a baseball game on the lunar surface seems impossible.

In 1938, however, people were free to imagine what that futuristic game might look like. And they did. In April of that year, the Hayden Planetarium of the American Museum of Natural History in New York "broadcasted" a game of baseball from the moon and the Associated Press was there.

The setting was realistic, 2,000 feet of painted close-ups of the moon's surface which the planetarium is showing. … "That's the field," he said, pointing to a shadowy area behind a moon crater. "It is a mile long and half a mile wide. It is in the shade because in the sun the temperature is the boiling point of water."

The game is called by Professor William H. Barton Jr., "a baseball fan as well as an astronomer." He describes the game in detail, telling us that the first batted ball was hit 1,500 feet in the air and caught a quarter of a mile a way. When the next batter smacks a home run, he reaches first base (curiously still only 90 feet away) in only three strides, circling the bases in only twelve. "But he goes around again. On the moon the rule is six times around the bases is needed for a home run. Just 72 strides." Shortstops make thirty foot leaps to soundlessly snag line drives.

It sounds like it was a pretty spectacular show – the kind of show that could get children's imaginations buzz for days. The AP does help provide a few facts about the moon as well:

The moon is so small its gravity is one-sixth that of earth. A 150-pound man there weighs 25. But with a ball player's muscles he can run in 30-foot leaps. A player like Ty Cobb would be expected to steal second in two jumps – 45 feet each.

Players would need oxygen respirators. But there is speculation whether creatures living on the moon for a million years might condition themselves without respirators. Recently astronomers have suggested that some color changes seen on the sides of the moon craters may be vegetation, and that maybe there is just a little rarefied atmosphere.

I love living in the future, with the internet and smart phones and digital television and everything, but it's sometimes nice to look back and see how wild our imagination used to be before scientific knowledge gave us a harsh dose of reality. It must have been quite the wonder to have been in the Hayden Planetarium that day, imagining players flying around the bases in ten-yard steps and making jumping catches thousands of feet away. (Certainly better than trashy teen novels/movies, that's for sure.)

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Imagination is always better than reality. I'm a Rangers fan, so the theory is proven. I sure wish the Rangers had lost to the Brewers, but there's that reality again.
One important difference: curve balls wouldn't curve, since they require air resistance. Nor would knuckle balls knuckle, sinkers sink, etc.

I'd recommend the fielders play REALLY deep, and bullpen management would be a very topical problem, because it's gonna be a hitter's game.
Interesting about sinkerballs. If it were just reduced air density, then sinkerballs would sink *more*, not less. Most pitches, including sinkerballs, are thrown with backspin, which counteracts gravity. A sinkerball has less backspin than a normal fastball, so it has more "sink". But with essentially zero air density, it would sink even more. But normal fastball would sink as much. In fact, there would be the same movement on all pitches, with the movement determined by gravity alone. Of course, a sinkerball will actually sink less on the moon than on earth, since gravity is only 1/6 as strong.

Responding to heyblue: The fastball speed would not change on the moon, since the reported speed is the release speed. What will be different is the speed at home plate, which will be the same as the release speed. (OK, I know pitchf/x reports speed at 50 ft, not at release point; so the speed at 50 ft will be just a bit higher than on earth).
I wonder how far away the mound would have to be from home plate. Wouldn't a pitcher be able to throw super-fast, given the lightness of the ball and the lack of air resistance? Would we see a 200-mph fastball from Ardolis Chapman?
One more comment on heyblue's post: the lightness of the ball will not affect the release speed. What matters is the mass (the "inertia") of the ball, not the weight. The mass is the same on the moon and earth, even though the weight is not.