Baseball in space? Calculating pitching speed on the Moon

QUESTION: Would a baseball pitch travel faster on Earth or on the Moon?

ANSWER: In order to figure out whether a baseball pitch travels faster on Earth or on the Moon, we need to know the forces that act on the ball once the pitcher releases it. Let’s think about a pitcher throwing a baseball horizontally from the pitching mound to home plate on Earth. Once the pitcher releases the ball, there are two forces acting on it: gravity and something called a drag force.

A drag force results when an object moves through a fluid. In this case, the object is the baseball and the fluid that it moves through is the air, which consists mostly of oxygen and nitrogen molecules. Since the baseball has to knock the air out of the way in order to move through it, the drag force causes the baseball to slow down. Let’s say the pitcher throws a 90-mile-per-hour fastball.

How much slower will the ball be moving on Earth due to the drag when it reaches home plate?

Calculating the size of the drag force can be a little complicated. It depends on the amount of air there is in a given volume, and on the size, shape and speed of the baseball. For a fastball, the size of the drag force depends on the value of the velocity times itself. I calculate that a 90 mph fastball will be moving about 10 mph slower when it crosses home plate on Earth.

Gravity will also be accelerating the ball vertically down as it travels to home plate and will cause its downward velocity to increase from 0 to about 10 mph. This downward velocity is not very important compared to the speed that the ball is moving horizontally. The effect of gravity does mean that the ball will drop about three feet from the height that the pitcher releases it by the time it crosses home plate.

There is almost no atmosphere on the Moon. This means that there is no drag force to reduce the horizontal speed of a baseball pitched there. So a 90 mph fastball will still be moving 90 mph when it crosses home plate on the Moon. The force of gravity is about six times weaker on the Moon due to its smaller size and lower mass. So the pitch will only drop about half a foot and be moving downward about 2 mph when it reaches the plate.

Finally, we see that a baseball pitched on the Moon will be traveling faster when it reaches home plate. But, would you rather be a batter on the Earth or on the Moon? The analysis so far has neglected to account for whether the ball is spinning.

Pitchers intentionally throw fastballs with backspin and curve balls with topspin. A spinning ball moving through air experiences an additional force, known as the Magnus force, which is due to the difference in the drag force on either side of the ball (one side is spinning into the oncoming air and the other side away). Since pitchers can throw baseballs that spin quickly, this effect causes fastballs to drop a few feet less than a spin-less pitch would and curve balls to drop a few feet more.

A pitcher on the moon would then have a significantly harder time fooling a batter. If there is ever a World-plus-its-satellite Series, my advice is to bet on the world.

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MEET THE STUDENT

Name: Joe Miller

Age: 10

Grade: 5

School: St. John the Evangelist, Diocese of Syracuse

Teacher: Anu Rai

Hobbies: Playing baseball and basketball, cooking, cleaning and working around the house

Career interests: Police officer, NBA all-star, NFL all-star, MLB all-star, astronaut, fireman

MEET THE SCIENTIST

Answered by: Stephen Levy

Title: Assistant professor of physics, Binghamton University

Department: Physics

Research area: Soft condensed matter

Interests/hobbies: Omaha hi-low