What happens to a bullet fired on the Moon? (Intermediate)

In reference to "Can I fire a gun on the moon?"-- what then happens to the bullet?

First, we know that the bullet has the same initial velocity on the Moon as it does on the Earth - that is, it exits the gun at the same speed. But as soon as it leaves the gun, it's a different story. First, the Moon bullet doesn't have to contend with air resistance. With so little friction, it can maintain its speed longer than the Earth bullet can. (It's analogous to shooting a hockey puck across ice, which has very little friction, and shooting across sand, which has a lot of friction. The puck will travel a lot farther on the ice!)

Now, there is the issue of gravity. Assuming your bullet doesn't hit anything (a pretty safe bet on the Moon, but don't try this on Earth!) and forgetting about air resistance, the time it takes for the bullet to fall to the ground depends on its initial velocity, the angle at which you shoot it, and the force of gravity.

You can use some basic physics to figure out how far the bullet will fly horizontally and vertically. Say you fire it at some angle "a" (a=0 degrees would correspond to shooting it straight in front of you; 90 degrees corresponds to shooting it straight up). It turns out that the bullet's horizontal range - the total distance it travels before gravity wrestles it to the ground - is given by the equation:

R = v2 × sin (2a) / g

g is a measure of the strength of gravity. On Earth, it is 9.8 m/s2. To find g on the Moon, we need another equation:

g = G×M/R2

G is the gravitational constant, M is the mass of the Moon, and R is the radius of the Moon. Anyway, on the Moon,

g = 1.6 m/s2

So, neglecting air resistance, the bullet will go about 6 times farther on the Moon than on Earth. Once you take air resistance into account, the Moon bullet has an even bigger advantage!

You might also ask, if the bullet were fired straight up, could it actually escape the moon's gravitational pull and fly off into space? To answer this, we have to compare the moon's "escape velocity" (the minimum velocity an object needs to escape the Moon's gravity) to the bullet's initial velocity. The moon's escape velocity is about 2.38 km/s, but a bullet typically travels at only about 1 km/s. So take cover - even in this case, what goes up must come down!

This page was last updated on September 20, 2015.

About the Author

Kate Becker

Kate Becker

With more than a decade of experience as a science writer, Kate Becker has written on a wide variety of science and science policy subjects for web, print, radio, and television, with an emphasis on astronomy and physics. As a researcher for NOVA and NOVA scienceNOW, the nation's premiere science documentary series, Kate investigated everything from human hibernation to invisibility cloaks. She studied physics at Oberlin College and astronomy at Cornell University, and she's had the good fortune to observe with the Arecibo Observatory in Puerto Rico and the Very Large Array in New Mexico, two of the very best places on this pale blue dot of a planet.

Website: www.spacecrafty.com 
Twitter: @kmbecker
Facebook: www.facebook.com/katembecker
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