How to Carry a Child Off Mars by Balloon

Over the last week, contemplation of balloons led me to wonder how large a balloon would be necessary to carry boy off the Moon and into space. This was, I thought, a very clever question. So I hopped online and found that pretty much anytime anyone starts thinking hard about balloons, or about the moon, this question occurs to them.

So in case you’re one of the eight or so people other than me who didn’t know the answer, here it is: it doesn’t matter how big the balloon is, because our moon doesn’t have an atmosphere. In the same way that chunks of styrofoam float in the ocean, helium-filled balloons rise because the air inside them is less dense than the air outside. On the moon, the balloon would sink. Which will be a total bummer for children of the future, whose families go to all the trouble of taking them to the moon for their birthday, and they can’t even have balloons.

Ever the creative and enterprising journalist, I then wondered: what about balloons on Mars? Unlike our moon, it’s got an atmosphere — a nasty CO2-laden miasma in which you’d promptly choke to death, but an atmosphere nonetheless. And cursory Googling reveals that most people’s interest in extraterrestrial balloon flight pretty much stops at the moon. (Which, given all the balloon-on-moon interest, seems a bit suspicious. Maybe Google’s trying to hide something. What’s up with all those blank spots in Google Mars, anyways?)

To figure out the size of the balloon — filled with hydrogen, the lightest gas, since helium’s still too dense to rise through Mars’ thin air — needed to yank a Falcon Heene-sized boy off the Red Planet, we’ll need some things I last encountered in school, kicking my ass and threatening my chances of graduation: equations.

B = DVg
B – Mg = Ma

“B” stands for buoyant force, which equals the amount of air displaced by a balloon. “D” is the density of displaced air, which is multiplied by “V,” or the volume of displaced air. The “g” stands for the pull of gravity on the balloon’s contents, including anyone who’s hanging on it for dear life.

In the second equation, “Mg” is the weight of the balloon and its contents. In order to get an upwards acceleration — a positive “Ma” — then buoyancy must be greater than weight.

The equations can be fleshed out thusly:

Buoyancy = (.02 kg per cubic meter, the density of Mars’ thin air) x (hypothetical volume of the hydrogen balloon) x (3.69 meters per second square, which is the gravity of Mars.)

Meanwhile, (buoyancy) – (8.39 kg, or Falcon’s mass on Mars) = (acceleration, which I’m just going to call one, because even though any positive number would send signify an airborne kid, that’s a nice round target number.) So:

B = (.020)(3.69)(V)
B – 8.39 = 1

The latter quation puts buoyancy at 9.39, leaving us with

9.39 = (.0738)(V) = 127

So the volume is 127 cubic meters, which translates to a spherical balloon with a radius of 3.12 meters, or about ten feet. That’s a pretty special balloon — but birthdays are all about special!

Of course, I’ve failed to account for many things, including the weight of the balloon and the child’s spacesuit. But I’m sure the Martians have all kinds of neat ultra-light materials, and have no trouble breathing on their own planet.

Posted by Brandon Keim (Web/Twitter)

Image: From NASA. Also, please visit the Pakistani Starfleet Explorers Flickr set, which I couldn’t use because the images aren’t licensed to the public and don’t quite fit anyways, but really, they’re just freaking awesome, and contain such gems as “Pakistani Honeymoon Over Io” and “The Bedford Battlestar One is in Hot Pursuit of the Slorpain Bird Being Queen” and the image that brought me there, “My Other Pakistani Home on Mars.”

Note: Credit for the equations, but no blame for mistakes, goes to Adam Weiner of Popular Science. He figured out that Richard Heene’s balloon really could have carried Falcon away. I’ve shamelessly cribbed his equations and plugged in Mars numbers.

For what it’s worth, this is the most complicated math I’ve done in my adult life. Every math class I was forced to take after my sophomore year of high school, I managed to get through with a mix of blind luck, teacher mercy and the tactics used in this post — known, in that context, as cheating. Kids, when they say you’ll need math, don’t believe them. Go take a cooking class!