MathScienceScience SundaySTEM

Science Sunday: Jumping on Mars and Other Extreme Sports

On March 8th, 2012 Disney’s John Carter was released in theaters to the general public.  Adapted from Edgar Rice Burroughs’ 1917 pulp novel, A Princess of Mars, the movie’s plot follows the swashbuckling antics of John Carter, a disillusioned Civil War veteran who is transported to Mars after he kills a Martian god on Earth and touches a magic talisman.  The native Martians, who call the red planet Barsoom, are fighting in an arms race for political control.  Or something like that.  Even if you do your homework and read the book before going into the theater, it’s pretty difficult to follow, but  John Carter’s plot issues are a topic for another post.  We’re here to talk about SCIENCE.

To a modern audience, Edgar Rice Burroughs’ vision of the red planet is a bit outdated.  A Princess of Mars was written in a simpler time, when a few Earth-bound, 19th-century astronomers proposed that the lines they observed on Mars’ surface were the dried remains of an ancient Martian civilization’s irrigation system.  The Martian canal theory has since been debunked, the lines turned out to be an optical illusion and the original suggestion that these surface marks were artificial in nature is now suspected to be the result of a mere translation error, but the thought of neighboring extraterrestrial life sparked the public conscience.  It spurned a small revolution in science fiction that produced not only several John Carter adventures but also H. G. Wells’ War of the Worlds.  These early works of so-called scientific romance not only paved the way for future science fiction authors such as Ray Bradbury, Arthur C. Clarke, Robert A. Heinlein and Isaac Asimov, who would later define and cement the genre, but also helped inspire scientists and science-enthusiasts such as Carl Sagan—yes, THAT Carl Sagan—to pursue work that pushed humanity’s reach farther into space.

So, putting its creative influence aside, how does John Carter stand up against the science that has been added to the human lexicon of knowledge since 1917, three years before women in the U.S. were given the right to vote?  We could easily probe at why the only water on Mars is frozen at the poles or the fact that the planet isn’t, in fact, covered with patches of red moss, but I’m interested in physics, and unfairly biased, so let’s talk about John Carter’s ability to catapult himself fifty feet into the Martian air at will and land without breaking his legs.

In the book, A Princess of Mars, John Carter’s first experience with alien gravity comes when he wakes up on Mars, lying on the ground, and tries to stand up for the first time:
 

Springing to my feet I received my first Martian surprise, for the effort, which on Earth would have brought me standing upright, carried me into the Martian air to the height of about three yards.  I alighted softly upon the ground, however, without appreciable shock or jar….My muscles, perfectly attuned and accustomed to the force of gravity on Earth, played mischief with me in attempting for the first time to cope with the lesser gravitation and lower air pressure on Mars.  (Burroughs 40)
 

The movie has John Carter’s actor, Taylor Kitsch, flailing around and taking several face-plants into the dirt for a good ten minutes.  Kitsch winds up crawling around on his belly to keep from flying away at dangerous speeds with each miscalculated step.  Over time, his character learns to control his giant leaps and use them to his strategic advantage in combat.  Both book and movie claim that this phenomenon is the result of liberating John Carter’s body from the more suppressive gravitational and atmospheric conditions that his body grew up with on Earth.  The question is: is this really what would happen to a human on Mars?

 

Figure 1: John Carter jumping on Barsoom in his first movie teaser

 

That’s right, the answer is no, they would black out and suffocate because Mars’ atmosphere has almost no oxygen and is 95% carbon dioxide.  If you were wearing only John Carter’s loincloth and leather booties, you would also freeze.  Movie busted.  Wow, that was quick.

J/k.  No one’s getting to the end of this article that easily.

Okay, ignoring the obvious physiological limitations, a person jumping on Mars is fundamentally the same as a person jumping on Earth: you kick up off the ground with a certain amount of force, reach a maximum height, and fall back down.  A jumping person is a projectile following a set path shaped like a parabola, following what is called a ballistic trajectory.  A trajectory is the path that an object will follow under influence of 1) the initial launch conditions (i.e. the object’s height, velocity, and angle to the ground at launch) and 2) gravity.
    
Isaac Newton put together the fundamental theory of gravitation early in the 17th century: any two objects that have mass are attracted to each other with a certain amount of force.  We can calculate the quantity of this gravitational force (F) with the following equation:

 

 

Before you start to panic, all this equation says is that the strength of the gravitational pull on two objects depends on the mass of each object (m_1 and m_2) and the distance between them (r).  The closer two objects are, the stronger the gravitational pull.  G is just the gravitational constant.  Since you have mass and Earth has A LOT of mass, this force has a perceivable effect on your body that keeps your center of mass tethered to the planet’s center of mass.  That’s gravity.

We can easily use this equation to calculate the amount of force due to gravity that John Carter feels when he’s standing on Earth or when he’s standing on Mars.  To apply the equation’s variables to our problem: m_1 is the planet’s mass (or: m_planet), m_2 is John Carter’s mass (or m_JohnCarter), and r is the distance between the center of the planet and the surface (or r_planet), where John Carter is standing in the starting position right before he leaps.  Here’s the equation again, just to make things extra clear.

 

 

All we need to do is pull up some numbers to punch into the equation.  Luckily, NASA exists and keeps tabs on these things, so we have this handy-dandy Mars Fact Sheet that we can use instead of getting some instruments and figuring out the values ourselves.  I can also make an educated guess as to John Carter’s weight (about 137 lb sounds good to me) and plug that value into the Google search engine to get his mass (62.1 kg).

 

 

 

Calculators at the ready, or maybe you're brave and want to do it out by hand.  Or just use WolframAlpha.  Watch your units.  While we’re waiting, let’s look at this awesome photograph comparing the sizes of Earth and Mars.

 

 

Figure 2: Size comparison between Earth (left) and Mars (right), for your oogling convenience, courtesy of NASA and Wikipedia

As seen above, Mars is smaller than Earth and has less mass.  Ready?  The answers are: on Earth, John Carter feels a gravitational force of 612.3 Newtons and on Mars, he feels a force of 233.2 Newtons.  Therefore, there is less gravity on Mars than there is on Earth and John Carter’s ability to jump farther and higher on Barsoom makes sense to a certain extent.

In the book, Burroughs gives us some actual numbers to work with when John Carter makes good use of his newfound ability to make an evasive combat maneuver to the shock of Barsoom’s native aliens, the Tharks:  
 

I gave a very earthly and at the same time superhuman leap …My effort was crowned with a success which appalled me no less than it seemed to surprise the Martian warriors, for it carried me fully thirty feet into the air and landed me a hundred feet from my pursuers and on the opposite side of the enclosure. (Burroughs 48)
 

Let’s just take Carter at his word and assume that his measurements are accurate.  On Barsoom, he is able to jump over a horizontal distance of 100 feet (30.5 meters) and reach a height of 30 feet (9.1 meters).  The only other instance of humans walking on another not-Earth heavenly body is the astronauts on Earth’s moon.  For comparison, the force John Carter would feel on the moon is 100.8 Newtons, about half of the force he feels on Mars.  Here's a video of Apollo 17 astronaut Eugene Cernan testing out the best way to gleefully traverse the lunar surface:

Transcript: “Hippity-hoppity, hippity-hoppity, hippity-hoppin’ over a hill and dune.  Da-da-da-da-da-da-da-da.  Da-da-da.  Hippity-hoppin’ a-long.”

Here is another video of Cernan giving a more thoughtful analysis to his, er, technique:

Abridged transcript: “This is the best way for me to travel, uphill or downhill…Two-legged hopMan, I can cover ground like a kangaroo!”

The astronauts are able to cover a lot more ground with one hop than they could on Earth, sure, but they’re not quite reaching distances of 100 feet.  Astronauts do wear a lot of heavy gear to protect themselves from the harsh conditions on the moon while John Carter is able to prance around Barsoom half-naked. Still, there is a scene in the movie where John Carter is able to pitch himself between two rooftops of a giant city while carrying a Martian soldier, so it would take a lot more than a heavy space suit to hamper his movement.

A human would experience a greater range of movement if they tried to walk or jump on the Martian surface, so the super-jumping in John Carter is absolutely plausible.  Super-jumping over 100 feet, though?  Not possible, especially not without any additional training.

Entertaining the idea of an ancient Martians civilization takes a little more ingenuity for modern-day, post-suffrage, science fiction writers, now that NASA exists and we have little motor vehicles roving around up there bringing back beautiful, high-resolution images and video of the desolate and very alien life-less surface.  Hey, don’t just pass over that link, I put that there for a reason.  Go back.  Click it.  I mean it.

Okay, fine, here’s a picture:

 

 

Figure 3: A press release image of the "Columbia Hills" on Mars, assembled from a series of shots taken by Mars Rover Spirit in 2004 on March 12 and 13

THAT right there is a photo taken of the surface of Mars by the Mars Exploration Rover, Spirit.  You are looking at another world that no other human being has ever yet set foot on.  Just let that sink in. 

Now you're all set to go write or enjoy some science fiction.

 


Resources:

John Carter Mars Series by Edgar Rice Burroughs (1917).  The version I read was published in 2011 for the NOOK by FLT.

Fundamentals of Physics, 8th Edition by David Halliday, and Jearl Walker,  Halliday and Resnick (2008).   Published John Wiley & Sons, Inc.  Chapter 4: Motion in Two and Three Dimensions and Chapter 13: Gravitation were the ones primarily used for this post.

An Observational History of Mars by Dave Snyder.

Online LaTeX Equation Editor.

Further Reading (nonfiction literature on the planet Mars and how else space affects the human body):

The Case for Mars: The Plan to Settle the Red Planet and Why We Must by Robert Zubrin (1996)

Packing for Mars: The Curious Science of Life in the Void by Mary Roach (2010)

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alyssa

alyssa

Alyssa is a recent liberal arts graduate with a B.A. in physics and a background in wrangling high-vacuum equipment. She is an aspiring science writer who writes when she's not busy hunting for full time work in nanomaterials and renewable energy. She likes to get her energy by drinking coffee and absorbing electromagnetic radiation from the Sun.

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