Episode 43: February 15, 2013
Science in the Movies
by Lee Falin, PhD
One of my all-time favorite science fiction movies is John Carter. It has the perfect mix of action, romance, adventure, superior story-telling, and just a touch of Victorian steampunk. I’m ashamed to say, however, that I very nearly gave up on the film soon after the protagonist’s arrival on Mars.
This moment of weakness came about when I first witnessed John Carter’s remarkable jumping ability, which the film attributes to the lower gravity of Mars. Thankfully, I was able to keep from thinking too much about this long enough for me to enjoy the rest of the film. But today, I allow my thoughts free reign as we explore the science required to calculate just how high someone can job while visiting the red planet.
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White Men Can’t Jump
The first clue we’re given as to why John Carter can jump the way he does comes from scientist/warrior princess Dejah Thoris. She attributes his jumping ability to his higher bone density. Additionally, we can assume that the lower gravity of Mars also plays a role.
As we learned in my episode on density, the density of something is its mass divided by its volume. In other words, how much stuff is crammed into the space it takes up. It’s important to note that this definition of density isn’t the exact same one that doctors are using when they talk about bone density. To a doctor, bone density means the amount of mineral content in your bones. While that’s slightly related to the physical definition of density, it isn’t exactly the same thing.
Unfortunately, neither of these ideas has anything to do with jumping. While it is true that people with higher bone density typically also have greater muscle strength, bone density itself is only useful for preventing fractures, not for increasing your jumping skills.
Additionally, the denser something is in the physical sense, the more mass it takes up in the same space, so the more force would be required to accelerate that mass. So let’s ignore this issue of bone density and focus on the difference between Earth’s gravity and the gravity of Mars.
Does This Planet Make Me Look Fat?
As you probably are well aware, gravity is the force that causes objects to be attracted to one another. There are several forces that do this: magnetism, electrostatic forces, and nuclear forces. However, gravity is interesting because the amount of gravitational pull an object has is related to its mass. The force exerted on an object by gravity is called weight.
The weight of an object can be calculated by multiplying its mass times the gravitational acceleration applied to it. The acceleration due to gravity on Earth is 9.8 m/s2 while the acceleration due to gravity on Mars is only 3.71 m/s2. This means that the gravity on Mars is about one third as powerful as that on Earth.
You can figure out what your weight on Mars would be by multiplying your weight on Earth by a factor of 0.38. Or you can use this handy calculator from NASA to figure out your weight on every planet in the solar system at once. So let’s assume that Carter weighs around 175 pounds on Earth. That would make him about 66 pounds on Mars (that’s quite a diet!).
NASA tells us that an easy way to calculate how high you can jump on Mars is to use that same gravity factor, but applied to your jumping height on Earth. Just take how high you can jump on Earth and divide it by 0.38, and you’ll know approximately how high you could jump on Mars. (Assuming you could still breathe on Mars.) If we give John Carter a lot of credit and assume he can jump 48 inches on Earth, which is about as high as some people believe Michael Jordan could jump in his prime (depending on how you measure it.) This means that Carter would be able to jump about 10.5 feet on Mars. That’s about as high a jump as you would need to jump from the ground to the top of the roof of a one-story house.
So while you would be able to jump pretty high on Mars, you wouldn’t be able to jump anywhere near as high as John Carter does in the movie. If you’re looking for tips on improving your own jumping ability on Earth, check out these tips from Get-Fit Guy, which are considerably easier than teleporting yourself to Mars.
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Man Jumping, Mars and Taylor Kitsch images from Shutterstock