Jumping with John Carter of Mars
In the film John Carter, the hero jumps over 100 feet in the air during his Mars adventures. Everyday Einstein looks at the science behind his feats of strength.
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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..
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.