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Juno to Jupiter: The Mind Blowing Math of NASA

Jupiter photo from Hubble telescope
Jupiter as seen by Hubble telescope, courtesy of NASA
I remember sitting in Mr. Taylor's math class. Frankly, I was always pretty good. Geometry and trigonometry came easy to me. Algebra and calculus required much more effort. Most of what I learned came from studying with a good friend of mine, Addison. In college my math helped me understand macroeconomics, and Addison went on to manage a company focused on Big Data. We were pretty good at the maths.

NASA, however does mind blowing math. August 5, 2011 they launched a satellite at Jupiter. On July 4 of this year, while Addison and I were both celebrating independence with friends, him on the West Coast and me in the east, the geeks at NASA couldn't take the day off.

Mind Blowing Math Level I

Launching a satellite on a rocket isn't quite like shooting a gun.

If you shoot a rifle, most of us could hit the target after half a dozen practice shots.

A pistol is much more challenging because your barrel is shorter and fractions of a degree mean missing the target.

Archery is even more difficult. In archery you have to aim high because the pull of gravity makes the path of the arrow arch slightly. Every 10 feet of distance makes this shot dramatically harder.

Not only did NASA hit the target, but it was a bull's-eye and they only got one shot.

Mind Blowing Math Level II

So why did NASA land on July 4? If they're so good at math, wouldn't they have realized it's a holiday? Seriously, Addison and I would've both been happy to have a couple NASA dudes at our cookouts, assuming they brought Doritos or something.

Well you see, they wanted to land when Jupiter was in the neighborhood, only 345 million miles from Earth. Remember, every 10 feet or so makes a difference in archery, so if they could take a shot when Jupiter was close, as opposed to when it's 610 million miles away, it'd be much easier.

Remember, planets don't travel in circles. They travel in ovals, at different speeds. They are shooting at a moving target that gets closer and further away.
Juno satellite on its path to Jupiter - courtesy National Geographic

Mind Blowing Math Level III

Arrows fly much slower than bullets. Because of this, gravity has a much bigger influence. The more time it takes the arrow to hit the target, the more gravity comes into play.

Imagine shooting an arrow that will not land for five years. The effect of gravity will be huge.

NASA knew this, and took it mind blowingly further.

Satellites fly pretty fast, thousands of miles per hour. If you're going to shoot something at a target 345 million miles away, you definitely want the fastest possible spacecraft.

NASA said, "What if we could get extra speed from gravity? Gravity could help us instead of making it more difficult." So they shot this rocket at the path that the gravity of Earth would come into play more than two years later!

They were using the gravity of where the earth would be two years from now to influence the speed. They had to get close, but definitely not hit the target, because shooting yourself is a bad thing.

Back to the archery… You fire an arrow, and before the arrow reaches the halfway mark, you chase it down and stand in front of it. It's going to whizzz by your head, so close that your 1980s hairstyle will influence the path of the arrow.

In this case, the satellite increased in speed by 16,330 mph.

To get a better understanding, National Geographic created a pretty amazing picture. The satellite was shot so it would make a complete orbit around the sun traveling slower than Earth. Earth makes more than two orbits. When the earth and the satellite pass each other again, the gravity speeds things up similar to a car coming over the crest of the hill.

After all, when you are taking a 350 million mile road trip, you want to save on gas wherever you can.

Mind Blowing Math Level IV

Remember we are shooting a moving target, Jupiter.

The next level is even crazier. We aren't going to hit Jupiter. We are going to miss, on purpose.

You see, crashing into Jupiter is impressive enough, but if you're going to travel all that distance, you want to make sure to see the sights. Imagine driving to Arizona without bothering to check out the Grand Canyon.

We missed Jupiter, but we missed so close that the satellite got grabbed by Jupiter's gravity, and now it's orbiting the planet probably with a couple GoPros.

We want to drive by taking pictures, but we don't want to land. You see, the giant red spot is some pretty harsh weather. Imagine a hurricane. A big one can cover the lower half of Florida. This one is bigger. Bigger than Florida, bigger than the United States, bigger than the entire earth; it's actually about three times the size of Earth. Plus, this hurricane seems to never end.

It's a little dangerous to orbit Jupiter. If you use a telescope, you can see four moons. If you use a gigantic telescope, you'll realize that there are actually 67 of them orbiting Jupiter. Just saying, in this traffic make sure to use turn signals before merging.

Mind Blowing Math BOSS LEVEL

Pretty impressive so far… But wait…

The sun is a ball, orbited by a bunch of little balls. Those orbits aren't like the circles in our high school science books. In reality, the orbits are more like eggs, wobbling because each of the little balls influences the others slightly.

Keep waiting…

But the sun isn't stationary. Plus the orbits aren't necessarily flat.

The sun is streaking through space at tens of thousands of miles per hour. The planets are being dragged, not in circles or egg shapes, but in a spiral pattern.

If you actually drew orbits in three dimensional space, they would look like a corkscrew.

What this means is that, while the earth rotates once every 365 days, in that period of time the sun has traveled millions of miles. When we rotate back to the beginning, in three dimensional space we are millions of miles away. In fact, in the past 13 billion years, since the Big Bang, the earth has never been in exactly the same place twice, and never will be.

The satellite's name is Juno. It sounds like the capital of Alaska, but it is spelled like that movie about the teenage angst of a pregnant girl who's actually a lesbian in real life. Whatever.

So, Juno traveled 345 million miles, which took five years and two laps around the sun, to fly by earth so close it messed up our hair, toward Jupiter. When it arrived, it missed by just enough to become the 68th satellite, and the first man-made device in orbit. The entire time, we are all flying through space on a spinning ball, corkscrewing around another spinning ball.

I guess the guys at NASA had a pretty good reason to miss my July 4 pool party. By the way, boss level math nerds are welcome to the party next year, and you don't even have to bring Doritos.


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