Lagrange Points

Astronomers discovered the first asteroid in one of Earth's Trojan points today! Well, not today, but today is when I heard about it at least. The asteroid, 2010 TK7,  is located at the fourth lagrange point of the sun and earth.
For those who don't know, here's a science lesson. Take a stable orbit between two objects, like the sun and your mom. Or the earth.
Both of these objects exert gravitational pulls, the sun pulling everything towards it, technically into its gravity well, and the Earth doing the same, albeit on a smaller scale. Now take a theoretical third object, this time we WILL use your mom.
So your mom is on some random orbit around the sun.

I had way too much fun drawing this

Normally your mom would settle into a stable orbit around the sun based on the initial conditions, and her mASS. But then add the Earth in there, or any third, larger object for that matter.

Still more original then most disaster movies

Now, we are fast approaching what would be called a complex system. The sun and Earth are both pulling on your mom, and she hasn't seen this much action since 1974. Between the gravity, and the momentum that your mom gets as she ricochets around the solar system, its likely your mom will end up in a highly elliptical unpredictable orbit due to the sling shot effect.
However, there are 5 points, when viewing the earth sun orbital relationship, that if your mom ends up she can potentially stay in a geostationary orbit for a time even longer then her age. These are the Lagrange points,
points where potential satellites could remain in geostationary orbits.

Whats that mean you ask? It does not mean that it will stay in one absolute place, but one relative place. Relative, to the Earth. For example, anything at the L4 point will remain 60 degrees ahead of the Earth in its orbit.

You can always just take scientists words for it, and explain it as "Lagrange points, they stay in these positions because of gravity and the sun and earth, and the..magic magic magic, and that's how it works." But its actually pretty intuitive, just look at the easiest to understand, L1.
You have a sumo wrestler on one side of a seesaw, and a little kid on the other. It makes sense that there will exist one point between the two that their masses cancel out and the seesaw will balance in a relatively stable position.

These have awesome potential for utilization someday. Someday, they can be used as places to launch missions into interstellar space! We can ship materials up to the points, and have them remain there until we are ready to use them. We can save fuel by launching missions from a Lagrange point, as the escape velocity is much less then it would be to start on Earth. We could build mobile stations that could be stationed there and would in turn serve as stepping stones to other planets in the solar system. Think of it like an deep space gas station. Maybe even throw in a diner with a nice 10 dollar turkey dinner. And we are barely scratching the surface right now.
 I was introduced to the whole concept by the flashiest pimp in the glamorous world of appeal to the public science books, Neil deGrasse Tyson:

I first read about Lagrange points in Death by Black hole by Neil deGrasse Tyson, and they immediately fascinated me as a physics major. The feeling of excitement that came over me as I played over the idea in my head, figured out for myself why they made sense and fit in with the world, and the implications they could have for future space endeavors perfectly exemplifies why I find physics so interesting.
So interesting did I find them, that I got a diagram of the Lagrange points tattooed on my bicep:

I got really excited when I saw this, clearly.