This blog is still alive, just in semi-hibernation. When I want to write something longer than a tweet about something other than math or sci-fi, here is where I'll write it.
Thursday, February 18, 2010
Science Fun, Vol. 4: The three body problem
The revolutionary importance of Isaac Newton's Principia Mathematica cannot be overstated. The title translates to The Mathematical Principles of Physics, and like many scholarly works of the day, it was published in Latin so all learned people in Europe could easily read it. Even today when it has been translated into modern languages, people still call it the Principia, pronounced Prin-KEY-pee-ah.
As a revolutionary work, it stirred up controversy in its day, though now it is so widely accepted as the fundamentals of physics of objects larger than atoms that it is hard to imagine what the disagreements could have been. One of my favorite of Newton detractors is Robert Hooke, not because I agree with him, but because it shows that even smart people can be 100% wrong, and personal flaws of character are usually to blame. His name survives to this day in Hooke's Law, a differential equation that explains the action of a spring very precisely. Hooke said that there was nothing of much interest in the Principia, and if there was, Hooke himself had already figured it out.
BZZZZZZZZZZZZZZZZZ! Sorry, Bob, wrong answer, thanks for playing.
There is a lot to Newton's work, including the first understanding of the properties of optics and his three laws of motion. The concept of universal gravity may be the thing people associated most readily with Newton, what with the falling apple and all. Here's a fun experiment that you can do yourself that shows the unusual properties of gravity when three bodies are involved.
In space, the three bodies might be a star, a planet and a moon, but for this experiment, you will need a golf ball, a ping pong ball and the earth. The part of the earth you should use is a hard flat surface, like a table top. It also helps to have a transparent cylinder wide enough for the golf ball and ping pong ball to fit into easily. I cut an empty soda bottle to make the cylinder. A pint glass could work just as well.
If you hold either ball just above the rim of the cylinder and let it drop, it will bounce back, but not all the way back to your hand.
Wait a second. Didn't Newton say that every action has an equal and opposite reaction? Doesn't this experiment disprove Newton's so-called third law?
BZZZZZZZZZZZZZZZZZ! Sorry, Mr. Beck, wrong answer, thanks for playing.
On impact, some of the energy dissipates, absorbed by the ball or the earth. No ball will bounce all the way back to its original height on even the hardest surface.
But the second time you do this experiment, put the ping pong ball slightly above the golf ball and let them both drop straight down into the cylinder. Get ready to catch the ping pong ball, because it will bounce well above the top of the cylinder. Besides giving a good visual reference as to how high the ball bounced, the cylinder will also keep the ping pong ball from bouncing very far off line.
This experiment will not work with two golf balls or two ping pong balls. You need two bouncy balls with different masses. Dropping a golf ball on top and a basketball on bottom simultaneously will give you a similar result, though if the bounce is slightly off line and you might have to chase some distance after the golf ball. In space, where gravitational attraction often causes orbits instead of collisions, very unusual situations could arise under the right (and very unlikely) circumstances where a body could be accelerated to nearly infinite speed.
A lot of people talk about common sense, and in today's society it is revered beyond all proportion. The fun of science is when our expectations founded in common sense are blown out of the water. I propose we use a new term, vulgar sense, for the rigid ideas expounded most often by people who want to deny science when science runs counter to their strongly held and often nonscientific beliefs.