## Thursday, January 9, 2020

### Orbits

Before we look at what's up there, we need to understand how what's up there works. The same forces that operate down here drive what's up there. There's a problem though. An orbiting planet isn't the same thing as a mass whirling around on a string. For one thing, the string constrains the motion of a whirling object to a strict circle while gravity does not.

Frankly, it's hard to study orbital mechanics on Earth. Henry Cavendish finally nailed down the force of gravity, Newton's universal gravity constant, 71 years after Newton's death. He did it by suspending two very heavy objects at the opposite ends of a rod by a hanging, thin rod, and setting it oscillating. Then he did it again, setting a massive object near one of the hanging weights (the setup is called a torsion pendulum and its exquisitely sensitive.) The difference in the periods of oscillation gave him the information he needed to calculate the gravitation constant.

Other than that, have you ever tried to bring a planet into your bedroom?

Barring that, I have my gravity simulator (you saw it in the blog "Something about mass") and, although it isn't a perfect model of planetary orbits, it's surprisingly good.

First, let me point out that Newton learned more about mechanics by looking at the planets than by watching apples drop off a tree. As for the value of the acceleration of an object under the influence of gravity, Galileo had already done that work. Newton's first law of mechanics is actually Galileo's law of uniform motion. When Newton said, "If I have seen further, it is by standing on the shoulders of giants," he meant it quite literally. Newton was not a man given to bouts of humility.

Kepler's laws of orbital mechanics came before Newton. Newton's job was to tie it all together and figure out how the mechanics of planets was the same as the mechanics of an ox cart or that of a falling apple. So let's play with planets.

[Small ball around large ball]

The two balls are steel, so they're the same density. They don't orbit for long because they're close and exert more "gravity" and, more, because the model creates a lot more friction than the vacuum of space.

Newton deduced that the force of gravity between two masses increased with the product of the two masses and decreased with the square of the distances between them. He threw in a "universal gravitational constant" that makes the units and scaling work out. That's what Cavendish figured out years later.

The shape of the orbit is clearer when a smaller ball (BB) is used.

[Tiny ball orbiting around large ball]

Kepler worked out the shape of planetary orbits from the massive number of precise observations made by his mentor, Tycho Brahe. His first of three laws stated that planets move in elliptical orbits. Notice that, regardless how I start these balls rolling, they end up in elliptical orbits. That's not a result of the way the fabric is stretched. I tried to make sure that it was stretched evenly in the embroidery hoop.

For planets, as well as balls in the gravity simulator, the large ball is at one of the focuses of the small Ball's elliptical orbit.

Also, watch the way the ball speeds up in those tight turns. Kepler's second law states that the planets sweep out equal areas in equal times. That means that, when the planet is farther from the sun, it moves slower.

His third law is harder to see on the simulator, but it says that, of two planets, the one orbiting further from the sun will have been a longer period (year) than the other.

[Balls of equal size]

When two balls of equal size are on the simulator, they orbit each other. Actually, that's true of all the orbits. It's just that, when the difference is large, it's hard to see the larger ball move. Even in space, planets and stars orbit around common centers. For instance, binary stars sling each other around a common center.

[Three balls of different density]

Here, I roll a small steel ball, an aluminum ball, and a wooden ball around the large steel ball. You probably could have guessed that the less dense wooden ball would orbit the longest. Also, notice that it's orbit is less elliptical.

[Tiny ball with different forces]

Here, I tried to roll the ball at different speeds (including, off the simulator). Notice the shapes of the paths. Even the ball's path at "escape velocity" is curved.

In fact, not all orbiting bodies take an elliptical orbit, but they do all follow conic curves. The Earth's orbit is almost, but not quite, circular. On the other hand, comets and other "space junk" may just graze the gravitational field of the sun on a hyperbolic curve, or loop around once on a parabolic path, and never return.

[Swarms]

A collection of BBs make a nice little solar system. The really fascinating thing is when they are going in opposite directions.

[Two swarms]

Notice how they end up all going in the same direction! Ever wonder why all the planets orbit the sun in the same direction? Remember that, not only the sun is pulling them, but they are also pulling each other. It turns out that star systems are self-organizing.

The early history of Earth was violent. Collisions were common in the early solar system. In fact, our moon was probably the result of such a collision, a chunk knocked out of our planet by a traveling piece of space debris. Over time, such collisions became rarer. You've just seen one of the reasons why.

The gravity simulator is fun and offers a lot of possibilities for studying gravity and orbital mechanics. For instance, you could easily build a large version using a hula-hoop...or a trampoline! You might also check out different materials for the membrane. Plastic food wrap causes less friction.