### Trader Note

If no news and markets stagnant, chop top and bottom with impunity and stops.

# Gravity Thought Problem

Gravity Spheres

The thought problem is a foundation for early physics. It is a wonderful way to elucidate ideas. So, here’s one I’ve been rolling over.

Gravity. One gram of substance has the same gravitational pull as a gram of another substance. This means that one gram of Helium has the same gravitational pull (as a large enough distance) as a gram of a neutron star core. The volume of a single gram of this substance is vastly different, however.

Let’s look at a more tangible example. Imagine you have a sphere of lead that weighs a kilogram. You also have a sphere of ice that weighs a kilogram. They both weigh the same, thus have the same gravitational pull, at a distance.

From the center of the sphere, the mathematic point can be defined as a gravitational pull of one kilo of material. The left side of the sphere looks the same as the right side from the perfect center.

So, if we cut the two spheres down the middle, leaving hemispheres, and join one half of water with one half of lead. So, from the perfect center, the point of gravity pull (mathematic equivalent) is exactly the same. Gravity lines radiate out from this new object the same as the originals.

Now imagine the first two spheres in free space (no nasty planets or gravity wells to mess with our thoughts). From a standard mathematic description, an object would orbit these two spheres at the same velocity for the same distance. That means that the pull of gravity (in math) is defined by a pull from the center of the sphere, keeping it falling at the sphere at a constant rate. Of course, having to do the mathematic pull for every point in a sphere becomes prohibitive and that is why the math is simplified to a point.

But we are not looking at the math but the reality. If that object in orbit moves closer to a sphere, it’s going to scrape across the ice faster than the lead because the size of the ice is greater than the lead.

If the orbiting object is danger close to the ice sphere, then we are missing something in our math. For instance, if the orbiting object is a popsicle stick, the center of mass, in a mathematic equivalent is not evenly distributed. The front and back edge of the stick in orbit will experience smaller amounts of gravitational pull than the middle.

How does that work? Well, if the ball of ice is a combination of individual points (like each molecule of ice) pulling on a single molecule of the stick, then the part of the stick closest to the ice ball will have stronger forces acting on it. For instance, every line drawn from one point on the ball to one point on the stick will be smaller (these are gravity lines, and shorter lines means stronger pulls).

I don’t think any of this is too profound, even if a picture would help.

So, let’s imagine that same stick in orbit around a half ball of ice and lead. From the molecules of the stick, the gravitational pull has now changed. The lines from the surface of the lead are longer and the lines from the surface of the ice are shorter. There is also a nasty edge that must be taken into account.

At the halfway point on our mixed sphere, for instance (this gives us a nice straight edge, making the geometry easier). From the center point on our stick, each point on this diameter line will be a balanced distance from the same point on the other side. If the half is ice, then the points will be father out, thus pulling less. If on the lead side, the center is going to be pulled on more by gravity.

From a calculation of points, we could see that density of material effects gravitational pull. So, when doing a gravity calculation, why is there no space in the equation for density of material? This is so that the calculation is simplified.

The early moon landing found that their orbit of the moon had some problems with a straight point gravity calculation. That is because the moon is not a homogeneous substance. It has heavy spots and light spots. As the capsule passed a light spot, the gravitational pull changed. When they passed a heavy spot, they needed to go faster to maintain the same altitude (orbit distance is based on speed vs. a gravitational pull). These perturbations in mass created unique shaped orbits.

If you’ve looked at a globe recently, you may have noticed that there are land masses interspersed with masses of water. Along the path of the moon, these differences in density will effect the rotation of the planet. As the poles melt and freeze, the amount of water on the lunar line vary. This variation changes the pull of gravity.

Add in the complication of tidal forces (where the planet AND the water move around) and you will see that calculating an accurate pull of gravity from moon to earth becomes very difficult.

I believe that variations in gravitational pull would cause the planet to alter it’s spin. This would not be noticeable over a short term, but along a great time line, the planetary rotation would pendulum.

This means that the forces would pull on the planet in the direction of the moon, until the planet catches up to the moon. Of course, angular acceleration effecting change would have to pull the rotation past a point of equilibrium (like pushing a pendulum). Past that equilibrium point, the earth would be rotating faster than the pull of the moon. So, the moon would begin to act on the earth counter to it’s rotation. This would begin to slow the planet. This slowing pull would effect the earth by pulling it backwards. This would go on until the angular momentum of the earth became slower than the moon (it could even stop, but doesn’t have to) before the rotation flows in reverse of the moons pull. This of course would pull the planet backwards until it passed equilibrium and started back in the forward direction.

At the same time this is going on, various parts of the planet are being pulled on (tectonic motion) and move around on that heavy floating core, which also rotates. So much movement!

Of course, we haven’t taken into account the pull of the moon on the planet. Did you know that the moon and sun are not on the same orbital path? That is why we don’t enjoy 2 eclipses a month. They form an x shape in space by plane of orbits. We only get to enjoy an eclipse when these two heavenly bodies cross, AND line up.

If they don’t line up, we get a partial eclipse.

Orbits are ellipses, so when the moon is close and the sun is far away, even if the orbits line up, all we get is an “annular eclipse.” For those that have seen a totality and annular totality, the difference is very important. That is because during an annular eclipse, there is a ring of sunlight around the moon, making it less impressive than in a totality. In a totality, it looks like there is a black hole where the sun used to be.