"Lazy is wonderful."
THE DAILY ASTRONOMER
Today, being rather more inclined to be outside enjoying this sublimely Dantean heat, I decided just to talk to you, instead of actually writing anything. Yes, I've done that before. In fact, you're welcome to join me on my lovely little stroll.
When I eventually discuss this matter in a DA. I probably should explain a few terms, since in modern parlance, the words "velocity" and "acceleration" are often used synonymously. We refer to this stone's location, now resting on the fragrant wood chips lining the trail, as "position." The change in the stone's position is called "velocity." Right now, it is not moving relative to the ground so its velocity is zero. Mind you, it is on an orbiting planet, so it is moving relative to the Sun and the stone is in a solar system moving around the galactic nucleus, so it is moving relative to the gaalctic plane. One must always specify an object's velocity relative to something else. Finally, "acceleration" measures the change in an object's velocity.
We generally think of acceleration as causing an object's velocity to increase. However, it can cause a decrease as well. As the stone rose and fell, it was constantly accelerating toward the ground at a certain rate, which is approximately 10 meters per second per second. So, if I had thrown the stone upward at 10 meters per second, the stone would ascend for only one second until coming to rest. It would then continue to accelerate downward and, had I actually caught the damn thing, the stone would have returned to my hand at the velocity of 10 meters per second.
In the stone example, the accleration is constant, while the velocity is always changing. This example leads us neatly to the next issue. How someone falling through Earth can experience different accelerations, including no acceleration at the core and why the acceleration is maximum at the rims of both holes.
The stone experiences constant acceleration because Earth's matter remains below it as it falls. The acceleration toward the ground, known properly as "surface gravity," is constant because the amount of matter pulling on it doesn't change. Every particle on Earth attracts it. Now, if we dropped this stone through the hole in yesterday's example, all of the planet's matter would be below it when we first dropped it in the hole. However, as it falls, the stone will have increasingly more matter above it. This matter will exert an upward pull or acceleration. As the stone approaches the core, this upward pull will increase because there will be increasingly more material above it. The downward acceleration will slowly decrease due to the upward acceleration. When the stone reaches, the core, there will be as much matter above it as below it. The accelerations counterbalance and equal zero for just a moment. However, the stone's been accelerating, but at a continuously decreasing rate, during its descent toward the core, so it is still moving. As it passes the core and moves toward the south pole, the upward acceleration will continue to increase as the downward acceleration decreases. The stone's velocity will eventually decrease until it comes to rest at the rim of the south pole hole. It then falls back toward the north pole.
In the first example of the stone rising and falling on Earth's surface, the acceleration was constant. In the second example, the acceleration was always changing. In both examples, the stone's velocity was always changing under the influence of both the constant and variable accelerations.
When I eventually decide to write the DA to explain the difference, I hope it will make sense. But, then again, I don't have to worry about that...not just yet.
You know, it is afternoons like this, when the sky arcs over the distant hills and the clouds seem as phantoms behind the thick haze that one feels as though the deep summer heat has, ironically, frozen time. So that the world will remain forever steeped in this exquisite dream state. Yes, I know you know that's impossible. Some things are better left unsaid.