THE SOUTHWORTH PLANETARIUM
207-780-4249 www.usm.maine.edu/planet
70 Falmouth Street Portland, Maine 04103
43.6667° N 70.2667° W
Founded January 1970
"Lazy is wonderful."
*THE DAILY ASTRONOMER*
*Tuesday, July 19, 2016*
*Accelerating*
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.
Yesterday someone wrote us in reference to the second Pandora question, the
one about falling through Earth. A couple matters bothered the reader.
One, the concept of the person coming to rest at the south pole for a
moment while at the same time being at the point of maximum
acceleration. How can something at rest be accelerating? Also, as the
guy descends, how can he accelerate toward zero acceleration at the core?
You know, I think that is why I love Pandora's Jar so much. It is similar
to Almathea's goat horn that which was self-replenishing and
inexhaustible.
I think the best way to address the first question is to use the example of
this stone right by your foot. I'm going to lift it in my hand and toss
it straight up. Watch what happens. Yes, I know you know what's going
to happen. The stone is going to travel upward a certain distance and as
it ascends, its velocity will decrease until it reaches its maximum
height. It will then by a rest for a moment before descending back to my
hand....well, ok, back to the ground. During that entire time, from
the moment the stone leaves my hand to the time it returns to the ground,
it experiences a downward acceleration resulting from Earth's gravitational
pull. Here, we see that a stone can be at rest and still be accelerating.
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.