Terminal Velocity and the Flat Earth

I was just thinking about this, and wondering about an object's terminal velocity, and how it is explained in the Flat Earth Model.

Consider this:

On the round Earth model, every object has a point where they no longer accelerate towards the Earth. This is called the "terminal velocity." Obviously, this isn't exactly "explained" on the round Earth model all too well, but it's part of the magical force called gravity, I guess, which is relatively O.K.

However, on the flat Earth model, why would there be a terminal velocity? Wouldn't the Earth continue accelerating up towards an object indefinitely, meaning it would appear as if the object continued accelerating until it hit the ground?


A consideration that could possibly be taken into account would be the air underneath someone counteracting the acceleration at a certain point, but in that case, you'd have to make some adjustments to pretty much everything pertaining to the Earth's acceleration.

Any thoughts?

~D-Draw

If the air wasn't in the way, you could keep accelerating towards the earth.

That's the same reason why particle accelerators are vacuums.

Due to the General Theory of Relativity, that "gravitational force" you feel could actually be the acceleration of the Earth; you jump up, and the accelerating Earth smashes into you as you lose your acceleration due to air resistance. General Relativity states that accelerating reference frames and frames undergoing gravitational attraction are indistinguishable.

Due to the General Theory of Relativity, that "gravitational force" you feel could actually be the acceleration of the Earth; you jump up, and the accelerating Earth smashes into you as you lose your acceleration due to air resistance. General Relativity states that accelerating reference frames and frames undergoing gravitational attraction are indistinguishable.

Albeit true, I do have one problem: why isn't the Earth slowed by air resistance?  How much energy would be needed to keep it accelerating despite air resistance?

Because it's supposedly held in by their ice wall and it would then travel with the earth.

Wait.

So in a perfect, airless vacuum, you'd jump higher, if not hover?

Only if the earth wasn't accelerating, or gravity did not exist.

But with gravity, you'd still fall back, and with no gravity, you'd keep moving.

But if the earth is accelerating, from what Tom said, we wouldn't lose the acceleration by jumping but for the air resistance.

Tom's a liar, I proved that in another thread. Don't believe him.

But if the earth is accelerating, from what Tom said, we wouldn't lose the acceleration by jumping but for the air resistance.

Wait, if the air is accelerating with the Earth, why is there air resistance?

This is called the "terminal velocity." Obviously, this isn't exactly "explained" on the round Earth model all too well, but it's part of the magical force called gravity, I guess, which is relatively O.K.

Actually it is explained rather well, and it would work the same in either model. An object reaches terminal velocity when air resistance equals the objects weight, and so it stops accelerating.
In the round Earth model, air resistance increases because the object is moving faster and faster into the air (and thus hitting more air molecules in less time). In the flat Earth model, it increases because the air is moving faster and faster into the object. Either way it will have the same effect.

In the flat earth model, the earth is accelerating upwards. As it accelerates upwards, it pushes air along with it. The air cannot escape over the sides, because there is a wall/dome/infinitely wide earth keeping it from escaping. So the air is pushed along by the earth. This forms a pressure gradient, and therefore on each small bit of air, there are mismatched forces from the different pressures above and below, and these mismatched forces keep each bit of air accelerating at the same rate as the earth.

This explains the atmosphere.

If a skydiver jumps out of a plane (in the FE model), he moves via inertia, and since the air around him is accelerating, the air starts moving upwards faster than he is. Since there is a difference in relative speeds, friction with the air exerts a force on the sky diver roughly proportional to the difference in speeds. When the difference in speeds is great enough, this force causes an acceleration which is exactly equal to the rate at which the flat earth is accelerating, and so the relative speed between the earth and the skydiver stays constant (until the skydiver opens his parachute, changing the constant, and causing the skydiver to reach a new terminal velocity until he reaches the earth).

This is the FE explanation for terminal velocity.

Ah. You see, I learn something new every day, here. Thanks for the explanations.

~D-Draw

But if the earth is accelerating, from what Tom said, we wouldn't lose the acceleration by jumping but for the air resistance.

Well, Tom is not correct.  As soon as you left the earth, you would stop accelerating and would continue on at a constant velocity (neglecting air resistance).

"Neglecting air resistance"?  You mean to tell us that there is air in this spacial region off the edge of the Earth?

And what mechanism, precisely, is responsible for the continuous upward acceleration of the entire planet?

And what mechanism, precisely, is responsible for the continuous upward acceleration of the entire planet?

We call it the Universal Accelerator. No, we can not explain how it works, we can only observe its effects. Like Round Earthers and their "gravity".

Newton's Law states that momentum is conserved, and the gravitational force in the classical model doesn't violate this principal.  Your universal accelerator, however, does, because it's accelerating everything upwards and nothing downwards.  As a result, you're throwing most of classical mechanics out the window without even realizing it.

The problem isn't that the idea is absurd (even though it is absurd).  There are plenty of modern theories which started off as absurd hypothesis.  The difference between them and yours is that the other hypothesis at least had a coherent model that built on existing observations.  None of them required massive conspiracy and the rejection of huge quantities of scientific observation to remain.

"Neglecting air resistance"?  You mean to tell us that there is air in this spacial region off the edge of the Earth?

No, I was talking about being on the earth.  But if you jumped off the edge, you would just continue at a constant velocity, while the earth continued to accelerate.

Hold on, wait a second.

I thought you guys called it the "universal accelerator".  If a human being who jumps off the side of the Earth falls, then what, exactly, is being accelerated?  We know that the stuff of which the Earth is made falls straight down as far down as we have mined, which is miles down in some cases.  What's affected by the "universal accelerator"?

Newton's Law states that momentum is conserved, and the gravitational force in the classical model doesn't violate this principal.  Your universal accelerator, however, does, because it's accelerating everything upwards and nothing downwards.  As a result, you're throwing most of classical mechanics out the window without even realizing it.

The problem isn't that the idea is absurd (even though it is absurd).  There are plenty of modern theories which started off as absurd hypothesis.  The difference between them and yours is that the other hypothesis at least had a coherent model that built on existing observations.  None of them required massive conspiracy and the rejection of huge quantities of scientific observation to remain.

The only way to get conservation of energy in classical mechanics is to introduce a "gravitational potential energy" term which exists because it has to for energy to be conserved, and no other reason. One could just as easily get conservation of energy/momentum in the FE model by introducing similar terms. And how do you know that there is not matter elsewhere which is accelerating downwards to counter the acceleration of the earth and conserve momentum?

And how do you know that there is not matter elsewhere which is accelerating downwards to counter the acceleration of the earth and conserve momentum?

It's not in the FAQ. And the FAQ is all knowing. :roll:

skeptical:

You get conservation of energy in classical mechanics because a gravitational force field is a conservative vector field.  It takes energy to move upwards in a gravitational field--or, in an accelerative model, it takes energy to resist the acceleration due to this "Universal Accelerator".  In any case, a la Einstein, because a gravitational acceleration is indistinguishable physically from a linear acceleration, the physical rules of potential energy and conservation of energy must hold in both cases.

The amount of energy it takes to raise an object up [d] meters in Earth's gravity field at sea level, assuming a small value of [d], is [mgd].  Thus, an object m1 at height d1 has [m1gd1] - [m2gd2] more energy than an object m2 at height d2.  The difference in energies between an object and a given rest object is referred to as potential energy.

And, believe it or not, potential energy exists in other aspects of science, too.  Any linear harmonic oscillator works because of the sinusodial conversion of potential energy into actual energy, and back.

Consider this:  You have a mass hanging vertically on a spring.  This mass is oscillating up and down with SHO motion.  At the point of equallibrium, the object is moving the fastest, with a kinetic energy of (mv^2)/2.  If there is no such thing as gravitational potential energy, then where is the energy coming from when the object is at the node of its oscillation?  Where does the energy go when it's at an antipode?

To answer the second part of your question, if there is matter accelerating downward elsewhere, then what is the means by which that matter is being accelerated?  Where is it?  Are there giant thrusters under the Earth's surface emitting huge quantities of matter?

Lastly, we can MEASURE the existence of the gravitational force.  As a matter of fact, Newton himself did it when he proposed its existence.  It is extremly difficult because the force is so very weak, but here is the general idea:  Take a large, massive, balanced armature and suspend it by a thin strand.  Take another larger object and put it near one end of the armature.  Ground both elements and hermetically seal the whole apparatus.  Wait a few days, and measure the angular deflection.

skeptical:

You get conservation of energy in classical mechanics because a gravitational force field is a conservative vector field.  It takes energy to move upwards in a gravitational field--or, in an accelerative model, it takes energy to resist the acceleration due to this "Universal Accelerator".  In any case, a la Einstein, because a gravitational acceleration is indistinguishable physically from a linear acceleration, the physical rules of potential energy and conservation of energy must hold in both cases.

The amount of energy it takes to raise an object up [d] meters in Earth's gravity field at sea level, assuming a small value of [d], is [mgd].  Thus, an object m1 at height d1 has [m1gd1] - [m2gd2] more energy than an object m2 at height d2.  The difference in energies between an object and a given rest object is referred to as potential energy.

And, believe it or not, potential energy exists in other aspects of science, too.  Any linear harmonic oscillator works because of the sinusodial conversion of potential energy into actual energy, and back.

Consider this:  You have a mass hanging vertically on a spring.  This mass is oscillating up and down with SHO motion.  At the point of equallibrium, the object is moving the fastest, with a kinetic energy of (mv^2)/2.  If there is no such thing as gravitational potential energy, then where is the energy coming from when the object is at the node of its oscillation?  Where does the energy go when it's at an antipode?

Isn't this just a very long-winded and unnecessarily detailed way of saying, "The only way to get conservation of energy in classical mechanics is to introduce a 'potential energy' term which exists because it has to for energy to be conserved, and no other reason"?

To answer the second part of your question, if there is matter accelerating downward elsewhere, then what is the means by which that matter is being accelerated?  Where is it?  Are there giant thrusters under the Earth's surface emitting huge quantities of matter?

What is the means by which mass curves spacetime in its vicinity? Does every subatomic particle have a little tiny torque wrench that it uses to tighten and loosen the nuts and bolts holding together the fabric of space? Or is it fair to say that science, with the billion dollars spent on research, simply has some unanswered questions still. Is it so unreasonable to allow FE theory, with exactly zero dollars in government research grants, to put forth a model that explains gravity, but leaves some unanswered questions?

Lastly, we can MEASURE the existence of the gravitational force.  As a matter of fact, Newton himself did it when he proposed its existence.  It is extremly difficult because the force is so very weak, but here is the general idea:  Take a large, massive, balanced armature and suspend it by a thin strand.  Take another larger object and put it near one end of the armature.  Ground both elements and hermetically seal the whole apparatus.  Wait a few days, and measure the angular deflection.

Here we have a decent argument, and I don't think that FE theory has an answer for it, at least not unless they ditch the "accelerating upwards" model (which would be a shame, as it is delightfully effective at demonstrating how ignorant the majority of REers on this website are in the area of physics) and replace it with something else, perhaps the infinite flat plane earth, which would nicely exert a constant downward force according to RE models of gracity.

My "unnecessarily long-winded explanation" was making a point that you oversimplified and missed as a result.  It should have been obvious from my posting that my point was that conservation of energy is a consequence of the shape of a gravitational field.  A gravitational field can be considered conservative because there is no closed path in an object may take in this field which will leave the object with more energy than it had to begin with.  ALL physically consistent fields are conservative vector fields.  The concept of potential energy is simply a handy tool for physicists to use for open paths--that is to say, paths which do not end up where they started--but the mathematical concept of conservation is in no way dependent upon it.

The problem with Flat Earth isn't that you're providing a hypothesis which has some loose ends.  The problem is much broader than that.  The problem is that you're trying to replace a prevalent, and repeatedly verified scientific theory with a crappy, incomplete hypothesis that relies more on conspiracy than scientific inspection.

And I'd grudgingly admit that most of the people in here I've seen advocating round Earth don't seem to have a very good grasp of physics.  The fact that FErs have a better idea of Newtonian and even Einstenian mechanics is disturbing.

My "unnecessarily long-winded explanation" was making a point that you oversimplified and missed as a result.  It should have been obvious from my posting that my point was that conservation of energy is a consequence of the shape of a gravitational field.  A gravitational field can be considered conservative because there is no closed path in an object may take in this field which will leave the object with more energy than it had to begin with.  ALL physically consistent fields are conservative vector fields.  The concept of potential energy is simply a handy tool for physicists to use for open paths--that is to say, paths which do not end up where they started--but the mathematical concept of conservation is in no way dependent upon it.

All this means is that it is possible to define a potential energy function without running into internal contradictions. It is, as you say "a handy tool" that comes out from defining a quantity to make things work nicely. My point is that if momentum is not conserved, you could define an additional term, analogous to the definition of potential energy, to make momentum be conserved, and then we would get a nice consistent statement for a certain physical law. Since this is essentially what we do with energy, what would be the problem with doing it for momentum as well, assuming the resulting "law" yields correct results?

And I'd grudgingly admit that most of the people in here I've seen advocating round Earth don't seem to have a very good grasp of physics.  The fact that FErs have a better idea of Newtonian and even Einstenian mechanics is disturbing.

This has a lot to do with the fact that they're all pretty bright people who are acting as devil's advocates, and don't actually think the Earth is flat.

The problem with Flat Earth isn't that you're providing a hypothesis which has some loose ends. The problem is much broader than that. The problem is that you're trying to replace a prevalent, and repeatedly verified scientific theory with a crappy, incomplete hypothesis that relies more on conspiracy than scientific inspection.

That's the problem with acting as a devil's advocate for a theory which is quite clearly unrealistic. The best you can do is make it as realistic as possible leaving as few loose ends as possible, and sometimes make sacrifices in the interests of humor (how did you think the bit about the elephants and the tortoise ended up in the FAQ anyways?) or making REers look stupid, which is the main reason we're all here anyways.

skeptical:

I didn't realize.  Thanks for the information.

And you are right about adding a single constant to everything to make the conservative fields work out nicely.  It's called regauging.  The problem, though, is that regauging has to operate on everything--including the rocks and things.  Universes with different gauges for acceleration (or momentum) don't behave differently; a gauge is relevant only for a frame of reference.

I thought you guys called it the "universal accelerator".  If a human being who jumps off the side of the Earth falls, then what, exactly, is being accelerated?  We know that the stuff of which the Earth is made falls straight down as far down as we have mined, which is miles down in some cases.  What's affected by the "universal accelerator"?

We aren't sure. None of the elements we have discovered so fare are affected by it, because anything that was would appear to float.

I am not sure if the FET has anything to say on this, but I am inclined to think that it is only one elements that is effected by the UA. I believe that this element makes up the bottom of the Earth.

CodeMercenary:

Perhaps an even better analogy would be the following:
Sometime in the 1920s, Arthur Compton must have had a train of thought that went something like this:
"Holy smokes! Momentum is not being conserved. But wait, that doesn't make any sense, momentum is a conserved quantity, so it must be conserved. How shall I resolve this paradox? Perhaps photons carry some momentum? That would explain my data... But photons are massless objects, so their momentum by the conventional definition is zero. Well, I'll define their momentum anyways, and everything comes out, so we'll just go with it."

So what's wrong (in principle) with FEers saying that if the FE accelerates, then either there is some mass (somewhere we don't know about) accelerating in the opposite direction so that momentum is conserved, or else we need to broaden the definition of momentum so that momentum will be conserved, just as Compton broadened the definition to include massless particles.