Regarding the constant terms, I believe that they are units necessary for measurement and I perceive them as units not as orbital quantities.

I was thinking that in F/M = a something strange happens. Both F and M are eliminated, so, if F/M = a were to be a ratio a should vanish with them, but it doesn’t. There is hidden in a the ratio R/T^2, which to me, is not the Newtonian acceleration but density at R, because T is not time but period.

So, the sling-type rotational “acceleration” that Newton projected to Keplerian orbit cancels because there is no such acceleration in the orbit but R/T^2 remains because it is not the “centripetal acceleration” supposed by Newton but density at R. I’m still trying to understand this, so, I appreciate the comments.

You cannot quantify “Newtonian mechanics” because it does not have a unit and it’s not a quantity but you may say “Newtonian force predicts orbits” and that’s a scientific statement and it can be discussed on scientific grounds.

That’s moronic. “Newtonian force predicts orbits” is a ridiculous thing to say. Force doesn’t predict anything, because it’s a quantity, and quantities can’t predict. Newtonian Mechanics is a system of equations into which you can feed information about the universe and a time parameter and it will tell you where everything will be at that time and how fast it will be moving. That is predicting the motion of objects. I cannot fathom how you could question this fantastically simple notion.

If you agree that a given problem f(x,y) is independent of z, then you must agree that any given problem f(x,y) is independent of z.

I don’t see why. Take friction.

If I drag a book along a table, then I have to overcome friction. Friction is equal (we’ve tested this) to the weight of the object being dragged multiplied by a number which varies from material to material, called mu. It doesn’t depend on the area of contact, although one might think that it did.

It seems more intuitive to say it’s pressure times area times mu, but since pressure is weight over area, the areas cancel. But you can’t say that the problem is independent of the area because if the area wasn’t there then there would be no friction.

It’s an analogy: the maths is quite different for forces in orbits, but I doubt you have the ability to understand the distinction anyway, because you are a dullard.

When physicists say that “the orbit is independent of mass” but they refuse to admit that “the orbit is independent of force” they are practicing the old scholastic art of casuistry.

Unfortunately, no, they’re just better at maths than you.

Because when you say a=GM/r^2, all of that equals F/m. The orbital period (T) equals 2*pi*sqrt(a^3/GM), which is 2*pi*sqrt(F^3/GMm^3), which is clearly not independent of F.

The m isn’t important: F is proportional to m, so any changes you make to m are canceled by the resulting change to F, since F=GMm/r^2. Since F is defined by m and a, it makes no sense to ask a question like “what if you double F?”. F=ma. If you change the orbit, a changes and so does F. There’s no escaping it. F and a, and therefore F and the orbit, are intrinsically linked. You just don’t need to mention F to calculate the orbit.

For example, the volume of a cube is l^3, and the density is m/v, so you don’t need to know l. In fact, you never need to know l, because it’s always just cube root v, but you can’t say that density is independent of l, because it equals m/l^3 — clearly a function of l.

You eliminate the term F but you claim that “it’s still there.”

I eliminate it from one equation. It sticks around in other equations. All the equations have to be true all of the time, not just the one we’re looking at. For example, if we look at pendulums, the speed of the bob depends on its weight and the distance it’s swinging, but if we were to take a Kepler-style equation, we would find that T = k*sqrt(L), where L is the length of the string. But since the bob is moving, it has a speed, and that depends on its mass. And T is really only a property of that movement. It’s absurd to say that the swing is independent of speed or mass or distance, just because there are equations that those numbers aren’t in.

Focussing purely on orbits is like focussing purely on T of a pendulum.

Regarding your algebraic manipulations of F=ma and F=GMm/R2: Let’s draw a line in physicists’ derivation of Kepler’s rule from definitions of force. This is the line separating formulas where force terms appear and the formulas where force terms do not appear. The line passes through the equation where F and F are equated to each other to eliminate them by saying F=F. Therefore, anything above F=F is metaphysics.

I’m afraid that’s total nonsense.

In physics, force is the universal cause of everything.

No, it isn’t.

Nature is telling you that your assumption that m is an orbital quantity is wrong.

The phrase “orbital quantity” is one you have just made up and one which doesn’t mean anything.

you include it in the derivation but then you have to eliminate it because nature does not care about Newton’s authority.

No, I include it in the derivation because it appears in Newton’s Laws and Newton’s Laws are what I am deriving from. Manchester doesn’t appear in Leeds, but if you want to give directions from Manchester to Leeds, the first will be “drive out of Manchester”. I eliminate it because it cancels. Eliminating it was never the aim, nor was keeping it. Derivation goes where it wants.

Since mass cancels out of equations it must be a label for something else. What is that thing Newton defined as mass? It is R3/T2.

That’s really not true: I have mass and I’m not orbiting anything, so I have no R or T. Mass is a property of matter.

Newton labeled the proportionality R3/T2 “mass.”

None of that made any sense.

R3/T2 remains in the equation. (Actually, it is the equation.)

No, it’s an expression. Equations contain an equals sign. That’s why they’re called equations. Because they equate things.

he planet does not have a property called mass

It does. The gravity felt by people on the planet is equal to its mass times G/r^2, where r is the planet’s radius.

Newton defines mass as a “measure” of matter. He never says mass is a property of matter.

That’s purely a matter of semantics and depends on your definitions. Either is correct if you’re consistent.

Therefore, people living on that planet will notice changes only if you change density

That’s not true at all. If you double the radius and keep the density the same, then gravity on the surface will double. You can’t eliminate M by introducing density.

You are describing the underlying proportionality R3/T2 by using superfluous Newtonian authority terms that you know you will eliminate.

Yes, I am. And that doesn’t make me wrong.

you are confusing yourself by using the same label f for both GM/r2 and ma.

That’s like saying you’re confusing yourself by using the label 5 for 1 4 and 2 3. The whole point in defining something like F is that all the equations for F must hold FOR THE SAME F. If you think equating two instances of F is wrong then no wonder you’ve not understood this.

Then you are an exception among physicists in your belief that force is not instantaneous action-at-a-distance. That the Newtonian force is defined as instantaneous action-at-a-distance is well established.

I am not an exception. You are merely ignorant. Newton thought force caused instantaneous action at a distance, in fact it’s just very-nearly-instant. We still use the instant equations because it’s much easier and they’re close enough for all practical purposes we’ve yet discovered. And we call that approximation “Newtonian Physics”. It’s not right, but it’s damn useful, and it can be derived from what is right if you approximate c to infinity.

I respect your belief in instantaneous action-at-a-distance. You can invoke it to explain commercializations of the occult such as done by Uri Geller.

Uri Geller is a fraud and not a good one.

To me instantaneous action-at-a-distance doesn’t exist by principle. When I look at magnetism I say I don’t know enough about magnetism to say what it is because I haven’t studied it in depth but I know by principle that it is not instantaneous action-at-a-distance. To me this is the scientific view.

That is not remotely scientific. Not least because instantaneous action at a distance exists: look up quantum entanglement.

Also note that, unlike gravity, magnetism can be shielded, therefore, I don’t think that magnetism propagates instantaneously. So your analogy does not hold.

No, magnetism travels at lightspeed just like gravity. Just like all forces.

Now you are assuming that Newtonian gravity in the formula F=GMm/R2 travels with the speed of light. It doesn’t. By definition, in Newtonian physics, if the sun disappeared now, you would know it now, not eight minutes later. What is the scientific conclusion that I reach from this? I say Newton’s force is absurd because it travels instantaneously and I dismiss it. And what is your conclusion? You pretend that Newtonian force travels with the speed of light to save Newton’s authority.

Newton thought force was instant. All his equations assume that it is. We still use them because the nearly-right simple equations are more useful than the accurate needlessly-complicated ones. I have never pretended that the approximate intant ones are true.

You don’t need to invoke general relativity to refute instantaneous action-at-a-distance. There is a more fundamental reason: Instantaneous action-at-a-distance violates laws of thermodynamics. If instantaneous action-at-a-distance existed you could build perpetual motion machines.

That’s patently untrue. There is no connection between locality and thermodynamics. If you have found one, please explain it.

In your previous paragraph you proved how Newtonian force violates locality and thermodynamics. Now you are assuming that the same force still exists and holds orbits together. Once you eliminate force on the grounds that it violates laws of physics then all its manifestations such as holding orbits will be gone too. This is the same assumption you’ve been making in regards to equations: force is eliminated but it must remain to fulfill Newton’s doctrines.

INSTANT force violates locality (not thermodynamics). And INSTANT force doesn’t exist. NEARLY-INSTANT force does exist but does not violate locality (or thermodynamics). What is the problem here?

Do you know how John Anderson computes the Voyager anomaly? He takes residuals between computed positions and the actual positions computed from radar echos sent by the spacecraft. Nothing “Newtonian” enters into computations. He then translates the discrepency between computed and observed values into Newtonian language and sends out a press release.

I don’t know or care what you’re talking about or what point you hope to demonstrate by this. Anderson can do what he wants for all I care, and I suspect you’re hopelessly misrepresenting him.

Physics deals with physical quantities. Anything which is not a physical quantity is metaphysics. Qualitative metaphysical statements such as “Newtonian mechanics accurately predicts how objects will move . . . ” is outside of physics. “Newtonian mechanics” is not a physical quantity therefore it cannot predict anything in physics.

And it is wrong to say that “force is not physically manifest.” On the contrary, force is a physical quantity. A physical quantity is defined as a number multiplied by a unit. You cannot quantify “Newtonian mechanics” because it does not have a unit and it’s not a quantity but you may say “Newtonian force predicts orbits” and that’s a scientific statement and it can be discussed on scientific grounds.

Your claim, then, is a tautology.

That statement was written to make clear to physicists that casuistry does not belong to physics. If you agree that a given problem f(x,y) is independent of z, then you must agree that any given problem f(x,y) is independent of z. But in physics f(x,y) is independent of z as long as z is not force. In physics Newton’s authority comes before scientific principles. When physicists say that “the orbit is independent of mass” but they refuse to admit that “the orbit is independent of force” they are practicing the old scholastic art of casuistry.

You can stop writing it, but it’s still there.

You eliminate the term F but you claim that “it’s still there.” In mathematics if a term appears on both sides of an equation we eliminate that term, e.g., we can eliminate m in ma=m/r2 to get a = 1/r2. To be a scientist means that when you eliminate a term that term is gone without a trace. There are no ghost terms in mathematics. If Newtonian doctrine breaks down when you eliminate a term you must still uphold the authority of mathematics and ignore what Newton says. This is science, not metaphysics ruled by authority. Only medieval doctors of philosophy go into deep discussions about the properties of terms that do not exist in the equations. Such invisible terms, such as force, have a technical term in scholasticism, they are called dormitive virtues. You don’t believe force is a physical quantity that is gone when it is eliminated but you make it a dormitive virtue that appears and disappears as you need it. All this to save Newton’s authority.

. . . F=ma and F=GMm/r^2. Therefore ma=GMm/r^2. . .

Regarding your algebraic manipulations of F=ma and F=GMm/R2: Let’s draw a line in physicists’ derivation of Kepler’s rule from definitions of force. This is the line separating formulas where force terms appear and the formulas where force terms do not appear. The line passes through the equation where F and F are equated to each other to eliminate them by saying F=F. Therefore, anything above F=F is metaphysics. Your arguments about force, such as how doubling force will double mass and so on are metaphysical arguments on Newtonian vaporware F and m so that you can say force F really exists in GM/R2 = a even though there is no F in GM/R2 = a.

But, as a physicist, you don’t have to rationalize the existence of force in GM/R2 = a. In physics, force is the universal cause of everything. Force is not visible in GM/R2 = a but for Newtonian physicists it is still there because the world is permeated by Newton’s force as proved by Newton’s laws.

Of course, you could argue that doubling the mass of the planet won’t make any difference since the orbit is independent of m . . .

Nature is telling you that your assumption that m is an orbital quantity is wrong. You assume that mass is an orbital quantity to save Newton’s authority and you include it in the derivation but then you have to eliminate it because nature does not care about Newton’s authority. The conclusion must be that orbits are independent of m. But then you notice that even though m is gone the planet itself is still there.

Since mass cancels out of equations it must be a label for something else. What is that thing Newton defined as mass? It is R3/T2. In definition 1, Newton defined quantity of matter or mass in terms of density: mass = volume * density. This is a description of Kepler’s rule R3/T2. Therefore, Newton labeled the proportionality R3/T2 “mass.” We know that Kepler’s rule is the definition of density and orbits are described by Kepler’s rule and therefore orbits are not independent of density for a given volume. So the label m is eliminated but R3/T2 remains in the equation. (Actually, it is the equation.) The planet does not have a property called mass distinct from R3/T2. This becomes clearer if you read Newton’s definition. Newton defines mass as a “measure” of matter. He never says mass is a property of matter. So Newton is not stupid but people who came after Newton didn’t pay attention and made mass a property of matter and they keep writing it in order to eliminate it.

Therefore, people living on that planet will notice changes only if you change density, i.e., if you change either radius R or period T, because these are the only orbital parameters, not F, not m. For instance, R/T2 is the density at R, or the surface gravity of the planet, and it varies as 1/R2. You cannot change the surface gravity of a planet without changing its orbit. I think by your own example you proved that F and m are irrelevant in orbit calculations.

The acceleration is not proportional to the planet’s mass because force is and that balances the equation. But it is proportional to the force, because objects’ masses don’t change.

You are describing the underlying proportionality R3/T2 by using superfluous Newtonian authority terms that you know you will eliminate. This is metaphysics because you are arguing that F is proportional to m but neither is an orbital parameter.

f :: m is irrelevant because both f and m are eliminated. In the case of a :: f, you are confusing yourself by using the same label f for both GM/r2 and ma. Your a :: f is nothing other than R/T2 :: 1/R2 hidden under Newtonian symbolism. Next time you can start directly from R/T2 :: 1/R2 and you wouldn’t have to write and eliminate superflous authority terms.

No, I’m saying [force] not supernatural or occult.

Then you are an exception among physicists in your belief that force is not instantaneous action-at-a-distance. That the Newtonian force is defined as instantaneous action-at-a-distance is well established.

Have you ever seen a magnet? Those can do action at a distance.

This is a matter of principle. By principle, I believe that instantaneous action-at-a-distance does not exist in nature. Similarly, I believe that perpetual motion machines do not exist. If you claim that you invented a perpetual motion machine I would dismiss it on principle. But I respect your belief in instantaneous action-at-a-distance. You can invoke it to explain commercializations of the occult such as done by Uri Geller. To me instantaneous action-at-a-distance doesn’t exist by principle. When I look at magnetism I say I don’t know enough about magnetism to say what it is because I haven’t studied it in depth but I know by principle that it is not instantaneous action-at-a-distance. To me this is the scientific view.

Also note that, unlike gravity, magnetism can be shielded, therefore, I don’t think that magnetism propagates instantaneously. So your analogy does not hold.

Ah, but [the orbit] does [care.] If the sun vanished instantly . . . we wouldn’t know for eight minutes.

Now you are assuming that Newtonian gravity in the formula F=GMm/R2 travels with the speed of light. It doesn’t. By definition, in Newtonian physics, if the sun disappeared now, you would know it now, not eight minutes later. What is the scientific conclusion that I reach from this? I say Newton’s force is absurd because it travels instantaneously and I dismiss it. And what is your conclusion? You pretend that Newtonian force travels with the speed of light to save Newton’s authority.

Anything else would be a violation of locality. . .

You don’t need to invoke general relativity to refute instantaneous action-at-a-distance. There is a more fundamental reason: Instantaneous action-at-a-distance violates laws of thermodynamics. If instantaneous action-at-a-distance existed you could build perpetual motion machines.

After that we’d fly off at a tangent. . .

In your previous paragraph you proved how Newtonian force violates locality and thermodynamics. Now you are assuming that the same force still exists and holds orbits together. Once you eliminate force on the grounds that it violates laws of physics then all its manifestations such as holding orbits will be gone too. This is the same assumption you’ve been making in regards to equations: force is eliminated but it must remain to fulfill Newton’s doctrines.

Whatever you think of them, Newton’s Laws make very specific predictions about how planets will behave.

See my response to your first point above. “Newton’s laws” and “Newtonian mechanics” are names of a consistent system of units developed over many centuries. Newton’s laws is not a physical quantity. Newton’s laws can make no predictions because they are metaphysical definitions. In physics only physical quantities are used, the rest is metaphysics.

We’re not really sure what’s up with the Voyager probe. . .

Do you know how John Anderson computes the Voyager anomaly? He takes residuals between computed positions and the actual positions computed from radar echos sent by the spacecraft. Nothing “Newtonian” enters into computations. He then translates the discrepency between computed and observed values into Newtonian language and sends out a press release.

For circular orbits, my recollection is that “R/T^2 = k a” where “k” is a constant, maybe “(2 pi)^2″.

I think that Kepler’s second law supports the claim made in the post that orbits are not sling-type rotations created by hurling objects and keeping the radius constant as assumed by Newton. For circular orbits Kepler’s second law is an assertion of uniform motion. But still, increasing R will keep the areas proportional by the third law, as far as I understand. If we have two orbits s, r and S, R then R^2/r^2 = s^2 r/S^2 R. I would appreciate comments/corrections.

To get acceleration in Kepler’s laws, you have to deal with a law that relates time with orbits. That would be the 2nd law, the one that says the line connecting the planet and the sun sweeps out equal areas in equal times. Turning this into a statement about acceleration might be arduous but should be possible.

Either that or Kepler’s laws do not fully describe the orbit.

I just wanted to clarify that I have no issue with physicists using Newton’s laws. … I am objecting to using the consistency of this system to argue that force must be true because “Newtonian mechanics works.”

Your case, as I understand it, then, is: “Newtonian mechanics accurately predicts how objects will move, but force is not physically manifest”. Is that right? I’m not sure if that position really means anything.

I am making a very simple and specific claim: If a given problem is independent of a term that problem is independent of that term.

Your claim, then, is a tautology. How pointless you are.

They eliminate a term, such as mass m, from orbit calculations and say that “mass m is eliminated, therefore, the orbit is independent of m.” I’m saying that force F is eliminated from orbit calculations therefore orbits are independent of force F.

The thing is, though, that although the F cancels, it’s not really true that the orbit is “independent of F”. You can stop writing it, but it’s still there. F=ma and F=GMm/r^2. Therefore ma=GMm/r^2. But we can also write ma=GMm/r^w=F. Then when we cancel the m, we have to say a=GM/r^2=F/m. If we double the planet’s mass then GMm/r^2 doubles, so F doubles, so F/m stays the same. Therefore a and GM/r^2 stay the same, too. Since a is all we’re really interested in, the orbit is independent of m.

If you double F, then ma doubles and GMm/r^2 doubles. This means you have to double the mass of the planet, the mass of the star, or the gravitational constant, or divide the radius by root 2. Of course, you could argue that doubling the mass of the planet won’t make any difference since the orbit is independent of m, but the people on that planet will suddenly notice that everything weighs twice as much as it used to and it’s suddenly the days last longer.

It’s a subtle distinction. I can quite see how you’d miss it — I had to think pretty hard to articulate it just now. The acceleration is not proportional to the planet’s mass because force is and that balances the equation. But it is proportional to the force, because objects’ masses don’t change.

Newtonian physics uses action-at-a-distance Newtonian occult force to describe orbits. Are you saying that Newtonian force is not a part of physics?

No, I’m saying it’s not supernatural or occult.

What makes force a quantity unsuitable to model nature is the fact that it is defined as action-at-a-distance. If you are assuming action-at-a-distance your model will not work. There is no action-at-a-distance in nature.

Have you ever seen a magnet? Those can do action at a distance. You can drag a paperclip around with them without touching the paperclip. If you rub a plastic rod vigorously enough with a soft cloth, you can charge it up and bend the stream of water coming out of a tap with it. How can you explain these without invoking some kind of action-at-a-distance?

The so-called “Newtonian forces” do not enter the orbital formulas. We eliminate the force terms. The orbit does not know and does not care if F moves with the speed of light or instantaneously. F is not a factor in orbit computations.

Ah, but it does. If the sun vanished instantly (which it won’t), we wouldn’t know for eight minutes. We’d keep seeing it in the sky, and keep feeling its heat. And we’d keep orbiting the spot where it was for eight minutes. Anything else would be a violation of locality, a prediction of general relativity. I don’t know if this has been tested specifically yet, but that’s what the current thinking says would happened and we’ve certainly not falsified it.

After that we’d fly off at a tangent, since M now equals zero, so GMm/r^2=0, therefore ma=0 therefore a=0 so we just keep going in a straight line (that’s what a=0 means).

This answers more or less every statement in your post, so that’s why I’ve not quoted much of this one.

“A planet behaving in a way other than the Newton’s laws say it should. . .” is a meaningless statement.

No, it’s not. Whatever you think of them, Newton’s Laws make very specific predictions about how planets will behave. “A planet behaving in a way other than the Newton’s laws say it should. . .” means a planet whose behaviour does not match those predictions. We’ve never found a planet (or indeed anything at all) which does not follow those predictions. (We’re not really sure what’s up with the Voyager probe, but we’re not going to write off the whole of mechanics until we’re sure what’s up with it.)

Do you see any “Newton’s laws” in R3/T2?

That is a meaningless statement. Well, question.

Force does not appear in the simple formula we consider in this discussion to describe simple orbits.

Neither does Brazil. Does Brazil exist?

In this discussion orbits are assumed to be circular and on the plane of the ecliptic and we will not compute precise orbits here. We are only comparing R3/T2 and GM/R2 = a.

So your argument is: “if we ignore everything except orbits, then assume all orbits are circles which they’re not, then we can eliminate a letter from the equation and if we do that and employ a little sophistry then we can pretend it doesn’t exist”. You’re a moron.