User talk:Donteras

Newton's gravity

Hi Donteras. Talk pages are not intended for general discussion about the topic of an article, but are there specifically for discussing possible improvements to the article itself. I'm just leaving a quick comment here on some remarks you made at Talk:Newton's law of universal gravitation.

As you note, the motions of bodies in the solar system are dominated by the Sun. Small particles will tend to follow the same path, even if some of them are much more massive than others.

In Newton's model of gravity, this is because the particles experience a force towards the Sun, which is proportional to their mass. Since F = ma, the accelerations of the particles, and their orbits, are therefore the same, as the mass in the force equation cancels with the mass in "ma".

Take a large mass, like the Sun, with mass "M". Take a small mass "m", like a comet, at a distance "r". By Newton's force equation for gravity, the force is

$F=G{\frac {Mm}{r^{2}}}$

Therefore the acceleration of the smaller object, obtained by "F = ma", is

$a=G{\frac {M}{r^{2}}}$

Note that the acceleration, and the orbit, is independent of the mass of the smaller object. This is also why dropping a feather and a hammer on a airless body like the moon leads to the same acceleration.

If the smaller body is very massive, then one also starts to need to take account of the smaller body on the Sun, because the Sun also experiences the same force. But the same force applied to a comet, and applied to the Sun, have very different effects! In the case of Jupiter, there starts to be some significant effects on the Sun; for all other planets the effect is pretty much negligible.

Einstein gets almost the same effects, but not in terms of a force. Instead, a massive object in Einstein's model introduces some curvature into space and time, and other objects simply follow along the "geodesics" in the curved spacetime, regardless of their own mass. The effects are almost identical; in our solar system only Mercury has motions that have a detectable difference from the predictions of Newton's and Einstein's gravitational models. —Duae Quartunciae (talk · cont) 00:06, 18 August 2007 (UTC)

You can rearrange the same formula anyway you want, you still don't make it true. I really wish reality and truth could win out over the fact that everybody else is wrong. Wouldn't it be great if you guys could be the first to publish this formula correctly since it was changed?

Also notice how your rearranging only works in a special case. If it were right, wouldn't it work in almost all situations?

I did not rearrange. I did some basic algrebra with two standard equations, Newton's gravitational law and Newton's first law, and used them to derive different equation, for a different quantity. I showed that Newton's laws mean that the acceleration of an object in a gravitational field does not depend on its mass. If you replace the multiplication of masses in Newton's law of gravitation with an addition, you find that falling masses on the Earth all have almost exactly the same force, which is absurd. Heavy objects, and light objects, fall at the same speed (if the effects of air resistance can be ignored). That means the heavy object must have a larger force, to accelerate its greater mass. —Duae Quartunciae (talk · cont) 21:31, 18 August 2007 (UTC)

Why your formula cannot work

Donteras, I will make a good-faith attempt to explain to you why your proposed formula: $F=G{\frac {m_{1}+m_{2}}{r^{2}}}$ for the force exerted on mass 2 by mass 1 cannot be correct. Let’s call the mass of the earth M₁. Let objects 2 and 3 have masses of m₂ and m₃, respectively. Consider the situation when m₂ and m₃ are both much smaller than M₁, the mass of the earth.

If Masses 2 and 3 are connected together (with a lightweight connection) to make one object, their combined mass is m₂ + m₃, and then your formula says that the total force the earth exerts on them is: $F=G{\frac {M_{1}+(m_{2}+m_{3})}{r^{2}}}=G{\frac {M_{1}+m_{2}+m_{3}}{r^{2}}}$. I’m assuming that r stays almost the same when they are separated.

If we then separate them, the force on m₂ is $G{\frac {M_{1}+m_{2}}{r^{2}}}$, and the force on m₃ is $G{\frac {M_{1}+m_{3}}{r^{2}}}$, so that the total of the forces on the two of them is $G{\frac {M_{1}+m_{2}}{r^{2}}}+G{\frac {M_{1}+m_{3}}{r^{2}}}=G{\frac {2M_{1}+m_{2}+m_{3}}{r^{2}}}$

This is larger than the total force on the two objects when they are together. Since we are assuming that M₁ is much larger than either m₂ or m₃, 2M₁ + m₂ + m₃ is just about twice as large as M₁ + m₂ + m₃. Therefore, the total force on the objects when they are separated is just about twice as large as when they are together. The weight of an object is how hard the earth pulls on it. According to your formula, if we break a one pound loaf of bread in two, the pieces have a total weight of very close to 2 pounds.

Also, it does not stop there. By the same argument, the force with which the earth pulls on a crumb of bread pulled off the loaf is almost as much as the force with which the earth pulled on the whole loaf. Suppose we crumble that loaf of bread into 1,000,000 crumbs . Since the force with which the earth pulls on each crumb is almost as much as the force with which it pulled on the whole loaf, the total of the forces with which it pulls on the 1,000,000 crumbs is almost 1,000,000 times as much as the force with which it pulled on the whole loaf before it was crumbled. So, by crumbling a 1 pound loaf of bred into 1,000,000 crumbs we get a pile of crumbs on which the earth pulls with a fore of 1,000,000 pounds. Do you believe that that is reasonable? For that matter, using your formula, the earth would pull on a single air molecule almost as hard as it pulls on a battleship.

Newton’s formula does not have this problem. According to it, the earth pulls on m₂ with a force of $F=G{\frac {M_{1}\times m_{2}}{r^{2}}}$, and on m₃ with a force of $F=G{\frac {M_{1}\times m_{3}}{r^{2}}}$. The total of these forces is $F=G{\frac {M_{1}\times m_{2}}{r^{2}}}+G{\frac {M_{1}\times m_{3}}{r^{2}}}$, which comes to $F=G{\frac {M_{1}\times (m_{2}+m_{3})}{r^{2}}}$ with the aid of a little high school algebra. This last force is also the same force with which the earth would pull on masses m₂ and m₃ if they were joined together.

I would also like to point out that, even if someone had a genuine advance in physics, Wikipedia would not be the place to publish it. Read the policy on original research if you don’t believe me. Wikipedia is an encyclopedia, not a research journal. Wikipedia writes about things that are already verifiable and notable; it is not a shortcut to make things verifiable and notable. Cardamon 22:57, 18 August 2007 (UTC)

Ok, first of all, if I were right, this wouldn't have been original research, it would have been the way Newton's law is. Second, you are right. It's not reasonable. I'm sorry I was wrong. I'm sorry about the toes I may have stepped on in my zeal for the truth. Now I have two intellectual tasks ahead of me: finding and reanalyzing the absurdities I've seen published as a result of this formula (they may actually be true) and trying to figure out why forces multiply instead of add. It still doesn't make sense, but I'm gonna have to make it do so, since that is the way it seems to be. —The preceding unsigned comment was added by Donteras (talk • contribs) 04:37, August 21, 2007 (UTC).

Hi Donteras. It's a trick to be able to identify a good intuitive picture that helps the maths make sense.

Try this thought. A heavy thing is hard to move. If you have two large blocks sliding on the ice, you have to push the heavy one harder to get the same motions.

Also a heavy thing weighs more. A heavy backpack pushes down harder on you than a light one.

These two effects are inertia (how hard it is to move a thing) and weight (how hard a thing pushes under gravity). They turn out to be the same. Inertial mass equals gravitational mass. It seems obvious because we are so used to it, but they are actually very different concepts. Contrast this with electromagnetic forces. The forces on a particle in an electric field depend on its charge, and the rate at which it moves depends on its mass, and these are different. So different particles accelerate at different rates, depending on the charge to mass ratio. But in a gravitational field, the ratio of weight to mass is always one, so all particles accelerate in the same way.

Newton's equation for gravitational force is calculating the force, and you can measure the force with a bathroom scale. A heavy object pushes harder on the scale than a light one. So the force is proportional to the mass of the object. An object pushes harder on the scale when on Earth than on the Moon. So the force is also proportional to the mass of the planet. The total force is the product of both masses. But to get the acceleration, you have to divide by the inertial mass, which happens to be the same as the gravitational mass used to calculate the force.

End effect: for two objects, A and B, pulling on each other through gravity, the rate of acceleration for object A depends only on the mass of object B; and vica versa. —Duae Quartunciae (talk · cont) 05:11, 21 August 2007 (UTC)

I think I figured it out. M1 puts out an M1 sized gravitational field. M2 is affected by an M2 "sized" portion of that field. Since gravity has energy we know by e=mc² that it also has mass. That means that gravity is attracted to gravity. Because of this, M2's "size" is proportional to its mass and not its surface area. That also means the formula as it stands only takes one of the gravitational fields into account. This is fine for measuring weight, but for orbital mechanics we need to take both fields into account. This oversight is the probable reason that Newton's laws are off by a factor of 2. Donteras 04:17, 28 August 2007 (UTC)

Woah! The first two sentences (about an M1 sized field and being affected by an M2 size portion) might be a convenient way to think about it and recognize the need to multiply M1 and M2. The rest is all wrong, I'm afraid. Newton's laws are very accurate indeed; off by only a very small factor in extreme cases. The idea that only one of two fields is taken into account is wrong as well. Newton's law is a force law, which defines the force between two masses. The field can be thought of as a measure of the force on a test mass around an object. That is, the force law comes first, and the field is derived from it as a consequence. If you have two masses M1 and M2, it makes no sense to ask of the effect of M1's field on M1. M1 is in the field of M2, and M2 is in the field of M1. Each mass experiences a force, proportional to its own mass and to the field of the other mass.

The comments about relativity are also mistaken. There is energy in a gravitational field, but it does not have mass. This is getting into very deep waters indeed, which caused all kinds of confusion as people first started to work out the theory of energy and gravitational waves. The situation is now pretty well understood, but to explain it requires reference to some some pretty technical terms.

Basically, in relativity gravity is expressed through geometry. The Einstein field equations relate a stress-energy tensor, which deals with how energy and momentum is distributed through spacetime, to the Einstein tensor, which in turn is a based on the metric tensor for spacetime. Put intuitively, matter and energy determines the geometry of spacetime, and then the geometry of spacetime determines the motions of particles. The energy of matter and electromagnetic fields is captured in the stress energy tensor; but there is also energy in gravitational fields, and gravitational waves; and this is NOT captured by the stress energy tensor. Dealing with gravitational energy is very hard work; and generally it cannot be done with tensors and it cannot be mapped to locations in spacetime. Instead, it needs to be handled with a pseudotensor, such as the Stress-energy-momentum pseudotensor of Landau and Liftschitz. But that is way too much detail than really needed. In most cases, the gravitational energy involved is negligible. You really only need to use it in very extreme cases like a supernova or rapidly rotating neutron stars. —Duae Quartunciae (talk · cont) 05:23, 28 August 2007 (UTC)

I'm not ignoring you. I'm just very busy. I am learning quite a bit from this conversation and I do value your insights.

First of all, if you believe Newton's laws to be very accurate, you are mistaken. Most of the times when they say "very accurate" they mean very close. Close does not mean accurate. Mercury's orbit completely fails to obey Newton's law and the orbits of Neptune and Pluto deviate enough to make people believe in Planet X. Obviously you are also unaware of why Einstein's theory won out over Newton's. At one time, both theories were off by a factor of 2, but Einstein's theory is creative enough that he could just make something up to make up the difference. The idea is neat, but warped time is the same thing as warped space. He can't get twice the effect by stating the same idea twice.

I was never concerned with M1's effect on M1. M1 pulls on M2 with the force of (oh, say,) X. M2 pulls on M1 with the (same) force of X. The means that relative motion between M1 and M2 is governed by the force of 2X. BTW all energy has mass. What makes you think that some does and some doesn't? And it is significant. Consider the slingshot maneuver. There is a momentum transfer there. I hope you have learned enough Einstein to know that momentum has mass, so basically the slingshot maneuver involves mass transfer. The spacecraft and the planet don't touch (hopefully) so the transfer is done strictly with gravity. That means that if the theory does not take the mass of gravity into account, then it's a flawed theory.

You might have to define the word "tensor" for me. If I had to guess as to the meaning, I would say that it's a tensing vector, which is a directional force. Of course it has to be that way. By definition, you can't make a non-moving object move unless you apply a force (this is mentioned in the intro to the Principia). I didn't make up this definition, but it does suggest that any theory that tries to eliminate force from gravity is doomed to fail unless you can hide it behind weird words.

Donteras 04:47, 2 October 2007 (UTC)

I might have failed to mention that except for Newton's mathematical error and Einstein's warped space, the two theories are just 2 ways of saying the same thing. Therefore, if gravity's attraction to gravity is implied in Newton's theory, it is also implied in Einstein's. Einstein's theory is so complicated that finding such an implication is probably a needle-in-a-haystack exercise. Those special situations where you have to pay attention to the mass of gravity are very likely a little inaccurate because the mass of gravity is already implicant in the equations.

Donteras 04:05, 7 October 2007 (UTC)