# Why two mass attracts each other?

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Woah. I would think so. I can't imagine why anyone would pick up a GR textbook before Newton. It is insanely simple compared to GR. Just one formula, based on Kepler and Galileo's laws.

You definitely have a different perspective. Then again you've probably had the most non-conventional education.

I probably didn't say that very well. It just turned out that the first physics I studied was GR. Even that was different because that initial text is an undergraduate text that focused on using the metric to evaluate the physics and I was in my late 40's. That's still the most revealing book I've read and I was able to start it after just learning calculus [big 'just' for me].

Einstein orbits naturally precess and Newtonian orbits don't naturally precess.

It isn't clear what you mean by "Newtonian orbits don't naturally precess" but it is a fact that , in his works , Newton studied the orbits precession .

brucep is talking about the Two Body problem in Universal Gravitation.

This is precisely what Newton studied, the orbital precession in the case of a 2-body setup.

It means for two bodies with no external perturbations Newtonian orbits will have 0 precession.

This is incorrect, look here.

Both "Universal Gravitation" and "Newtonian orbits" refer to the inverse-squared law central force where: $$\vec{F} = - \frac{G m_1 m_2}{r^2} \hat{r}$$.

Tach's page describes aphysical speculation by Newton so that he would better understand his own theory.

Wikipedia said:
With the publication of his Principia ... Newton provided a physical theory that accounted for all three of Kepler's laws, a theory based on Newton's laws of motion and his law of universal gravitation. In particular, Newton proposed that the gravitational force between any two bodies was a central force F(r) that varied as the inverse square of the distance r between them. Arguing from his laws of motion, Newton showed that the orbit of any particle acted upon by one such force is always a conic section, specifically an ellipse if it does not go to infinity. However, this conclusion holds only when two bodies are present (the two-body problem); ... Newton's theorem of revolving orbits was his first attempt to understand apsidal precession quantitatively. According to this theorem, the addition of a particular type of central force—the inverse-cube force—can produce a rotating orbit; the angular speed is multiplied by a factor k, whereas the radial motion is left unchanged.
...
Consider a particle moving under an arbitrary central force F₁(r) ...
Imagine a second particle with the same mass m and with the same radial motion r(t), but one whose angular speed is k times faster than that of the first particle, where k is any constant. ... Newton showed that the motion of the second particle can be produced by adding an inverse-cube central force to whatever force F₁(r) acts on the first particle
... If k² is greater than one, F₂ − F₁ is a negative number; thus, the added inverse-cube force is attractive, ... By contrast, if k² is less than one, F₂−F₁ is a positive number; the added inverse-cube force is repulsive ...
If k is close, but not equal, to one, the second orbit resembles the first, but revolves gradually about the center of force; this is known as orbital precession .... If k is greater than one, the orbit precesses in the same direction as the orbit ...; if k is less than one, the orbit precesses in the opposite direction.
Specifically, if F₁(r) is universal gravitation, F₂(r) is universal gravitation plus an unphysical cubic term that looks like this:
$$\vec{F}_{\tiny 2} = \left[ - \frac{GM m}{r^2} - ( k^2 - 1 ) \frac{L_{\tiny 1}^2}{m r^3} \right] \hat{r}$$

However, in Universal Gravitation, k=1, k²=1, F₁ = F₂, and there is no precession in the two-body problem.

Finally, Newton used his non-physical mathematical exploration to try to explain the more complicated behavior of matter when there is more than 2 bodies.

Wikipedia said:
Newton used his theorem of revolving orbits in two ways to account for the apsidal precession of the Moon.[citation omitted] First, he showed that the Moon's observed apsidal precession could be accounted for by changing the force law of gravity from an inverse-square law to a power law in which the exponent was 2 + 4/243 ... As a second approach to explaining the Moon's precession, Newton suggested that the perturbing influence of the Sun on the Moon's motion might be approximately equivalent to an additional linear force ... Newton showed that this force law could not account for the Moon's precession

But even as Newton was developing perturbation theory, he limited himself to geometrical means of exploring the math, and his success was limited.
http://en.wikipedia.org/wiki/Lunar_theory

Wikipedia2 said:
After introducing his diagram 'to find the force of the Sun to perturb the Moon' in Book 3, Proposition 25, Newton developed a first approximation to the solar perturbing force, showing in further detail how its components vary as the Moon follows its monthly path around the Earth. He also took the first steps in investigating how the perturbing force shows its effects by producing irregularities in the lunar motions. (In this part of the enterprise, Newton's success was more limited: it is relatively uncomplicated to define the perturbing forces, but heavy complexities soon arise in the problem of working out the resulting motions, and these were to challenge mathematical astronomers for two centuries after Newton's initial definition of the problem and indication of the directions to take in solving it.)
For a selected few of the lunar inequalities, Newton showed in some quantitative detail how they arise from the solar perturbing force.
Much of this lunar work of Newton's was done in the 1680s, and the extent and accuracy of his first steps in the gravitational analysis was limited by several factors, including his own choice to develop and present the work in what was, on the whole, a difficult geometrical way, and by the limited accuracy and uncertainty of many astronomical measurements in his time.
...
The main aim of Newton's successors, from Leonhard Euler, Alexis Clairaut and Jean d'Alembert in the mid-eighteenth century, down to E.W. Brown in the late nineteenth and early twentieth century, was to account completely and much more precisely for the moon's motions on the basis of Newton's laws, i.e. the laws of motion and of universal gravitation by attractions inversely proportional to the squares of the distances between the attracting bodies. They also wished to put the inverse-square law of gravitation to the test, and for a time in the 1740s it was seriously doubted, on account of what was then thought to be a large discrepancy between the Newton-theoretical and the observed rates in the motion of the lunar apogee. However Clairaut showed shortly afterwards (1749–50) that at least the major cause of the discrepancy lay not in the lunar theory based on Newton's laws, but in excessive approximations that he and others had relied on to evaluate it.
Most of the improvements in theory after Newton were made in algebraic form: they involved voluminous and highly laborious amounts of infinitesimal calculus and trigonometry. It also remained necessary, for completing the theories of this period, to refer to observational measurements.

But for the two-body problem in universal gravitation, elliptical orbits do not precess.

http://archive.org/texts/flipbook/flippy.php?id=anelementarytre04godfgoog

... as Newton was developing perturbation theory, he limited himself to geometrical means of exploring the math ...
That was the only type of proof considered valid in Newton´s day. Just as some current mathematicians do not consider a computer proof "by exhaustion" (all possibilities calculated) to be valid.

Everyone with the slightest interest in physic or math, should spend at least a couple of hours actually reading (no make that studying) his Principles of Mathematics just to see how powerful, complete and detailed geometric proofs can be in the hands of a real genius!

Everyone with the slightest interest in physic or math...
... should spend at least a couple of hours actually reading (no make that studying) his Principles of Mathematics

Both "Universal Gravitation" and "Newtonian orbits" refer to the inverse-squared law central force where: $$\vec{F} = - \frac{G m_1 m_2}{r^2} \hat{r}$$.

Tach's page describes aphysical speculation by Newton so that he would better understand his own theory.

Specifically, if F₁(r) is universal gravitation, F₂(r) is universal gravitation plus an unphysical cubic term that looks like this:
$$\vec{F}_{\tiny 2} = \left[ - \frac{GM m}{r^2} - ( k^2 - 1 ) \frac{L_{\tiny 1}^2}{m r^3} \right] \hat{r}$$

However, in Universal Gravitation, k=1, k²=1, F₁ = F₂, and there is no precession in the two-body problem.

Finally, Newton used his non-physical mathematical exploration to try to explain the more complicated behavior of matter when there is more than 2 bodies.

But even as Newton was developing perturbation theory, he limited himself to geometrical means of exploring the math, and his success was limited.
http://en.wikipedia.org/wiki/Lunar_theory

But for the two-body problem in universal gravitation, elliptical orbits do not precess.

http://archive.org/texts/flipbook/flippy.php?id=anelementarytre04godfgoog

Nice post. Pretty interesting. I like to wonder what Newton would have discovered if he knew what Maxwell would discover in the distant future.

In a hand-wavy fashion, we could say that the C.C. represents dark energy.

At this point the cosmological constant is the 'dark energy'. WMAP results confirm the predictions of Guth's Inflation model. I always like saying that, LOL. Personally I really like the way that turned out [so far]. Regardless what Einstein said it turns out 'even' the prediction he thought was wrong was right. Science is 'one thing' the human race got right.

I could in high school, but not well. I read it in English translation. I did as practice of my German, in college, by reading Das Kapital in the original, but I had an English translation in the other hand, used when confused.

At this point the cosmological constant is the 'dark energy'. WMAP results confirm the predictions of Guth's Inflation model. I always like saying that, LOL. Personally I really like the way that turned out [so far]. Regardless what Einstein said it turns out 'even' the prediction he thought was wrong was right. Science is 'one thing' the human race got right.
Perhaps so. What is it the way that turned out that you like?

Perhaps so. What is it the way that turned out that you like?

Inflation turned cosmology into a testable science. I followed Guth's idea since shortly after he wrote his non mathematical book on cosmology and his inflation idea. It turns out it evolved into testable cosmology. What's not to like. The weirdest thing is after 30 years of it's 'known existence' very few non practicing cosmologists know anything about it. You'd think it would be a big deal in forums like this but instead most still believe all the matter in the universe was stuffed into a singularity and was spewed out when it popped it's load.

The Sun's gravitational force decides the orbit of a planet.

No, it is the geometry of space-time around the sun which determines the orbits.

I probably didn't say that very well. It just turned out that the first physics I studied was GR. Even that was different because that initial text is an undergraduate text that focused on using the metric to evaluate the physics and I was in my late 40's. That's still the most revealing book I've read and I was able to start it after just learning calculus [big 'just' for me].
Immediately from calculus to DG is quite a big leap. Especially since you skipped Newton.

Inflation turned cosmology into a testable science. I followed Guth's idea since shortly after he wrote his non mathematical book on cosmology and his inflation idea. It turns out it evolved into testable cosmology. What's not to like. The weirdest thing is after 30 years of it's 'known existence' very few non practicing cosmologists know anything about it. You'd think it would be a big deal in forums like this but instead most still believe all the matter in the universe was stuffed into a singularity and was spewed out when it popped it's load.
Oops. I should have said "What do you like about the way that it turned out?" Not enough sleep LOL.

To the layman, inflation sounds the same as "spewing out". Many also confuse it with the accelerating universe. Also, it's always been pictured as some kind of "bell-shape".

Immediately from calculus to DG is quite a big leap. Especially since you skipped Newton.

Oops. I should have said "What do you like about the way that it turned out?" Not enough sleep LOL.

To the layman, inflation sounds the same as "spewing out". Many also confuse it with the accelerating universe. Also, it's always been pictured as some kind of "bell-shape".

When you start using terms like "sounds the same as..." and "confuse it with..." for what people think then it just means nobody actually did any homework on the subject before having a confused opinion. I do it all the time just not when discussing science. The accelerating universe is a [possible] further consequence of the original inflation event. Where the vacuum expectation value didn't fully reach minimum at the end of the original inflation event and is finishing up as we observe in the present. Finishing up probably isn't the best analogy.

One problem I have with space-time explanations of mass attraction, is you begin with a variable that lacks substance, instead of using substantial things like mass and energy. We can't store time or space-time in a bottle and run experiments on a just a pure sample of space-time. We can do that with mass. Space-time is always indirectly measured by means of changes observed within tangible things. Red shift is a tangle change in energy, used to infer something you can't save in a bottle; emperors new clothes?

Let us ask science questions like, is it possible to measure space-time, in a vacuum without any tangibles, to make sure space-time is self standing and not just a mental construct that stems indirectly from measurable substance? If we can't isolate space-time, isn't this just game engine science? Game engine science is where you move math instead of substance to create magic tricks. The scientific method should require we isolate a sample of space-time to use as a standard. It avoids this why?

I was trained as an engineer so I understand practical utility and how this can fool some into reading too much into the practical utility of a procedure. I remember an old timer who did chrome plating. He was the best and his personal secret was he used to spit chewing tobacco into the vat. From a pure chemistry POV this made little sense to me. But from an applied science POV his unique ability to plate things so well made that claim seem real enough for other to assume it was true. Is space-time the chewing tobacco in the vat of substantial variables?

One problem I have with space-time explanations of mass attraction, is you begin with a variable that lacks substance, instead of using substantial things like mass and energy. We can't store time or space-time in a bottle and run experiments on a just a pure sample of space-time. We can do that with mass. Space-time is always indirectly measured by means of changes observed within tangible things. Red shift is a tangle change in energy, used to infer something you can't save in a bottle; emperors new clothes?

Let us ask science questions like, is it possible to measure space-time, in a vacuum without any tangibles, to make sure space-time is self standing and not just a mental construct that stems indirectly from measurable substance? If we can't isolate space-time, isn't this just game engine science? Game engine science is where you move math instead of substance to create magic tricks. The scientific method should require we isolate a sample of space-time to use as a standard. It avoids this why?

I was trained as an engineer so I understand practical utility and how this can fool some into reading too much into the practical utility of a procedure. I remember an old timer who did chrome plating. He was the best and his personal secret was he used to spit chewing tobacco into the vat. From a pure chemistry POV this made little sense to me. But from an applied science POV his unique ability to plate things so well made that claim seem real enough for other to assume it was true. Is space-time the chewing tobacco in the vat of substantial variables?

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One problem I have with space-time explanations of mass attraction, is you begin with a variable that lacks substance, instead of using substantial things like mass and energy.

This makes no sense, since GR uses the stress-energy-momentum tensor as the source term of gravity; that tensor is a representation of mass and energy.

Space-time is always indirectly measured by means of changes observed within tangible things.

So is energy. Or momentum. Or potential. Or any number of other concepts in physics.

The scientific method should require we isolate a sample of space-time to use as a standard. It avoids this why?

Actually, no. The scientific method only requires us to extract numerical predictions from the model as a whole, and then compare it to experiment and observation. The scientific method does not actually concern itself with the specific mechanisms of the model; you could, if you wanted to, write a model which explains gravity in terms of microscopic pink unicorns - so long as all predictions of that pink-unicorn explanation line up with experiment and observation, you'd have a valid model of gravity, until such time as a contradiction or a wrong prediction surfaces. The scientific method simply goes : Ask a question - formulate a hypothesis - extract predictions - test those against observation - analyse the outcome, and amend the hypothesis if necessary.
So far as predictions and observations go, GR does a pretty good job in explaining the effects of gravity.

Quasi-phyiscal = gravity and virtual particles?

No, it is the geometry of space-time around the sun which determines the orbits.

"geometry is the science of patterm"..Fuller

A friend reminded me that it was the shape--- patterned outline ---of the vehicle that affected the air-flow, however, the vehicle was made of molecules erg atoms.

This above by "geometry of space-time" seems to be very similar to the "shape/geometry of", however, in the case of the vehicle, it is the associated molecules/atoms, whereas in Markus's above, there is only the geometry of space-time( gravity ) aka gravitational spacetime.

Quasi-physical--- beyond our detectability --- space-time or spacetime = gravity = mass-attraction = bosonic force = ultra-micro graviton assumed to be exchanged between mass A/Sun and mass B/planet.

Metaphysical subcatagory of mathematics called geometry, pattern, shape like a spiral, or a triangle or square etc.....i.e. the metaphysical pattern/shape is not the medium of mass or the force exchanged between massess.

Yes, the metaphysical shape/patterned outline of a vehicle affects the air-flow, but ionly via the inter-actions/relationships with atoms/mass.

It appears very clear to me, that, there exists an ultra-micro force of gravitational spacetime( gravitons ) far beyond our ability to ever quantize ergo focus in any practical( mechanistic ) way, as we do with EMRadiation( photons ) which we do quantize via the electron( mass ).

Lee Smolin predicted humans would quantify gravity by around the year 2015 via geometry. I think he was way too optimistic.

r6

Although the space distortion by mass POV is probably better discription for accurate calculations, it is not an answer to the Why question. My joking answer of many pages back does as well as any (I think) attempt to answer the why question:

"Inanimate love" is as good an answer as any to the why question.

Although the space distortion by mass POV is probably better discription for accurate calculations, it is not an answer to the Why question. My joking answer of many pages back does as well as any (I think) attempt to answer the why question:

"Inanimate love" is as good an answer as any to the why question.

Inanimate love between two masses, the attraction?

The Sun's gravitational force decides the orbit of a planet.

No, it is the geometry of space-time around the sun which determines the orbits.

Can you explain the difference between 'effect of force on a mass' and 'effect of curvature(or geometry) of space-time on a mass'?

hansda -- your claim is both wrong and stupid.

My claim is based on "observable fact".

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