How Newton could have developed his law of gravitation

[lidal]

The main idea here is that we should go to great lengths to test our laws in physics,

1. against nature.

2. against intuition and logic

 

We have one or both of two alternatives

1. To rigorously check our laws of physics against nature AND/OR

2. Our laws of physics should be based on sound logical consistency. This requirement should be even more tight if we can't test our theories in the laboratory or if there is some (apparent) discrepancy between a law of physics and actual observations.

 

So physicists should either have been able to explain 'elliptic' orbits with (extreme) logical consistency or should have 'explored' the universe to find at least one solar system in which Newton's law of gravitation was observed exactly: circular orbits.

Ideally, the problem of reference frames that accompanied Newton's laws should not have been tolerated and Newton's laws should not have been accepted as complete. If this was done, the problem of reference frames would have been solved much earlier.

 

 

The complete discussion is found on the attached PdF.

How Newton should have scifor.pdf

[Przemyslaw.Gruchala]

 

 

The main idea here is that we should go to great lengths to test our laws in physics,

 

We have such devices with great distances from us - satellites, such as Viking..

http://en.wikipedia.org/wiki/Viking_%28satellite%29

 

If device is programmed to immediately answer with confirmation message as soon as it gets command from us from Earth, by observation of delay in reply we can confirm that radio waves have exact speed as we think they have and calculate exact distance to satellite.

[Klaynos]

Newtonian gravity contains elliptical orbits. The observations agreed with the numerical predictions.

[swansont]

Intuition and logic alone have had some spectacular failures in figuring out science. Intuition and logic gave us circles and spheres as perfection, which led to epicycles, It gave us the idea that heavy objects fall faster than light ones. It told us that there must be an aether.

 

The only method for testing ideas with the goal of calling it science is with experiment. Until that is done, no idea can be accepted as valid and true. And it doesn't matter if the idea is counter-intuitive; intuition is subjective, and science is not.

[michel123456]

Newtonian gravity contains elliptical orbits. The observations agreed with the numerical predictions.

In the pdf, the argument states otherwise

 

The main idea in this paper is that physicists should have either ‘explored’ the

universe to discover a ‘solar system’ in which Newton’s law of gravitation applied

exactly or should have explained the discrepancy between the implication of the

simple Newton’s law of gravitation (circular orbits) and actual observation (non

circular or ‘elliptic’) orbits, with sound logical consistency and validity.

I am not aware of such a discrepancy.

[swansont]

In the pdf, the argument states otherwise

 

One of them is wrong. Can you guess which?

[D H]

From the attached paper,

Then he imagined that the orbit should be circular. He thought there was no reason for the orbit to be non circular. He formulated his simple law (equation) of gravitation. The simple law predicted a simple orbital shape: circular.

Sigh.

 

This is completely wrong. lidal, before you go any further down this path of trying to disprove physics, you need to learn some physics.

[elfmotat]

Lidal, may I ask why you believe elliptical orbits aren't compatible with Newtonian gravity? Because they are.

[imatfaal]

Just to make it quite clear that Newton was totally aware that planets followed elliptical orbits

 

 

PROPOSITION XIII. THEOREM XIII.

The planets move in ellipses which have their common focus in the
centre of the sun; and, by radii drawn to that centre, they describe
areas proportional to the times of description.

 

The maths is dealt with in earlier sections - and he probably states it in earlier parts - but this is a pretty unequivocal statement. If you insist that the orbits are circular the maths becomes much easier but the results are no longer consistent with reality. It was Kepler and Brahe who (decades before Newton) has shown that the planets follow elliptical (although very slight) orbits as the result of close observation and massive calculation. Newton's genius was tying it all together in theory and combining with the same force that makes the proverbial apple fall

[lidal]

In the pdf, the argument states otherwise

 

I am not aware of such a discrepancy.

Ok, correction: " a discrepancy" NOT "the discrepancy"

It has been presented as a discrepancy in the new theory. How can a simple law of gravitation lead to a complex (non circular) shape of orbit? A simple law should lead to a simple orbital shape: circular.

Intuition and logic alone have had some spectacular failures in figuring out science. Intuition and logic gave us circles and spheres as perfection, which led to epicycles, It gave us the idea that heavy objects fall faster than light ones. It told us that there must be an aether.

 

The only method for testing ideas with the goal of calling it science is with experiment. Until that is done, no idea can be accepted as valid and true. And it doesn't matter if the idea is counter-intuitive; intuition is subjective, and science is not.

Yes, the only way of proving an idea (a theory) is with experiment. But, how do we select those ideas in our minds in the first place? Can we test all of the hundreds of ideas which happen in our minds with experiments? Intuition and logic are powerful tools to select a few sensible ideas to be tested experimentally out of thousands of speculations .

 

If we observe nature behave counterintuitively, then the problem is with a limitation in our power of logical and intuitive thinking. Perhaps the explanation of those phenomena required discovery of new logic and new intuition. Intuitive and logical ideas are self evident. The failures with logical and intuitive thinking is just because we didn't think logically and intuitively enough. We simply made subtle mistakes in our thinking.

 

There is no decisive explanation to the cause for 'elliptic' orbits. If people are easily satified with some adhoc explanations, then that is a problem. Science always progressed not because of people who were satisfied with existing explanations, but because of those who were not.Those people always have/had higher standards for the explanations they accept.

 

How can one be satisfied with " time dilation" and " space contraction ". It is completely counterintuitive. Self contradiction. Well, one may consider "length contraction" and test it.

From the attached paper,

 

Sigh.

 

This is completely wrong. lidal, before you go any further down this path of trying to disprove physics, you need to learn some physics.

Two bodies revolving about a common bary center? Conservation of energy and angular momentum? Conic sections?

 

 

If an explanation existed on why the orbits are 'elliptic', someone would have posted it here in a single line.

 

I will write the new explanation in a single line as follows:

 

'Elliptic' orbits and Perihilion advance are due to absolute motion of the solar system in space.

 

The new theory can describle the exact mathematical expression of the orbit, why an 'elliptic' orbit takes a specific shape and orientation in space, why the perihilion point is to the left or to the right, what happens during acceleration, .... .

 

 

We have such devices with great distances from us - satellites, such as Viking..

http://en.wikipedia.org/wiki/Viking_%28satellite%29

 

If device is programmed to immediately answer with confirmation message as soon as it gets command from us from Earth, by observation of delay in reply we can confirm that radio waves have exact speed as we think they have and calculate exact distance to satellite.

"going to greath lengths " just means " make every possible effort "

Newtonian gravity contains elliptical orbits. The observations agreed with the numerical predictions.

1. Newton's law of gravitation, in its simplest form, predicts the simplest shape of orbit: circular.

No fundamental explanation exists so far on why the orbits are elliptic, the exact shape (mathematical expression) of the orbit , why a specific orientation of the 'ellipse' in space, ...

 

2. The theory proposed in my previous post doesn't imply an 'elliptic' orbit. The orbits are not elliptic.The exact shape is known after solving the differential equations. A qualitative analysis showed that the orbit will have bigger radius on one side (say left side) than on the opposite (right) side. So the new theory answers the questions in (1). The orientation of the perihelion and aphelion points is such that the line connecting them is always perpendicular to the path of the sun in space.

 

I just claimed that the new theory is logically consistent and can explain two phenomena : 'elliptic' orbits and perihelion advance. Theories should be compared both with respect to their logical consistency and validity and with respect to agreement with observations. Experimental evidences should be reconsidered if some problem in the logical consistency or validity or satisfiability of the theory is discovered or if a better theory is discovered.

 

Lidal, may I ask why you believe elliptical orbits aren't compatible with Newtonian gravity? Because they are.

Elliptic orbits are not compatible with the simple Newton's law of gravitation we know. They are compatible with a 'transformed' or 'distorted' form the law.

 

Just to make it quite clear that Newton was totally aware that planets followed elliptical orbits

 

The maths is dealt with in earlier sections - and he probably states it in earlier parts - but this is a pretty unequivocal statement. If you insist that the orbits are circular the maths becomes much easier but the results are no longer consistent with reality. It was Kepler and Brahe who (decades before Newton) has shown that the planets follow elliptical (although very slight) orbits as the result of close observation and massive calculation. Newton's genius was tying it all together in theory and combining with the same force that makes the proverbial apple fall

I did not insist that the the orbits are circular. I proposed an explanation for why they are not circular. Newton and Kepler knew the orbits were 'elliptic', but did not explain why.Why a specific 'ellipse'? While formulating his simple law of gravitation, Newton had to ignore the 'imperfections' of the orbit shapes to simplify the problem.

Edited March 16, 2013 by lidal

[Klaynos]

Newtonian gravity includes, predicts and explains elliptical orbits, your assertion that it doesn't remains false. In you pdf I see no maths, therefore there can be no predictions. It is not a theory.

 

Humans hare evolved in very specific circumstances, why would the humanbrain therefore be capable of intuitive thought about concepts so remote from its everyday experiences?

[John Cuthber]

Do you understand that this (unevinced) assertion

"A simple law should lead to a simple orbital shape: circular.".

is just plain wrong?

A simple law leads to one of a collection of simple paths, all of them are conic sections, some count as orbits and some of those are circles.

But they are all simple in that they are the shape you get from the intersection of a plane and a cone.

[uncool]

One simple reason for you, lidal:

 

Since the set of paths is rotationally symmetric around the barycenter (that is, given a path, if we rotate the entire path at once, we get another path), we can model them using differential equations based entirely off of the radius and the time. Circles then correspond to constant functions. By Newton's 3 laws, this differential equation is a second-order differential equation - so the set of functions that satisfy the differential equation has 2 degrees of freedom. But the set of circles doesn't have 2 degrees of freedom - it has 1. So no, Newton's law of gravity - and in fact, any law of gravity that doesn't reduce Newton's laws to a first-order differential equation - predicts non-circular paths.

 

Now, if you want to see the math that shows that Newtonian gravity leads to elliptical orbits, you could have looked it up in a lot of places. Here is one: http://www.math.wisc.edu/~robbin/234dir/kepler.pdf

=Uncool-

[swansont]

If we observe nature behave counterintuitively, then the problem is with a limitation in our power of logical and intuitive thinking. Perhaps the explanation of those phenomena required discovery of new logic and new intuition. Intuitive and logical ideas are self evident. The failures with logical and intuitive thinking is just because we didn't think logically and intuitively enough. We simply made subtle mistakes in our thinking.

 

There is no decisive explanation to the cause for 'elliptic' orbits. If people are easily satified with some adhoc explanations, then that is a problem. Science always progressed not because of people who were satisfied with existing explanations, but because of those who were not.Those people always have/had higher standards for the explanations they accept.

 

That seems contradictory. You claim that you can use intuition and logic, even if it requires new logic and intuition, yet elliptical orbits can't be the result of thought? Of course, this is moot because elliptical orbits were observed and explained before gravity, and are perfectly consistent with Newton's law of gravitation.

 

How can one be satisfied with " time dilation" and " space contraction ". It is completely counterintuitive. Self contradiction. Well, one may consider "length contraction" and test it.

 

You just claimed it was no big deal that it's counterintuitive. You just need better intuition. (and these have been tested, and confirmed)

 

1. Newton's law of gravitation, in its simplest form, predicts the simplest shape of orbit: circular.

 

No, a circular orbit is the conclusion of limited logic and intuition.

 

[imatfaal]

!

Moderator Note

 

Tangent regarding the Human mind and its capacity for abstract thought split off to new topic here in Speculations.

 

http://www.scienceforums.net/topic/73674-human-innovation-and-ingenuity-and-whether-it-has-changed-split-from-how-newton/

 

[lidal]

One simple reason for you, lidal:

 

Since the set of paths is rotationally symmetric around the barycenter (that is, given a path, if we rotate the entire path at once, we get another path), we can model them using differential equations based entirely off of the radius and the time. Circles then correspond to constant functions. By Newton's 3 laws, this differential equation is a second-order differential equation - so the set of functions that satisfy the differential equation has 2 degrees of freedom. But the set of circles doesn't have 2 degrees of freedom - it has 1. So no, Newton's law of gravity - and in fact, any law of gravity that doesn't reduce Newton's laws to a first-order differential equation - predicts non-circular paths.

 

Now, if you want to see the math that shows that Newtonian gravity leads to elliptical orbits, you could have looked it up in a lot of places. Here is one: http://www.math.wisc.edu/~robbin/234dir/kepler.pdf

=Uncool-

 

Elliptic orbits are only the solutions of those differential equations for conservation of energy and for conservation of angular momentum of a planet revolving around a sun. They are only a result of maths.

 

If infinite number of orbits are possible, what determines a specific orbit? I think we agree that Newton's law of gravitation should predict a single orbit, for a given set of initial conditions. The new theory predicts a single orbit for a given set of initial conditions.

 

Those differential equations are based on, at least, one fundamental mistake: the conservation laws applied only to the planet.

The conservation laws should be applied to the sun-planet system (assuming external force on the system is absent) and this is possible only if we use a reference frame not fixed with the sun, and this reference frame should be an absolute reference frame.

 

The orbits are non circular but not elliptic, according to the new theory.They are not symmetric.The orbit has smaller size on, say, the left side, and a bigger size on the right side (depending on the sense of rotation of the planet around the sun), when looking in the forward direction of the path of the sun in space.

 

Someone might say " No, observations show that the orbits are elliptic". But observations depend on the theories. For example, if some deviation from elliptic shape has been observed, they say " departure from the exact elliptic shape may be because of the effect of other planets and or other galaxies? .... ".

 

Newton's explanation was sufficient to satisfy the people at his time because they didn't even know the cause of revolution of planets before Newton's laws, let alone the cause of elliptic orbits. Actually all Newton did was only solve the differential equations for the conservation laws and say that any conic section is possible. However, no one has been able to interprete those solutions as they were/are not accurate, i.e elliptic orbits are difficult to interpret (they lead to new questions, as the ones mentioned below).

 

Anyone, even anyone with little education, can challenge the existing explanation: then why is the sun at the left or at the right focal point of the ellipse (if the orbit is symmetric), or why is the perihilion point to the left or to the right, which specific ellipse, why a specific orientation of the 'ellipse' in space and so on.

 

I am very clear about the new theory than Newton's explanation for 'elliptic' orbits and this is because Newton's explanation is incomplete, i.e it provokes other questions as above. I know, however, that the differential equations leading to elliptic orbits are based on a fundamental mistake: they are based on a reference frame fixed to and moving with the sun. It takes some time and effort to clearly and completely show the details on why a wrong theory is wrong. But I would like to work on a more promising new theory than try to figure out the details of why a fundamentally wrong theory is wrong, because of limitation of time and other resources.

 

The new theory is :

Newton's laws of motion and gravitation should be redefined with respect to an absolute reference frame.

[uncool]

Elliptic orbits are only the solutions of those differential equations for conservation of energy and for conservation of angular momentum of a planet revolving around a sun. They are only a result of maths.

They are the result of math - math which includes Newton's law of gravity. Ellipses are not a solution to the differential equations if you use a simple inverse law of gravity, nor if you use an inverse cube. I've already shown you the math that uses the inverse square law to get the ellipse.

If infinite number of orbits are possible, what determines a specific orbit?I think we agree that Newton's law of gravitation should predict a single orbit, for a given set of initial conditions. The new theory predicts a single orbit for a given set of initial conditions.

Initial position and initial momentum. Removing the angle, as I did, leaves us with total energy (kinetic and potential) and angular momentum (I'm not including initial radius and initial derivative of radius because you're looking at orbits, not at points on orbits).

Those differential equations are based on, at least, one fundamental mistake: the conservation laws applied only to the planet.

The conservation laws should be applied to the sun-planet system (assuming external force on the system is absent) and this is possible only if we use a reference frame not fixed with the sun, and this reference frame should be an absolute reference frame.

It's clear that you haven't seen the actual calculations. The two-body problem under any radially symmetric law of gravity can be reduced to a one-body problem. The conservation laws for the two-body problem reduce to the conservation laws for the one-body problem, so considering the one-body problem is sufficient.

The orbits are non circular but not elliptic, according to the new theory.They are not symmetric.The orbit has smaller size on, say, the left side, and a bigger size on the right side (depending on the sense of rotation of the planet around the sun), when looking in the forward direction of the path of the sun in space.

 

Someone might say " No, observations show that the orbits are elliptic". But observations depend on the theories. For example, if some deviation from elliptic shape has been observed, they say " departure from the exact elliptic shape may be because of the effect of other planets and or other galaxies? .... ".

No, observations don't depend on theories. Further, when there have been departures from the elliptical orbits, that has given us the ability to predict the existence of more planets - this is how Neptune was discovered.

Newton's explanation was sufficient to satisfy the people at his time because they didn't even know the cause of revolution of planets before Newton's laws, let alone the cause of elliptic orbits. Actually all Newton did was only solve the differential equations for the conservation laws and say that any conic section is possible. However, no one has been able to interprete those solutions as they were/are not accurate, i.e elliptic orbits are difficult to interpret (they lead to new questions, as the ones mentioned below).

Please explain what you mean by "no one has been able to interpret those solutions". If you mean that people haven't been able to use Newton's laws to predict where planets will be, then you are completely and utterly wrong.

Anyone, even anyone with little education, can challenge the existing explanation: then why is the sun at the left or at the right focal point of the ellipse (if the orbit is symmetric), or why is the perihilion point to the left or to the right, which specific ellipse, why a specific orientation of the 'ellipse' in space and so on.

You've just asked the same question in 3 not-very-different ways; you're only asking about why a certain angle. And the answer to that is the same as it is for any differential equation: initial conditions.

I am very clear about the new theory than Newton's explanation for 'elliptic' orbits and this is because Newton's explanation is incomplete, i.e it provokes other questions as above. I know, however, that the differential equations leading to elliptic orbits are based on a fundamental mistake: they are based on a reference frame fixed to and moving with the sun. It takes some time and effort to clearly and completely show the details on why a wrong theory is wrong. But I would like to work on a more promising new theory than try to figure out the details of why a fundamentally wrong theory is wrong, because of limitation of time and other resources.

It would be a better use of time and "other resources" to actually learn the theory than to declare it wrong without knowing what it says.

The new theory is :

Newton's laws of motion and gravitation should be redefined with respect to an absolute reference frame.

If you look at any calculation of the two-body problem, you will see one of two ways it is reduced to the 1-body problem:

 

1) One body is so massive that it can be assumed to be still, or

2) The problem is looked at with respect to the barycenter.

 

The first is actually a special case of the second, since as the sun is so massive, the barycenter is effectively where the sun is, and barely moves. So your "new" theory is what has already been known - for hundreds of years. Further, it doesn't address ellipses at all.

 

As an addendum: your claim that Newton's law doesn't predict ellipses has been rebutted. If you're going to continue claiming that Newton's law doesn't predict ellipses, then please try answering the math. Otherwise, please accept that your initial claim was false.

=Uncool-

Edited March 17, 2013 by uncool

[elfmotat]

Lidal, the solution to any second-order differential equation of position requires two initial conditions: initial position and initial velocity. If you specify those two initial conditions then you get a unique solution. The general solution to [math]GM/r^2 = \ddot{r}[/math] is an ellipse, and the exact form of the ellipse depends on initial conditions.

[Przemyslaw.Gruchala]

Lidal, I am confused. So you don't believe in that spacetime is curved?

Edited March 18, 2013 by Przemyslaw.Gruchala

[elfmotat]

Lidal, I am confused. So you don't believe in that spacetime is curved?

What does that have to do with anything?

[Przemyslaw.Gruchala]

What does that have to do with anything?

 

In curved spacetime planets are moving straight lines, so they're neither accelerated nor decelerated in time.

Sun is in constant movement around galaxy. This causes that curvature of spacetime is constantly changing for orbiting objects.

Edited March 18, 2013 by Przemyslaw.Gruchala

[imatfaal]

Let's keep this on track with the OP - rather than branch off into discussion of GR.