A singularity free N Body problem – solution

[snp.gupta]

Till now we are seeing the Dynamic Universe Model as alternative to other cosmological models. But now I want to project it as a simple singularity free N-body problem which was not solved till now say from 1880 onwards when king Oscar II announced the prize. Using this N-body solution we can achieve various results as follows.

1. Offers Singularity free solutions
2. Non- collapsing Galaxy structures
3. Solving Missing mass in Galaxies, and it finds reason for Galaxy circular velocity curves….
4. Blue shifted and red shifted Galaxies co-existence…
5. Explains the force behind expansion of universe.
6. Explains the large voids and non-uniform matter densities.
7. Explains the Pioneer anomaly
8. Predicts the trajectory of New Horizons satellite.

Mainly because, points 2,3 7 and 8 are not cosmological problems, they were N-body problems. Point 1 is required in both N-body solution as well as cosmology……


History:


Historically, King Oscar II of Sweden announced a prize to a solution of N-body problem with advice given by Gösta Mittag-Leffler in 1887.

He announced ‘Given a system of arbitrarily many mass points that attract each according to Newton's law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly.’
[This is taken from Wikipedia http://en.wikipedia.org/wiki/N-body_problem ].

The announced dead line that time was1st June 1888. And after that dead line , on 21st January 1889, Great mathematician Poincaré claimed that prize. Later he himself sent a telegram to journal Acta Mathematica to stop printing the special issue after finding the error in his solution. Yet for such a man of science reputation is important than money. [ Ref Book ‘Celestial mechanics: the waltz of the planets’ By Alessandra Celletti, Ettore Perozzi, page 27]. He realized that he has been wrong in his general stability result! But till now nobody could solve that problem or claimed that prize. Later all solutions resulted in singularities and collisions of masses, given by many people…..


Now................


I want to say that the Dynamic Universe Model solves this classical N-body problem where only Newtonian Gravitation law and classical Physics were used. In this mathematical frame work the solution converges at all points. There are no multiple values, diverging solutions or divided by zero singularities. You have to input various values of masses, accelerations, velocities and positions and distances with a time step to get the next set of positions depending on the Universal Gravitational Force on a particular body. I have not used the conventional methodology for the solution, but it is a numerical solution, which can be done with a person with a calculator. I tested it extensively, it is singularity free. Any discussion on this matter is welcome…………

Collisions of masses depend on physical values of masses and their space distribution only. These collisions do not happen due to internal inherent problems of Dynamic universe Model. If the mass distribution is homogeneous and isotropic, the masses will colloid. If the mass distribution is heterogeneous and anisotropic, they do not colloid. This approach solves many problems which otherwise can not be solved by General relativity, Steady state universe model etc…



To summarize in other words:



In Dynamic Universe Model, there are no singularities and no collisions if we use heterogeneous mass distributions. When homogeneous mass distributions are used, there are collisions but no singularities. Resultant Universal Gravitational Force is calculated for each body for every time step in all the three dimensions. Conservation of energy, moment etc, were taken into consideration as shown in the Mathematical formulation. Using exactly same setup of mathematics and SITA algorithm and same number of 132 masses, all the results are derived, in the last 17 years.

[pzkpfw]

This thread makes claims about the "Dynamic Universe Model" but provides no actual details about that model nor any proof of those claims.

Clearly it is a further attempt to promote a model that has already had its' chance in the ATM forum.

If anyone sees a need to re-open this thread please report this post, with details of why.

[PetersCreek]

Being the moderator who authorized snp.gupta to initiate this thread, I'm reopening it for discussion. From the summary I was given (included in the OP) it would appear that this thread is intended to address subjects sufficiently different from previous Dynamic Universe Model threads to warrant discussion.

snp.gupta,

Moderator pskpfw is certainly correct to indicate that so far, your thread is decicient of support for your assertions. I trust that support is immediately forthcoming. Otherwise, I'll lock this thread myself, with extreme prejudice.

[snp.gupta]

This thread makes claims about the "Dynamic Universe Model" but provides no actual details about that model nor any proof of those claims.

Clearly it is a further attempt to promote a model that has already had its' chance in the ATM forum.

If anyone sees a need to re-open this thread please report this post, with details of why.

Sir,

From the bolded words from your post , You are getting a feeling that I am hiding some thing, some details etc. I am not hiding any thing. Please ask all your questions….

I am working for the sake of humanity. I am not hiding anything. Please ask me the details you want. May be my technical terminology may be slightly different. You people from Physics stream, may be using same terms in a slightly different way. I am from Engineering background. May be sometimes I did not study some literature you are referring. Please give me some such details.

I am an open man. I don’t want any thing from any body. What ever the resources are available with me I am using them at my level. I did not use anybody else’s resources for this purpose.

Please feel free to ask your doubts and questions in this open forum, I will reply….

Regards

[snp.gupta]

snp.gupta,

Moderator pskpfw is certainly correct to indicate that so far, your thread is decicient of support for your assertions. I trust that support is immediately forthcoming. Otherwise, I'll lock this thread myself, with extreme prejudice.

Thank you sir,

I hope I will not go into such problem. Previously due to my computer failure on posting the first post, and availability of less resources, my 2nd post got delayed; which I have indicated before opening my thread.

I have no problem of sharing my views and answering your questions with in my available resources. I will support my assertions…….

[hhEb09'1]

You have to input various values of masses, accelerations, velocities and positions and distances with a time step to get the next set of positions depending on the Universal Gravitational Force on a particular body. I have not used the conventional methodology for the solution, but it is a numerical solution, which can be done with a person with a calculator. I tested it extensively, it is singularity free. Any discussion on this matter is welcome…………From that description, I would say that this was first done over three hundred years ago. A numerical solution is nothing new.

I'm even doubting the reliability of your method--you should provide more details.

[macaw]

Thank you sir,

I hope I will not go into such problem. Previously due to my computer failure on posting the first post, and availability of less resources, my 2nd post got delayed; which I have indicated before opening my thread.

I have no problem of sharing my views and answering your questions with in my available resources. I will support my assertions…….

Ok,

As a warm-up problem, let's consider only two bodies, on of mass m , the other of mass M>>m. The body of mass m is moving in a straight line towards the body of mass M under the gravitational force GMm/r^2. The initial distance between the bodies is d and their initial relative speed is 0. Solve the equation of motion for the smaller body.

If you managed to solve the first problem you will not have a problem posting the solution for the case of three bodies. Let's say that they are of equal mass, in order to make the exercise simpler and that they are separated by the distances d_12, d_23 and d_31.
Solve the problem, please. Symbolic solution, not numerical.

[WayneFrancis]

I eagerly await snp.gupta's answer to macaw's question. Please excuse me not holding my breath.

I'm with the mods here. All I see is an assertion with nothing to back it up. You can say that your model is independently verifiable but unless you provide the formulas how is anyone supposed to verify your claim?

[snp.gupta]

From that description, I would say that this was first done over three hundred years ago. A numerical solution is nothing new.

I'm even doubting the reliability of your method--you should provide more details.

Please ask me what type of details you need....

[snp.gupta]

.

I'm with the mods here. All I see is an assertion with nothing to back it up. You can say that your model is independently verifiable but unless you provide the formulas how is anyone supposed to verify your claim?


The paper is available at

http://www.bautforum.com/against-mainstream/90377-modified-paper-dynamic-univesrse-model-6.html#post1522851

[snp.gupta]

Ok,

As a warm-up problem, let's consider only two bodies, on of mass m , the other of mass M>>m. The body of mass m is moving in a straight line towards the body of mass M under the gravitational force GMm/r^2. The initial distance between the bodies is d and their initial relative speed is 0. Solve the equation of motion for the smaller body.

If you managed to solve the first problem you will not have a problem posting the solution for the case of three bodies. Let's say that they are of equal mass, in order to make the exercise simpler and that they are separated by the distances d_12, d_23 and d_31.
Solve the problem, please. Symbolic solution, not numerical.

You are exactly correct sir,

You have to use the equations given in

http://www.bautforum.com/against-mainstream/95912-singularity-free-n-body-problem-solution.html#post1613818

Dynamic Universe Model will work for 2 bodies or 3 bodies or 1 million bodies. All You have to do is to calculate Universal Gravitational Force (UGF) acting on each body using Newtonian Gravitational attraction as given by you here in your post. For a two body motion it will be simplified to Newtonian Gravitational attraction equation. For Three bodies and above, it will calculate UGF, with the same set of equations….

By the way what is ‘r’ in your equation? Probably you are confusing it with ‘d’

[snp.gupta]

Fortis
From your description you have not solved the N-body problem. You are (to the best of your ability) carrying out a numerical simulation of the N-body problem. That is not the same as solving the problem as is normally understood by this term.

http://www.bautforum.com/against-mainstream/95279-did-any-body-solve-singularity-free-n-body-problem-using-newtonian-gravitation.html#post1605964



You have to use the equations given at
http://www.bautforum.com/against-mainstream/95912-singularity-free-n-body-problem-solution.html#post1613818

You can say it is numerical calculation of values using equations given above. Generally in engineering terminology we use the term ‘simulation’ for depicting any problem on a computer. In a simulation computer will take some decisions. Here only simple calculations are done using a computer. They can be done with any person with a calculator.

I could not get your point, what else are required by you….?

[pzkpfw]

NOT

GOOD

ENOUGH.

You have had previous threads.

You were allowed this new thread because it seemed you had something new to add.

But you have provioded no new detail, and only links to your previous, locked, threads.

So far there seems little reason for this thread to exist. Please start answering the questions, here, in this thread.

Try - here in this thread - to provide some detail for the claims you made in the OP )post #1 of this thread).

Post #7 from macaw would be a good start.

[tusenfem]

You have to use the equations given at
http://www.bautforum.com/against-mainstream/95912-singularity-free-n-body-problem-solution.html#post1613818

You can say it is numerical calculation of values using equations given above. Generally in engineering terminology we use the term ‘simulation’ for depicting any problem on a computer. In a simulation computer will take some decisions. Here only simple calculations are done using a computer. They can be done with any person with a calculator.

I could not get your point, what else are required by you….?


Please stop linking to post to post to post.
These links do NOT lead to the equations that you claim.

[snp.gupta]

NOT

GOOD

ENOUGH.

You have had previous threads.

You were allowed this new thread because it seemed you had something new to add.

But you have provioded no new detail, and only links to your previous, locked, threads.

So far there seems little reason for this thread to exist. Please start answering the questions, here, in this thread.

Try - here in this thread - to provide some detail for the claims you made in the OP )post #1 of this thread).

Post #7 from macaw would be a good start.

ok,

Just tell me how to bring equations into this post? It is not taking equations for copy and paste. There is a difficulty, how to write equations here, i requre blackboard and chalk.......

Ok, I will add some more words of explanation. In the mathematical section that paper, we can see equation 25, that gives the resultant UGF, after converting this equation into gravitational force it will become 'GMm/r^2' for two bodies in vector form.

For three and higher number of bodies it becomes multiples of number of bodies of 'GMm/r^2' in vector form, and so on. We just follow equation 25, it solves all....

Please ask me your doubts , if further explanation is needed....

[snp.gupta]

Please stop linking to post to post to post.
These links do NOT lead to the equations that you claim.


How to tell the same point repeatedly? Ok, i will tell verbally from now on....

Ok , dont worry.

[snp.gupta]

korjik

From previous thread....

http://www.bautforum.com/against-mainstream/95279-did-any-body-solve-singularity-free-n-body-problem-using-newtonian-gravitation.html#post1605894

If your dynamic universe model gives a solution to the n-body problem, why havent you published the solution?


I want to publish it, Can you please help me in that respect....

Probably my English explanation is not that very good. That’s why you people are facing problem from my explanations, I feel.

That’s why I am asking you people to put your quarries repeatedly, till my explanation becomes meaningful to you

[captain swoop]

Macaw posted this problem for you to solve As a warm-up problem, let's consider only two bodies, on of mass m , the other of mass M>>m. The body of mass m is moving in a straight line towards the body of mass M under the gravitational force GMm/r^2. The initial distance between the bodies is d and their initial relative speed is 0. Solve the equation of motion for the smaller body.
start by showing how your theory solves it, add some numbers.

[slang]

Just tell me how to bring equations into this post?

Try this (http://knol.google.com/k/michael-chelen/embed-equation-online/gxxp1ckx8nad/2).

[snp.gupta]

macaw

Prom previous post.
http://www.bautforum.com/against-mainstream/95279-did-any-body-solve-singularity-free-n-body-problem-using-newtonian-gravitation.html#post1605810

you mean, it was disproved


It is new for them. People are trying to under stand now.

[snp.gupta]

Try this (http://knol.google.com/k/michael-chelen/embed-equation-online/gxxp1ckx8nad/2).


It is for LaTeX, which i dont know.

Is there any website that converts Microsoft Equation editor outputs which can be shown here on forum?

Meanwhile I will try to learn this also, ASAP....

Thank you

[snp.gupta]

Macaw posted this problem for you to solve start by showing how your theory solves it, add some numbers.

Yes, something I already wrote. Some I will post with MS equation editor ASAP....

What actually you mean by ' add some numbers'? I I could not get your point, Please explain me.

[tusenfem]

It is for LaTeX, which i dont know.

Is there any website that converts Microsoft Equation editor outputs which can be shown here on forum?

Meanwhile I will try to learn this also, ASAP....

Thank you

If you use Mozilla Firefox as a browser, then load the add-on abcTajpu, which will give you access to unnumerous symbols.

Then there are for easy use the commands
[sub - /sub] for subscript
[sup - /sup] for superscript

That will get you underway.

[hhEb09'1]

The paper is available at

http://www.bautforum.com/against-mainstream/90377-modified-paper-dynamic-univesrse-model-6.html#post1522851


You have to use the equations given in

http://www.bautforum.com/against-mainstream/95912-singularity-free-n-body-problem-solution.html#post1613818

You have to use the equations given at
http://www.bautforum.com/against-mainstream/95912-singularity-free-n-body-problem-solution.html#post1613818


Ok, I will add some more words of explanation. In the mathematical section that paper, we can see equation 25, that gives the resultant UGF, after converting this equation into gravitational force it will become 'GMm/r^2' for two bodies in vector form.

For three and higher number of bodies it becomes multiples of number of bodies of 'GMm/r^2' in vector form, and so on. We just follow equation 25, it solves all....

Please ask me your doubts , if further explanation is needed....I followed those links (and re-links) and never came to a place that had an equation 25.

You have to input various values of masses, accelerations, velocities and positions and distances with a time step to get the next set of positions depending on the Universal Gravitational Force on a particular body. I have not used the conventional methodology for the solution, but it is a numerical solution, which can be done with a person with a calculator. I tested it extensively, it is singularity free. Any discussion on this matter is welcome…………From that description, I would say that this was first done over three hundred years ago. A numerical solution is nothing new.

I'm even doubting the reliability of your method--you should provide more details.
As near as I can tell, you are merely describing a numerical solution, and the other documentation is deficient as well.

[macaw]

You are exactly correct sir,

You have to use the equations given in

http://www.bautforum.com/against-mainstream/95912-singularity-free-n-body-problem-solution.html#post1613818

Dynamic Universe Model will work for 2 bodies or 3 bodies or 1 million bodies. All You have to do is to calculate Universal Gravitational Force (UGF) acting on each body using Newtonian Gravitational attraction as given by you here in your post. For a two body motion it will be simplified to Newtonian Gravitational attraction equation. For Three bodies and above, it will calculate UGF, with the same set of equations….

By the way what is ‘r’ in your equation? Probably you are confusing it with ‘d’

r is the variable distance between the two bodies. As in the universal attraction law: F=GMm/r^2

So, now that you know, what is the equation of motion and what is the solution of the equation of motion?

[pzkpfw]

Is there any website that converts Microsoft Equation editor outputs which can be shown here on forum?

One way:

Just take a screen-shot of the equation being clearly displayed on your system. (The "Print Screen" key).

Use mspaint or similar to cut it down to just the bits you need to show. (Paste the clipboard into a new image).

Upload the image as an attachment to your post.


What actually you mean by ' add some numbers'? I I could not get your point, Please explain me.

Oh for goodness sake.

He means USE your equation. Do some REAL calculations with it.

Show your working.

[PetersCreek]

snp.gupta,

You assured me that you were ready to support, defend, and answer questions about your theory. It appears that you are not.

It is not up to other members to tell you how to best support your theory. You should have prepared this support long before now. At the very least, you should have anticipated the obvious questions and challenges to your theory, especially in regard to the main points you summarized, which contradict the mainstream. You should also have prepared your math...and a means to present it...since a purported N-body solution cannot adequately be presented without it.

Not to be too blunt...but as far as this moderator is concerned, you need to start getting your act together within the next couple of posts to avoid thread closure.

[snp.gupta]

If you use Mozilla Firefox as a browser, then load the add-on abcTajpu, which will give you access to unnumerous symbols.

Then there are for easy use the commands
[sub - /sub] for subscript
[sup - /sup] for superscript

That will get you underway.

I am using MS internet Explorer as browser, How to use this any Idea...

[snp.gupta]

I followed those links (and re-links) and never came to a place that had an equation 25.


You will have to open the paper on Dynamic Universe model , Go to mathematical back ground, see the equation 25

[snp.gupta]

Originally Posted by hhEb09'1

Originally Posted by snp.gupta
You have to input various values of masses, accelerations, velocities and positions and distances with a time step to get the next set of positions depending on the Universal Gravitational Force on a particular body. I have not used the conventional methodology for the solution, but it is a numerical solution, which can be done with a person with a calculator. I tested it extensively, it is singularity free. Any discussion on this matter is welcome…………


From that description, I would say that this was first done over three hundred years ago. A numerical solution is nothing new.

I'm even doubting the reliability of your method--you should provide more details.

As near as I can tell, you are merely describing a numerical solution, and the other documentation is deficient as well.

For example I take equation f(x) = x^2+5x+10 , put various values for x say zero, various other values and large numbers for infinity or minus infinity etc to test the behavior of equation for f(x), will call it as a numerical solution?

Here Equations set has many variables, x, y, z, a, b, c, d, f, g etc many…. How will you solve them and test the behavior of equations. Please give me an example, how it was done three hundred years back…

[snp.gupta]

r is the variable distance between the two bodies. As in the universal attraction law: F=GMm/r^2

So, now that you know, what is the equation of motion and what is the solution of the equation of motion?

I hope you you are not testing my class 10 high school knoledge. I passed it out. :)
What is actually in your mind , please spell out....

[snp.gupta]

One way:

Just take a screen-shot of the equation being clearly displayed on your system. (The "Print Screen" key).

Use mspaint or similar to cut it down to just the bits you need to show. (Paste the clipboard into a new image).

Upload the image as an attachment to your post.



Thank you sir,

This I will try

[macaw]

I hope you you are not testing my class 10 high school knoledge. I passed it out. :)
What is actually in your mind , please spell out....

No, I am asking you to solve the problem for the case n=2. Please answer the question.

[snp.gupta]

Oh for goodness sake.

He means USE your equation. Do some REAL calculations with it.

Show your working.

Originally Posted by macaw
Ok,

As a warm-up problem, let's consider only two bodies, on of mass m , the other of mass M>>m. The body of mass m is moving in a straight line towards the body of mass M under the gravitational force GMm/r^2. The initial distance between the bodies is d and their initial relative speed is 0. Solve the equation of motion for the smaller body.

If you managed to solve the first problem you will not have a problem posting the solution for the case of three bodies. Let's say that they are of equal mass, in order to make the exercise simpler and that they are separated by the distances d_12, d_23 and d_31.
Solve the problem, please. Symbolic solution, not numerical.

No , In his post he was asking me symbolic solution, thats why i referred to Equation 25 math section of paper.

For calculation of numerical solution in Dynamic Universe Model, you have to give me initial values of 133 masses. I.e. you will have to supply their initial three dimensional ‘positions, velocities, accelerations’ and actual values of masses. Then the numerical values can be calculated. I did it that way.

This calculations program can be setup 2 , 3 or 50000 as required, But it will take time for setting up and testing. It may be few months. You please give me other values

[PetersCreek]

I hope you you are not testing my class 10 high school knoledge. I passed it out. :)
What is actually in your mind , please spell out....

If you don't understand a question or challenge, say so and ask for specific clarification. macaw challenged you to apply your model to a 2-body problem. Please do so, if you can. If you cannot, just say so.

As I said before, get this thread moving in the right direction...and soon. You're running out of chances.

[snp.gupta]

snp.gupta,

You assured me that you were ready to support, defend, and answer questions about your theory. It appears that you are not.

It is not up to other members to tell you how to best support your theory. You should have prepared this support long before now. At the very least, you should have anticipated the obvious questions and challenges to your theory, especially in regard to the main points you summarized, which contradict the mainstream. You should also have prepared your math...and a means to present it...since a purported N-body solution cannot adequately be presented without it.

Not to be too blunt...but as far as this moderator is concerned, you need to start getting your act together within the next couple of posts to avoid thread closure.

Sir,
I need some rest and sleep in between, I am answering, your questions….

I am asking the unknown things about how to present equations on to this board. This is an examination for me. How can be the questions known to me? I will have to answer them spontaneously by seeing the questions.

Yes you are correct mainstream says it is not possible to solve N-body problem without a singularity. I am giving this possible solution I worked out and tested for 17 years.

Don’t worry sir, I am trying my level best, to explain my situation and solution as my limited English permits.….

[snp.gupta]

No, I am asking you to solve the problem for the case n=2. Please answer the question.

Equation of motion is ½ a t^2+v t+p
a is acceleration of particle, v is velocity of particle, p is position of particle at time t

[snp.gupta]

If you don't understand a question or challenge, say so and ask for specific clarification. macaw challenged you to apply your model to a 2-body problem. Please do so, if you can. If you cannot, just say so.

As I said before, get this thread moving in the right direction...and soon. You're running out of chances.

Yes sir,

i asked a clarification only. what actually in his mind.

This model can be applied for any number of masses. But i worked it out for 133 masses. I need time to set it for other number of masses. It can be done. I gave the equation of motion for 2 bodies. the model will become so....

[macaw]

Equation of motion is ½ a t^2+v t+p
a is acceleration of particle, v is velocity of particle, p is position of particle at time t

No, it is not. Please form the differential equation that describes the motion and you will find out that your simple-minded solution is incorrect.

[snp.gupta]

If you managed to solve the first problem you will not have a problem posting the solution for the case of three bodies. Let's say that they are of equal mass, in order to make the exercise simpler and that they are separated by the distances d_12, d_23 and d_31.
Solve the problem, please. Symbolic solution, not numerical.

Now for the case of three body part of your question,

The model simplifies to same equation of motion for each body.

Equation of motion is ½ a t^2+v t+p
a is acceleration of particle, v is velocity of particle, p is position of particle at time t

These particles collapse into each other, as they are in single line in your case.

And when they are not in single line, the above equation will change into three dimensional vector form, the resultant direction vector will change from time to time..,

[snp.gupta]

No, it is not. Please form the differential equation that describes the motion and you will find out that your simple-minded solution is incorrect.

No differential equation is formed here in Dynamic Universe Model. Only simple and tested engineering equations are used. I did not get your point, may be if this answer is not sufficient, please clarify…..

[macaw]

Now for the case of three body part of your question,

The model simplifies to same equation of motion for each body.

Equation of motion is ½ a t^2+v t+p
a is acceleration of particle, v is velocity of particle, p is position of particle at time t

For the second time, you got the wrong solution, this is more complicated than what you learned in 9-th grade kinematics.

For the second time, form the differential equation that describes the motion and try solving it. Correctly.

[macaw]

No differential equation is formed here in Dynamic Universe Model.

That's too bad because mechanics is based on solving differential equations.
Are you telling us that you don't know how to form the differential equations that describe the motion? If this is the case, how can you pretend that you solved the n-body problem?



Only simple and tested engineering equations are used. I did not get your point, may be if this answer is not sufficient, please clarify…..

The point is that you need to be able to form the differential equations that describe the motion. Do you know how to do this?
After you formed the differential equations that describe the motion, you need to solve them. Do you know how to do this?

[Geo Kaplan]

No differential equation is formed here in Dynamic Universe Model. Only simple and tested engineering equations are used. I did not get your point, may be if this answer is not sufficient, please clarify…..

You must understand that offering an alleged solution for N=133 raises many questions. An ungenerous skeptic might suspect that offering a solution for such a large number of bodies is motivated by the knowledge that no analytical solution is available to falsify it. That is why it is important to test your "solution" for the couple values of N for which analytical solutions are already available. If your method does not yield the known solution for N=2, then we know there's a problem. Indeed, you should have done this validation yourself in debugging your code. It seems from your inability to produce this reference solution that you have not performed this essential first check. So here's one direct question:

Q1: What checks, if any, did you perform to validate your code?

You also say that no differential equation is involved. Then that triggers the following question:

Q2: What "simple and tested" equations did you use in your simulator?

Finally,

Q3: Since these are "simple and tested" equations, it should be correspondingly simple to generate the solution for N=2 and perform the comparison. Would you now do so?

[WayneFrancis]

Try this (http://knol.google.com/k/michael-chelen/embed-equation-online/gxxp1ckx8nad/2).

Cool thanks slang,
http://www.codecogs.com/eq.latex?\frac{V_{1}+V_{2}}{\sqrt[]{1+\frac{V_{1}V_{2}}{c^{2}}}}
I like this toy.
better then my
(V1+V2)/√(1+(V1V2/C2))

[snp.gupta]

For the second time, you got the wrong solution, this is more complicated than what you learned in 9-th grade kinematics.

For the second time, form the differential equation that describes the motion and try solving it. Correctly.

These are all outcomes after solving equation 25, which I referred in Dynamic universe model. In simplified language i explained you these for case of 2 bodies and three bodies.

This is different direction, many people tried in that differential equations direction. But there is no outcome. These are some of the changes made in Dynamic Universe model. if you feel diff eqn is the proper direction , you can try your self. i can explain what is done here, what good it achieved
.

[macaw]

These are all outcomes after solving equation 25, which I referred in Dynamic universe model. In simplified language i explained you these for case of 2 bodies and three bodies.

Well, then they are the wrong outcomes because you don't know how to write the correct equation.
Let me try to help you: start with F=GMm/r^2. Now, add to this F=dp/dt where p is the linear momentum.

Q4: Can you write the correct equation now?



This is different direction, many people tried in that differential equations direction.

Really? I thought that all self-respecting physicists who know what they are doing use differential equations. You didn't know about this?



But there is no outcome. These are some of the changes made in Dynamic Universe model. if you feel diff eqn is the proper direction , you can try your self. i can explain what is done here, what good it achieved
.

Q5: Then explain what equation generates your wrong solution 1/2at^2+vt+p?

So, stop dodging and please answer the questions Q1-5. Under the BAUT rules you are expected to do this.

[snp.gupta]

That's too bad because mechanics is based on solving differential equations.
Are you telling us that you don't know how to form the differential equations that describe the motion? If this is the case, how can you pretend that you solved the n-body problem?




The point is that you need to be able to form the differential equations that describe the motion. Do you know how to do this?
After you formed the differential equations that describe the motion, you need to solve them. Do you know how to do this?


This approach is slightly different from forming differential equations and solving. We can not get solutions in that direction. People tried . You already know that. That’s why there was no singularity free solution earlier. Can you please tell me who got solution in that direction….?

[macaw]

This approach is slightly different from forming differential equations and solving.

Please stop dodging and answer the questions.



Can you please tell me who got solution in that direction….?

Certainly not you. The naive 1/2at^2+vt+p applies only in 9-th grade, not in serious physics and certainly NOT when the force is GMm/r^2.

Q6: So, you don't know how to derive the solution, right?

Q7: If you can't solve the simplest case (n=2) I gave you, how can you expect any of us to be convinced that you can solve the general case?

[Geo Kaplan]

This approach is slightly different from forming differential equations and solving. We can not get solutions in that direction. People tried . You already know that. That’s why there was no singularity free solution earlier. Can you please tell me who got solution in that direction….?

But for the case of N=2, your approach should yield the same solution as the differential-equation based solution, right? This goes to the question that I have asked that remains unanswered.

I would also like to point out that I just checked several online engineering textbooks. They seem to be full of differential equations, so I am mystified about the meaning of your phrase "simple and tested engineering..." equations.

[Tensor]

Cool thanks slang,
http://www.codecogs.com/eq.latex?\frac{V_{1}+V_{2}}{\sqrt[]{1+\frac{V_{1}V_{2}}{c^{2}}}}
I like this toy.
better then my
(V1+V2)/√(1+(V1V2/C2))

Yeah, but after years on the internet, I can read the bottom one with no problem.:)

[Fortis]

For calculation of numerical solution in Dynamic Universe Model, you have to give me initial values of 133 masses. I.e. you will have to supply their initial three dimensional ‘positions, velocities, accelerations’'and actual values of masses.
You should not have to supply any values for the accelerations. The should come from the masses of the bodies and the force law of Newtonian gravity.

Are you really inputting the accelerations by hand?

[snp.gupta]

You should not have to supply any values for the accelerations. The should come from the masses of the bodies and the force law of Newtonian gravity.

Are you really inputting the accelerations by hand?

No never, But possibity and provision exists....
Regards
=snp

[slang]

Cool thanks slang,

Welcome. One technical issue is that when that website fails or stops, all your equations disappear from your BAUT posts... so it's probably smart to use it sparingly, include the LaTeX code at the bottom of your post, and/or to save the resulting image to your harddrive, and upload it to BAUT as an attached image (which also has its drawbacks for unregistered readers :/ ), and/or also include the written version of the formula.

[tusenfem]

This approach is slightly different from forming differential equations and solving. We can not get solutions in that direction. People tried . You already know that. That’s why there was no singularity free solution earlier. Can you please tell me who got solution in that direction….?

Apparently you don't understand that your equation:
0.5 a t2 + v t + x0
IS a solution to a differential equation.
But then, you don't do the math, do you, you have it done for you by someone else.

This whole thread is going to be EXACTLY the same nonsense as before, isn't it?

[pzkpfw]

These are all outcomes after solving equation 25, which I referred in Dynamic universe model. In simplified language i explained you these for case of 2 bodies and three bodies.

This is different direction, many people tried in that differential equations direction. But there is no outcome. These are some of the changes made in Dynamic Universe model. if you feel diff eqn is the proper direction , you can try your self. i can explain what is done here, what good it achieved
.

You need to stop referring to equation 25 in some other paper, and put the equation HERE.

If that equation is not mainstream, or is mainstream but used in a non-mainstream way, you need to explain that HERE.

You then need to show how your equation or your use of it proves the many claims you made in post 1 of this thread.

So far you are doing your usual dance of making big claims and then dodging all questions.

[macaw]

No never, But possibity and provision exists....
Regards
=snp

Then stop dodging and answer the precise questions you have been asked. You are doing the same dance as in the previous threads.

[cjameshuff]

Welcome. One technical issue is that when that website fails or stops, all your equations disappear from your BAUT posts... so it's probably smart to use it sparingly, include the LaTeX code at the bottom of your post, and/or to save the resulting image to your harddrive, and upload it to BAUT as an attached image (which also has its drawbacks for unregistered readers :/ ), and/or also include the written version of the formula.

The LaTeX code is embedded in the URL, and there's other services providing similar functionality. If "http://www.codecogs.com/eq.latex?\frac{V_{1}+V_{2}}{\sqrt[]{1+\frac{V_{1}V_{2}}{c^{2}}}}" fails, you can edit the URL to use one of these services:
http://www.forkosh.dreamhost.com/source_mathtex.html#webservice

Some sites make this or similar services available to their users...it can be set up to check the referral header to restrict usage to posts on the forums. Maybe something to consider here...

[snp.gupta]

You need to stop referring to equation 25 in some other paper, and put the equation HERE.

If that equation is not mainstream, or is mainstream but used in a non-mainstream way, you need to explain that HERE.

You then need to show how your equation or your use of it proves the many claims you made in post 1 of this thread.

So far you are doing your usual dance of making big claims and then dodging all questions.

Dear sir,

I am not dodging any questions,

some questions need some serious thinking. and fresh mind, i need some time to think.

Some simple questions I am answering first.....

If you feel, that should not be done, I will have to stay in the same order, in which they were asked, then I will stay in that order.

I hope this is what you meant by dodging.

From now onwards I will stay in the same order they were asked, probably that will solve the problem of dodging? If not please explain me what is meant by dodging???

Regarding, equation 25, I am still not able to reproduce on forum page, I am helpless in this regard, that’s why I am referring it like that. My computer knowledge is limited….
I will make more trails….

[snp.gupta]

You must understand that offering an alleged solution for N=133 raises many questions. An ungenerous skeptic might suspect that offering a solution for such a large number of bodies is motivated by the knowledge that no analytical solution is available to falsify it. That is why it is important to test your "solution" for the couple values of N for which analytical solutions are already available. If your method does not yield the known solution for N=2, then we know there's a problem. Indeed, you should have done this validation yourself in debugging your code. It seems from your inability to produce this reference solution that you have not performed this essential first check. So here's one direct question:

Q1: What checks, if any, did you perform to validate your code?

You also say that no differential equation is involved. Then that triggers the following question:

Q2: What "simple and tested" equations did you use in your simulator?

Finally,

Q3: Since these are "simple and tested" equations, it should be correspondingly simple to generate the solution for N=2 and perform the comparison. Would you now do so?

Instead of going straight into answering your direct question, I also will put a prelude first. I will answer all your questions one by one.

Those days say about almost 17 years back, after writing those equations given in the mathematical background of Dynamic universe model, I started the lengthy process of solving those equations in the usual differential equations method. Soon I stopped on some day, as I was not reaching any end. I believe in Goddess Vak, She gave me this approach next day early morning. Later I worked out that solution for a year or two. I felt it is a promising approach. It is a numerical calculations approach. That time internet was not freely available in India. I was to search books and magazines, what ever possible with in my limited purse. That time I did not know what other researchers were doing exactly for N-body problem. I know they do with some expensive super computers. I don’t have expensive computers. Of course I don’t have them even today. I don’t know weather such prelude can be written in BAUT forum. If it is to be deleted, I will delete, please let me know about it, I will do that in my next edit.

Now coming to the points you indicated, testing of the solutions and of course visualizing the large output data which is very simplified now a days, and was very difficult those days.

A. There are many reasons for ‘why132 masses?’ question. This question has both the sides. For higher number of masses as well as lower side. Now for the higher side…

1. When this Dynamic Universe Model project was started in the beginning of 1990’s, the availability of computers to a common man in India was very scarce. It was that period, where processor is 8088. The PC with two floppy drives were endangered species and hard drives are entering the field. There were limitations of capacity of data handling.


2. Computers in those days used to take few hours to calculate something like 50 iterations, which drastically reduced to 8 to 10 min today with a five year old laptop.


3. Milkyway, our Galaxy has estimated 10^11 Stars approximately. Number of planets will be additional 10^12. We can estimate number of dwarf planets to be 1000 times the planets, say about 10^15. What about chunks of planets and asteroids? They may be a million times the number of planets, say about 10^18. All these figures were taken on the lover side for an approximation. Hence about10^19 masses and their position data are required for simulating a Galaxy. Now there are millions or trillions of Galaxies in the Universe. What will be the total number of masses required to simulate? It will be about 10^25 to10^28. Is there any Super computer on Earth which can handle such huge amount of data, today? Do we have all such data to feed the computer?


4. May be 132 masses, are less for a simulation. But even 3 body problem is not simple to solve. Even if we make a simulation with million or 10 million masses it will be on the order of 1020 times less than that is required for simulating the universe. We should be practical in our thinking. I don’t have access to higher computers. I am a poor man. I don’t have resources.

B. Coming for the lower side……….

Those days I did not think for the lower side at all. What I was aiming is to go for the highest. I did not took it in the way of mathematical induction process, that if it is true for n=2, and n=3, test for n and n+1. I got no way of testing that approach. I don’t have differential higher value to test my solution probably some of you can explain me how………………

[macaw]

I did not took it in the way of mathematical induction process, that if it is true for n=2, and n=3, test for n and n+1. I got no way of testing that approach. I don’t have differential higher value to test my solution probably some of you can explain me how………………

The fact is that you and your method cannot solve even the simplest case (n=2).

[pzkpfw]

snp.gupta, not much at all of that post actually answers the questions asked.

Thread locked while snp works out a suspension. Doesn't seem like anybody would have much to add. Report this post if you wish this thread to be re-opened.

[ToSeek]

Thread re-opened now that snp.gupta is back.

[Geo Kaplan]

Instead of going straight into answering your direct question, I also will put a prelude first. I will answer all your questions one by one.

You wrote a long, information-free prelude, and answered none of my questions. I remind you that you are obligated to answer our questions. I do not consider a long reply to be the equivalent of an answer.

Now that you're back from your suspension, please actually answer these questions. No preludes, allegories or disquisitions, please -- just answers.

[ITManager]

I am working for the sake of humanity. I am not hiding anything. Please ask me the details you want. May be my technical terminology may be slightly different. You people from Physics stream, may be using same terms in a slightly different way. I am from Engineering background. May be sometimes I did not study some literature you are referring. Please give me some such details.

I lost interest right there.

[snp.gupta]

You wrote a long, information-free prelude, and answered none of my questions. I remind you that you are obligated to answer our questions. I do not consider a long reply to be the equivalent of an answer.

Now that you're back from your suspension, please actually answer these questions. No preludes, allegories or disquisitions, please -- just answers.
Resp Toseek

I must thank you very much for this thing….

And i learned :
In these two days I learned a new technique, how to post equation on to board to some extent. Some equations I could not reproduce exactly. Probably you have to refer to Dynamic universe model paper for some of them. Thanks our friend who suggested this….

http://thornahawk.unitedti.org/equationeditor/equationeditor.php

The Equation 25:
\phi_{ext}\left(\alpha \right)=-\sum_{\beta=1,\alpha\neq\beta}^{N^{\gamma}}\frac{G m_{\beta}^{\gamma}}{\left|x^{\gamma\beta} \,-\,x^{\gamma\alpha}\right|}-\sum_{\beta=1,\alpha\neq\beta}^{N^{\delta\gamma}}\ frac{Gm_{\beta}^{\delta\gamma}}{\left|x^{\delta\ga mma\beta} \,-\,x^{\delta\gamma\alpha}\right|}

http://www.codecogs.com/eq.latex?\phi_{ext}\left(\alpha \right)=-\sum_{\beta=1,\alpha\neq\beta}^{N^{\gamma}}\frac{G m_{\beta}^{\gamma}}{\left|x^{\gamma\beta} \,-\,x^{\gamma\alpha}\right|}-\sum_{\beta=1,\alpha\neq\beta}^{N^{\delta\gamma}}\ frac{Gm_{\beta}^{\delta\gamma}}{\left|x^{\delta\ga mma\beta} \,-\,x^{\delta\gamma\alpha}\right|}

This is first time I am trying to see equation, it did not show on preview...

Let me tell you some thing in general for the questions in thread……

There are about 5000 different equations for 132 masses in Dynamic Universe model, which can be grouped into about 350 generic varieties. There were about 15 graphs for observing variations of various parameters, changing paths etc. Deriving these equations from the Tensor equations mostly from equation 25 is a long process and took me about 2 years. Because of the testing difficulties for higher number of masses, I tested all these 5000 equations each separately and established correctness separately, initially while I was doing the coding, I don’t know how to test these equation other wise, in totality. [ of course, I corrected many initial problems also. ]

Once I felt this SITA algorithm was working nicely on simulated data, I started inputting the real data from astronomical observations. If the system is correct, I must be able to verify with the real physical data also. That was the final real testing. Once I am thro and the output data was matching with the real observations, I started giving it to you, if some body interested, he can use this algorithm.

This can be developed for other cases like for instance 2 or 3 or 50,000 bodies. Initially, I did not develop it for this type of working. It can be done if needed. For your immediate question to show it for 2 bodies is difficult for me. I feel there is no isolated place in the universe to test the exactness values of movements of two bodies, excluding the other bodies. There is attraction force effect of other bodies is always present. You people are better knowledged and equipped than me, you can show me such places…????.. For example, on sea water which is very near to earth surface, you see the effect of distant moon and Sun. We can not ignore the effects of gravitation of other bodies, near a strong gravitation fields like earth.

That’s why I gave you that equation 1/2 at^2+vt+p can be an approximation for two bodies. I did not say it is exactly that equation, but it works for simple and better understanding for you, nothing else.

[snp.gupta]

\phi_{ext}\left(\alpha \right)=-\sum_{\beta=1,\alpha\neq\beta}^{N^{\gamma}}\frac{G m_{\beta}^{\gamma}}{\left|x^{\gamma\beta} \,-\,x^{\gamma\alpha}\right|}-\sum_{\beta=1,\alpha\neq\beta}^{N^{\delta\gamma}}\ frac{Gm_{\beta}^{\delta\gamma}}{\left|x^{\delta\ga mma\beta} \,-\,x^{\delta\gamma\alpha}\right|}

Eqn 25 please see the attachment

[snp.gupta]

I lost interest right there.

You please tell me what I will get by posting my all replies. Money??? None. No one ever gave me any money except showing hospitality after I go on my own expenses in conferences. Fame ???? None, I got only ill fame. You think only I am making tall claims….. No tall claims . Nothing.

In fact Dynamic Universe model has a large potential and it is showing many other wonderful results. I am presenting only those results that are precisely measurable and are with some better points…..

Because of my mad ness about this Dynamic Universe model, I lost many things in my life. My health is also a problem. In my limited time which is available, I am telling and answering what I can do. In my life I lost all my games due to this mad ness, now there is nothing else to loose….

[snp.gupta]

Well, then they are the wrong outcomes because you don't know how to write the correct equation.
Let me try to help you: start with F=GMm/r^2. Now, add to this F=dp/dt where p is the linear momentum.

Q4: Can you write the correct equation now?



Sir
See the attchment. I have taken care of all these things please go thro derivation.....

==============

http://www.codecogs.com/eq.latex?
Total \,mass \,of\, System = M= \sum_{\alpha=1}^{N}m_{\alpha}\qquad(2)
Total force on the particle  is F , Let F is the gravitational force on the  th particle due to th particle.
(3)
F_{\alpha}=\sum_{\alpha=1 ;\alpha\neq\beta}^{N}F_{\alpha\beta}\,-\,m_{\alpha}\bigtriangledown_{\alpha}\phi_{ext}(\a lpha)\qquad(3)
F_{\alpha}=\sum_{\alpha=1 ;\alpha\neq\beta}^{N}F_{\alpha\beta}\,-\,m_{\alpha}\bigtriangledown_{\alpha}\phi_{ext}(\a lpha)\qquad(3)
Moment of inertia tensor
Consider a system of N particles with masses M, at positions X, =1, 2,…N; The moment of inertia tensor is in external back ground field  ext.
(4)
http://www.codecogs.com/eq.latex?I_{jk}=\sum_{\alpha=1}^{N}m_{\alpha}x_{j} ^{\alpha}x_{k}^{\alpha}\qquad(4)
I_{jk}=\sum_{\alpha=1}^{N}m_{\alpha}x_{j}^{\alpha} x_{k}^{\alpha}\qquad(4)
Its second derivative is
(5)
\frac{d^{2}I_{jk}}{dt^{2}}}=\sum_{\alpha=1}^{N}m_{ \alpha}\left( x_{j}^{\alpha}x_{k}^{\alpha}+x_{j}^{\alpha}x_{k}^{ \alpha}+x_{j}^{\alpha}x_{k}^{\alpha} \right)
\frac{d^{2}I_{jk}}{dt^{2}}}=\sum_{\alpha=1}^{N}m_{ \alpha}\left( x_{j}^{\alpha}x_{k}^{\alpha}+x_{j}^{\alpha}x_{k}^{ \alpha}+x_{j}^{\alpha}x_{k}^{\alpha} \right)

[snp.gupta]

Apparently you don't understand that your equation:
0.5 a t2 + v t + x0
IS a solution to a differential equation.
But then, you don't do the math, do you, you have it done for you by someone else.

This whole thread is going to be EXACTLY the same nonsense as before, isn't it?

This is solution for the tensor equation 25. In its solution: I am reproducing this part of my anwer in sted of referring another post....

There are about 5000 different equations for 132 masses in Dynamic Universe model, which can be grouped into about 350 generic varieties. There were about 15 graphs for observing variations of various parameters, changing paths etc. Deriving these equations from the Tensor equations mostly from equation 25 is a long process and took me about 2 years. Because of the testing difficulties for higher number of masses, I tested all these 5000 equations each separately and established correctness separately, initially while I was doing the coding, I don’t know how to test these equation other wise, in totality. [ of course, I corrected many initial problems also. ]

I could not solve the total differential equation, my math knowledge is limited. What I can say is this method also offeres an alternative solution, which you may consider...

[snp.gupta]

....Certainly not you. The naive 1/2at^2+vt+p applies only in 9-th grade, not in serious physics and certainly NOT when the force is GMm/r^2.

Q6: So, you don't know how to derive the solution, right?

Q7: If you can't solve the simplest case (n=2) I gave you, how can you expect any of us to be convinced that you can solve the general case?

I tried a tensor solution, insted of trying for N-body Differntuial equations set....

Please check my other posts above.....

[snp.gupta]

Till now we are seeing the Dynamic Universe Model as alternative to other cosmological models. But now I want to project it as a simple singularity free N-body problem which was not solved till now say from 1880 onwards when king Oscar II announced the prize. Using this N-body solution we can achieve various results as follows.

1. Offers Singularity free solutions
2. Non- collapsing Galaxy structures
3. Solving Missing mass in Galaxies, and it finds reason for Galaxy circular velocity curves….
4. Blue shifted and red shifted Galaxies co-existence…
5. Explains the force behind expansion of universe.
6. Explains the large voids and non-uniform matter densities.
7. Explains the Pioneer anomaly
8. Predicts the trajectory of New Horizons satellite.

Mainly because, points 2,3 7 and 8 are not cosmological problems, they were N-body problems. Point 1 is required in both N-body solution as well as cosmology……


1. Offers Singularity free solutions

When there are two masses with the same coordinates exactly; SITA simulations give divide by zero error. I mean to say for example centers of Sun and Moon can not coinside with each other. Or any two masses. That means any one mass can have zero zero coordinates. no one another mass sit over there on it.

Other wise I did not find any devide by zero error. Or singularity....

Points 2- 8 were disucces in earlier threads. Any further questions or data are welcome.


Here basically, I want to ask the question ' did any body else Got solution for singularity free N-body solution? ' earlier......... Differential equations or otherwise ......?????

[pzkpfw]

This is solution for the tensor equation 25. In its solution: I am reproducing this part of my anwer in sted of referring another post....

There are about 5000 different equations for 132 masses in Dynamic Universe model, which can be grouped into about 350 generic varieties. There were about 15 graphs for observing variations of various parameters, changing paths etc. Deriving these equations from the Tensor equations mostly from equation 25 is a long process and took me about 2 years. Because of the testing difficulties for higher number of masses, I tested all these 5000 equations each separately and established correctness separately, initially while I was doing the coding, I don’t know how to test these equation other wise, in totality. [ of course, I corrected many initial problems also. ]

1. The above is an example of why you have trouble with your threads. The above is not evidence or proof of anything. It is a claim. People suggest that you avoid answering questions, because this sort of "answer" simply makes more unproven claims.

2. Take a look at post #66, use "edit" mode to see what was done to include your equation. You cannot simply put latex code in your post and expect an equation to appear.

Please also see the FAQ thread: http://www.bautforum.com/forum-rules-faqs-information/72891-frequently-asked-questions.html

[Fortis]

Resp Toseek

I must thank you very much for this thing….

And i learned :
In these two days I learned a new technique, how to post equation on to board to some extent. Some equations I could not reproduce exactly. Probably you have to refer to Dynamic universe model paper for some of them. Thanks our friend who suggested this….

http://thornahawk.unitedti.org/equationeditor/equationeditor.php

http://www.codecogs.com/eq.latex?\phi_{ext}\left(\alpha \right)=-\sum_{\beta=1,\alpha\neq\beta}^{N^{\gamma}}\frac{G m_{\beta}^{\gamma}}{\left|x^{\gamma\beta} \,-\,x^{\gamma\alpha}\right|}-\sum_{\beta=1,\alpha\neq\beta}^{N^{\delta\gamma}}\ frac{Gm_{\beta}^{\delta\gamma}}{\left|x^{\delta\ga mma\beta} \,-\,x^{\delta\gamma\alpha}\right|}
.
.
.

This can be developed for other cases like for instance 2 or 3 or 50,000 bodies. Initially, I did not develop it for this type of working. It can be done if needed. For your immediate question to show it for 2 bodies is difficult for me. I feel there is no isolated place in the universe to test the exactness values of movements of two bodies, excluding the other bodies. There is attraction force effect of other bodies is always present. You people are better knowledged and equipped than me, you can show me such places…????.. For example, on sea water which is very near to earth surface, you see the effect of distant moon and Sun. We can not ignore the effects of gravitation of other bodies, near a strong gravitation fields like earth.

That’s why I gave you that equation 1/2 at^2+vt+p can be an approximation for two bodies. I did not say it is exactly that equation, but it works for simple and better understanding for you, nothing else.
Please can you show what your system of equations look like for the two body problem, i.e. how the tensor equation (which you don't seem to have defined the terms for) reduces to the two body problem?

This should have been one of the first things that you did when you were devloping your model. After all, if it doesn't work for two bodies, then what hope have you for the general n-body problem?

[snp.gupta]

1. The above is an example of why you have trouble with your threads. The above is not evidence or proof of anything. It is a claim. People suggest that you avoid answering questions, because this sort of "answer" simply makes more unproven claims.

2. Take a look at post #66, use "edit" mode to see what was done to include your equation. You cannot simply put latex code in your post and expect an equation to appear.

Please also see the FAQ thread: http://www.bautforum.com/forum-rules-faqs-information/72891-frequently-asked-questions.html

Thank you sir,

1.You please suggest me where to start in such complex situation. All equations and processes are important and interdependent. I am not avoiding any question. I my self don’t know how to explain. That’s why probably you are feeling like that. How many equations i will explain? Equation 25 is the starting point. You have to use a pencil and eraser to carefully subdivide it into smaller parts.

2. I don’t know so much software. My knowledge in computers is low and simple. I saw what you did, thank you. I will do the same for others.

[snp.gupta]

Please can you show what your system of equations look like for the two body problem, i.e. how the tensor equation (which you don't seem to have defined the terms for) reduces to the two body problem?

This should have been one of the first things that you did when you were devloping your model. After all, if it doesn't work for two bodies, then what hope have you for the general n-body problem?

Sir,
Either two bodies or 132 bodies or 50000 bodies, the SITA simulation is same methodology. What difference will it make for you to understand the system if it is 132 bodies? I did not follow your logic. For two bodies, especially, it is dangerous, as it ignores the gravitation force of other bodies in the concept it self as there are no other bodies. Three is not that bad, You have to consider fluctuating gravitational forces. From four on words they will be forming more stable configurations. That’s why I avoided two and three from the beginning. Another thing is that I want to accommodate as many bodies as possible.

Two body problem is untrustworthy to start with, it will lead to confusions, as we can see the presumptions prevailing in the scientific world.

Shall I explain it for 132 bodies?

[agingjb]

I really would suggest that the application of an original approach to the n-body problem in Newtonian dynamics should, if only for the purposes of exposition (and corroboration), be demonstrated for the 2-body problem.

Of course it may, for all I know, be inherently inapplicable to two bodies, but, if this is the case, then this should be stated and the reason should be given.

[Fortis]

Sir,
Either two bodies or 132 bodies or 50000 bodies, the SITA simulation is same methodology. What difference will it make for you to understand the system if it is 132 bodies? I did not follow your logic. For two bodies, especially, it is dangerous, as it ignores the gravitation force of other bodies in the concept it self as there are no other bodies. Three is not that bad, You have to consider fluctuating gravitational forces. From four on words they will be forming more stable configurations. That’s why I avoided two and three from the beginning. Another thing is that I want to accommodate as many bodies as possible.

Two body problem is untrustworthy to start with, it will lead to confusions, as we can see the presumptions prevailing in the scientific world.

Shall I explain it for 132 bodies?
So your solution of the general n-body problem cannot deal with the case n=2. Is that what you are really saying?

[tusenfem]

This is solution for the tensor equation 25. In its solution: I am reproducing this part of my anwer in sted of referring another post....


Then SHOW us how the simple solution to F = dp/dt that I (and others and you) wrote down appears from this miraculous equation 25.

[tusenfem]

Sir,
Either two bodies or 132 bodies or 50000 bodies, the SITA simulation is same methodology. What difference will it make for you to understand the system if it is 132 bodies? I did not follow your logic. For two bodies, especially, it is dangerous, as it ignores the gravitation force of other bodies in the concept it self as there are no other bodies. Three is not that bad, You have to consider fluctuating gravitational forces. From four on words they will be forming more stable configurations. That’s why I avoided two and three from the beginning. Another thing is that I want to accommodate as many bodies as possible.

Two body problem is untrustworthy to start with, it will lead to confusions, as we can see the presumptions prevailing in the scientific world.

Shall I explain it for 132 bodies?


NO, you will NOT explain it for 132 bodies.
If your ominous equation 25 can handle N bodies, it can handle N=2, a simple check of whether your equations are correct. NOTHING can lead to "untrusworthy! cases.
Answer the questions and stop talking around things, otherwise you will get another infraction and/or time off.

[captain swoop]

snp.gupta Showing a solution for 2 Bodies is important because the mainstream already has a solution for n=2, we can therefore use it to check your solution.

[Geo Kaplan]

Sir,
Either two bodies or 132 bodies or 50000 bodies, the SITA simulation is same methodology. What difference will it make for you to understand the system if it is 132 bodies?

The logic has been explained to you, and everyone here who has done any science at all understands the rationale. I'll explain it again, so that you cannot claim ignorance (of this particular item): No analytical solution exists for N=132, but ONE DOES EXIST for N=2. So, PRESENT THE SOLUTION YOUR METHOD YIELDS for this KNOWN case. That's part of a verification step. Whether you're a scientist or an engineer doesn't matter -- both cultures rely on verification!

So, for the Nth time, stop your spamming, and just answer the question. If your idea truly has any value, this should be a simple task. Your bizarre resistance to this basic logic strongly suggests that you either have nothing to present, or something to hide.

Just answer the question. It shouldn't take pages and pages of verbiage. Look at a standard physics textbook -- you'll see how compact the solution is there.

[snp.gupta]

I really would suggest that the application of an original approach to the n-body problem in Newtonian dynamics should, if only for the purposes of exposition (and corroboration), be demonstrated for the 2-body problem.

Of course it may, for all I know, be inherently inapplicable to two bodies, but, if this is the case, then this should be stated and the reason should be given.

There are many practical difficulties. I will have to work out for such case with pencil and eraser for a year again. I gave the approximate equation already. I know this whole exercise will be fruit less. Because it gives practically useless set of equations as there will be no real application.

Reasons I already explained in this thread. If you want me to repeat again I will tell you…

[snp.gupta]

So your solution of the general n-body problem cannot deal with the case n=2. Is that what you are really saying?

Theoretically it is possible for any number of masses. I will have to work it out and tell you the exact solution, which will be time consuming process.....

[snp.gupta]

Then SHOW us how the simple solution to F = dp/dt that I (and others and you) wrote down appears from this miraculous equation 25.

why you want to start it from F= dp/dt ?

[tusenfem]

snp.gupta, you were told to answer the questions, and that does not mean answering them with questions.

You were asked to give the solution for 2 bodies. BECAUSE that has an analytical answer it is totally suited to check your solution from eq. 25 or whatever. So your answer: Because it gives practically useless set of equations as there will be no real application. is bogus, it is all BUT useless. You probably cannot do the work.

And it CANNOT be a time consuming process, as eq. 25 reduces significantly for N=2. I could probably do it but I will not.

The 0.5 a t2 + v t + x0 is a solution to F = dp/dt.
YOU say this is a solution from your "tensor equation" and therefore you have to SHOW how your tensor equation comes to this solution. I did not tell you to start with F = dp/dt.

I hereby give you an infraction for not answering/dodging questions.

[macaw]

I tried a tensor solution, insted of trying for N-body Differntuial equations set....

Please check my other posts above.....

This is not an answer, your "solution" has nothing to do with the problem you are being asked to solve. To remind you, I have asked you :

1. To form the equations that govern the physics of the two-body (n=2) problem.

2. To solve the above equations.

Please do so.

[macaw]

For two bodies, especially, it is dangerous, as it ignores the gravitation force of other bodies in the concept it self as there are no other bodies.

No, it isn't dangerous at all. It is a way to verifying that you can solve the problem with your method.

[tusenfem]

As snp.gupta is once more suspended (until 16 November) I close this thread until his return.

[hhEb09'1]

I have re-opened this thread at the OP request.

I don't believe that the OP is presenting an analytic solution, but it seems to be a numerical solution. Requests for an analytic solution from the OP would seem to be irrelevant. Anybody?

[cjameshuff]

I have re-opened this thread at the OP request.

I don't believe that the OP is presenting an analytic solution, but it seems to be a numerical solution. Requests for an analytic solution from the OP would seem to be irrelevant. Anybody?

A numerical solution is nothing new. There's a wide variety of such solutions, with well-understood convergence behaviors, sensitivity to rounding errors, etc. But snp.gupta isn't claiming to have yet another numerical solution. His basic claim is clearly that he has an analytic solution, given his constant references to King Oscar II's prize: "Given a system of arbitrarily many mass points that attract each according to Newton's law, under the assumption that no two points ever collide, try to find a representation of the coordinates of each point as a series in a variable that is some known function of time and for all of whose values the series converges uniformly."

I think it's very likely that he simply doesn't understand the difference, and only has a numerical model which fails in every way to satisfy the prize criteria, but since he won't give a simple two-body example to examine...

[hhEb09'1]

I think it's very likely that he simply doesn't understand the difference, and only has a numerical model which fails in every way to satisfy the prize criteria, but since he won't give a simple two-body example to examine...Everything seems to point to that. I think that is where the conversations should lead.

I've just gone back through most of the thread, and I don't see where anyone has asked for a simple two-body example--they've just insisted on the two-body analytical solution. So, let's set up a two-body problem, and see where it takes us...

Mass A is 2x1030 kilograms, mass B is 6x1024 kilograms 150 billion meters away from A, moving at right angles to the line between them at a velocity of 30 thousand meters per second. Where are they after 20 million seconds?

Can you handle this problem snp.gupta? What else would you need to solve it? Do you need a velocity for A, or will your program develop one as it goes (in other words, assume it is zero to start, and see what happens)?

[cjameshuff]

I've just gone back through most of the thread, and I don't see where anyone has asked for a simple two-body example--they've just insisted on the two-body analytical solution. So, let's set up a two-body problem, and see where it takes us...

Because the two-body analytical solution is what he needs to provide.


Mass A is 2x1030 kilograms, mass B is 6x1024 kilograms 150 billion meters away from A, moving at right angles to the line between them at a velocity of 30 thousand meters per second. Where are they after 20 million seconds?

What's claimed is a general solution. Masses m1 and m2. Positions p1 and p2, initial velocities v1 and v2. He needs to give a solution that computes the position and velocity at any time t, regardless of what numbers you use for these values. A worked example would be better than anything he has given, but that two body analytical solution is necessary for checking against the known solution.

[macaw]

What's claimed is a general solution. Masses m1 and m2. Positions p1 and p2, initial velocities v1 and v2. He needs to give a solution that computes the position and velocity at any time t, regardless of what numbers you use for these values. A worked example would be better than anything he has given, but that two body analytical solution is necessary for checking against the known solution.

...but he can't. Despite repeated request, he can't do it. I started by asking him the symbolic solution for the 3 body problem, when he refused, I downgraded the problem to the 2 body one. Many posts and justifications later, still no answer.

[hhEb09'1]

Because the two-body analytical solution is what he needs to provide.Why?

If it is only numerical, there won't be an analytical solution available.

[cjameshuff]

Why?

If it is only numerical, there won't be an analytical solution available.

Because he claims to have the analytical solution.

[hhEb09'1]

Because he claims to have the analytical solution.I haven't been able to find where he makes that claim.

From the OP, as it reads now:You have to input various values of masses, accelerations, velocities and positions and distances with a time step to get the next set of positions depending on the Universal Gravitational Force on a particular body. I have not used the conventional methodology for the solution, but it is a numerical solution, which can be done with a person with a calculator.

[cjameshuff]

I haven't been able to find where he makes that claim.

He's made it repeatedly all through this and other threads about his "Dynamic Universe Model", here and on other forums. See the numerous references to King Oscar II's prize, including one in the opening post of this thread. King Oscar was quite specifically not looking for an iterative numeric approximation.

Numerical approximations aren't ATM, or in fact anything particularly remarkable. He did describe his algorithm as "numerical", but it's not the first time he's misused a term, and he clearly claims to have something new. He's also been pointed to the existing numerical approximations, and still claims to have something different and new.

Note: I do not expect him to actually post an analytical solution. I think he simply doesn't have the slightest idea what he's talking about. I expect him to either dance around and avoid the issue until the thread is closed again, or at best, post a badly broken numeric model that is wildly at odds with reality. But, however confused and erratic his claims are, he does claim to have an analytical solution, and that's what he needs to provide to comply with ATM rules.

And yes, he might well say he never made that claim, he's been consistently vague and evasive about the details and sloppy with terminology, but nothing else makes the slightest bit of sense.

[macaw]

Why?

If it is only numerical, there won't be an analytical solution available.

This is a very good question. This is precisely why I reduced the challenge to a two-body variant where there is no angular momentum (the initial speed is 0). For this particular case, there is no analytic solution because the problem reduces to forming a transcendental equation. Problem is, sne.gupta can't even form the equation of motion, let alone the transcendental solution.

[hhEb09'1]

I haven't been able to find where he makes that claim.

He's made it repeatedly all through this and other threads about his "Dynamic Universe ModelWhere has he made the claim in this thread?
And yes, he might well say he never made that claim, he's been consistently vague and evasive about the details and sloppy with terminology, but nothing else makes the slightest bit of sense.I can sympathize with the frustration, since I have asked for a few details myself, earlier. I think we might be able to straighten this whole thing out, with less frustration, if we ask the right questions.

[hhEb09'1]

Why?

If it is only numerical, there won't be an analytical solution available.

This is a very good question. This is precisely why I reduced the challenge to a two-body variant where there is no angular momentum (the initial speed is 0). For this particular case, there is no analytic solution because the problem reduces to forming a transcendental equation. Problem is, sne.gupta can't even form the equation of motion, let alone the transcendental solution.I meant analytical, not analytic, and I certainly know where you're going with this, but it appears to me to be a question that is incompatible with what the OP proposed.

If it is merely a numerical solution, we cannot expect the OP to produce an analytical solution from it. As cjameshuff has said, if it is just a numerical solution, this would not in and of itself be a major accomplishment--and it's not even clear that the infamous pitfalls of numerical solutions have been addressed.

[macaw]

If it is merely a numerical solution, we cannot expect the OP to produce an analytical solution from it.

This is precisely why I reduced the problem to a form for which only a numerical solution exists. The problem is so simple, even a freshman can solve. I am still waiting for sne.gupta to answer my challenge.....

[hhEb09'1]

Ok,

As a warm-up problem, let's consider only two bodies, on of mass m , the other of mass M>>m. The body of mass m is moving in a straight line towards the body of mass M under the gravitational force GMm/r^2. The initial distance between the bodies is d and their initial relative speed is 0. Solve the equation of motion for the smaller body.

If you managed to solve the first problem you will not have a problem posting the solution for the case of three bodies. Let's say that they are of equal mass, in order to make the exercise simpler and that they are separated by the distances d_12, d_23 and d_31.
Solve the problem, please. Symbolic solution, not numerical.
This is the problem you mean, right?
This is precisely why I reduced the problem to a form for which only a numerical solution exists. The problem is so simple, even a freshman can solve. I am still waiting for sne.gupta to answer my challenge.....snp.gupta

What do you mean, "only a numerical solution exists"? You seem to ask for a "not numerical" solution, right? In the problem I quote anyway. Is there another problem that you are referring to?

[cjameshuff]

Where has he made the claim in this thread?

Second sentence of the first post:
But now I want to project it as a simple singularity free N-body problem which was not solved till now say from 1880 onwards when king Oscar II announced the prize.

[macaw]

This is the problem you mean, right?
snp.gupta

What do you mean, "only a numerical solution exists"?


As opposed to a symbolic one.

You seem to ask for a "not numerical" solution, right?

No, I gave up on this request long ago, realizing that sne.gupta is unable to produce a non-numerical (aka a symbolic) solution.


Is there another problem that you are referring to?

Two-body solution, zero initial speed. Problem statement is at post #7, very early in the thread. He's been dodging the answer ever since.

[hhEb09'1]

Second sentence of the first post:I can see how you might infer that he might be making that claim, from that, but how do you reconcile your inference with this remark from the same post?:I have not used the conventional methodology for the solution, but it is a numerical solutionAs you and I have discussed, the OP has seemed to confuse the issue of which solutions have been attained already. And his numerical solution would then not be anything new, and is probably far surpassed by all the other approximate and numerical solutions that have been produced over the hundreds of years.

[Geo Kaplan]

I can see how you might infer that he might be making that claim, from that, but how do you reconcile your inference with this remark from the same post?:As you and I have discussed, the OP has seemed to confuse the issue of which solutions have been attained already. And his numerical solution would then not be anything new, and is probably far surpassed by all the other approximate and numerical solutions that have been produced over the hundreds of years.

I would be satisfied (for now) with snp.gupta showing a numerical solution for the two-body problem, with intermediate steps given. The idea all along has been to verify whether his method yields the same answer that is known to be correct for N=2. From his posts, we know that, surprisingly, he has never performed this basic check, which means that he has never performed a verification. That he is prematurely declaring victory is therefore apparent, and it is now incumbent upon him to show that his solution yields the same answer as the well-known analytical solution for N=2.

[cjameshuff]

I can see how you might infer that he might be making that claim,

I can not see how any other claim might be inferred. It's about the only thing he's been unambiguous about.


from that, but how do you reconcile your inference with this remark from the same post?

Simple: I think he doesn't know enough about the subject to speak coherently about it. However, he has been very clear that he is claiming to have a solution satisfying Oscar II's requirements...which means an analytical one. He's making a rather extraordinary claim, he needs to prove it. I don't think he has such a solution, but that doesn't change the fact that he needs to provide one to support his claims.

[Strange]

Is it worth someone trying to give a concise definition of numerical vs analytical methods to clear up any confusion that snp.gupta might have about what is meant?

[Geo Kaplan]

Is it worth someone trying to give a concise definition of numerical vs analytical methods to clear up any confusion that snp.gupta might have about what is meant?

At the risk of offending my math colleagues, here's an imprecise distinction that nevertheless might help the OP if he is indeed confused about this issue:

For the purposes of this thread, treat "analytical solution" as a formula (or set of formulas) that describes the form of the trajectories. Substitution of the boundary conditions, value of masses, etc. into the formulas yields numerical values for a specific case.

In a "numerical solution" there's just an algorithm that you run, and numbers come out. By my understanding of the wording of the original contest, only an analytical solution would've been acceptable.

There are many sub-classes of analytical solutions (e.g., closed-form; whether hypergeometric functions are allowed, etc.), but let's not worry about those fine distinctions just yet.

[hhEb09'1]

I can not see how any other claim might be inferred. It's about the only thing he's been unambiguous about.Well, I inferred differently, clearly. :)

Simple: I think he doesn't know enough about the subject to speak coherently about it. However, he has been very clear that he is claiming to have a solution satisfying Oscar II's requirements...which means an analytical one. He's making a rather extraordinary claim, he needs to prove it. I don't think he has such a solution, but that doesn't change the fact that he needs to provide one to support his claims.From the OP I inferred (my post #6 to this thread) that he did not think he had an analytic solution.

I will at the same time grant you that he probably thinks he has a solution worthy of the prize--not recognizing that his solution does not satisfy the requirements of the prize. There is a difference between claiming that he has an analytic solution to this famous problem, and claiming he has a solution.

It is, as you may know, very easy to construct an angle trisection with just a straightedge and a compass. (http://mentock.home.mindspring.com/trisect.htm) :)

[hhEb09'1]

=
For that, you gave me the values for two masses, distance between them and time step, Initial velocities and directions, for this problem. I will try to solve this problemThis thread will be re-opened when you can provide any of the solutions asked for.