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.

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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

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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…….

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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.

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.

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?

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

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The paper is available at

Modified paper of Dynamic Univesrse Model

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You are exactly correct sir,

You have to use the equations given in

A singularity free N Body problem – solution

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’

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You have to use the equations given at
A singularity free N Body problem – solution

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….?

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
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“A good scientist has freed himself of concepts and keeps his mind open to what is”
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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....

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

Ok , dont worry.

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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

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Try this.

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

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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

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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.

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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.

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善數, 不用籌策 (shàn shù, bù yòng chóu cè)
He who is good at counting, uses no counting tools
“A good scientist has freed himself of concepts and keeps his mind open to what is”
道德經, 二十七 (dào dé jīng, 27)

I followed those links (and re-links) and never came to a place that had an equation 25.
As near as I can tell, you are merely describing a numerical solution, and the other documentation is deficient as well.

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?

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.


Oh for goodness sake.

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

Show your working.

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

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

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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…

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