**All 4 Books are available for FREE Download as detailed below:**

**Book1. Dynamic Universe Model: A singularity-free N-body problem solution [ISBN 978-3-639-29436-1]---2010 October----VDM Germany**

Here
a solution to N-body problem-called Dynamic Universe Model (SITA) is
presented; which is singularity-free, inter-body collision free and
dynamically stable. The book talks about history and general
introduction and why anisotropic density distributions are to be taken.
The book also covers Mathematics and the final tensors formation
followed by Numerical Outputs. To prove that no singularities exist in
this model: three cases were taken 1. Non-zero Velocity position Vector
cross product, 2. The non-zero Polar moment of Inertia 3. The non-zero
Internal Distances between all pairs of point masses Their calculation
results are shown. Chaotic results with the Earlier Large Astrophysical
N-body Problem, and Exponential divergence and the various kinds of
errors, like Input and output Errors, are discussed and compared with
this model. This N-body problem solution can be used by any person who
has a PC for solving presently unsolved applications like Pioneer
anomaly, New Horizons satellite trajectory at the Solar system level,
Missing mass due to Star circular velocities and Galaxy disk formation
at Galaxy level etc.

This book is available foe FREE download at http://viXra.org/abs/1609.0139

https://figshare.com/s/901fe900ccab4d235a97

request reference: 9013970

request timestamp: 2016-09-10 19:13:01

viXra citation number: 1609.0139

latest version: v1

subject category: Astrophysics

Title: Dynamic Universe Model: A Singularity free N-Body problem solution

Authors: Satyavarapu Naga Parameswara Gupta

Abstract:

The failure to arrive at a singularity free solution for a general N-body problem for nearly 300 years has led people to treat this case of N-body simulations as being very turbulent. But I would like to reiterate and say that there is no reason for chaos here in Dynamic Universe Model. I am able to say this confidently after having worked on this Model for the last 18 years and creating 100,000 simulations using this SITA algorithm.

The trick here is to follow the law of Newtonian Gravitation fully without any deviation to calculate the Universal Gravitational force (UGF) on each mass. Other N-body simulations either deviated from this law or did not calculate UGF.

Apprehensions abound in any new field. As pointed earlier, my work in the last 18 years has given me enough confidence and I can say that the solution proposed hereunder will work almost in any physical situation and explain all the anomalies which arose due to the earlier theories. I can prove the working of the algorithm to any technical team.

Many people asked me the reason for selecting 133 masses. There are many reasons for this ‘why133 masses?’ question.

It was in the beginning of the 1990’s that the Dynamic Universal Model project began. The common man had minimal access to computers during this period in India. Processor 8088 prevailed. PC with two floppy drives was becoming redundant and was being slowly replaced by the hard drive. This resulted in limitations to data handling capacity. Computers used to take a few hours to calculate something like 50 iterations. Today, these iterations can be done in 8 to 10 minutes with a five – year old laptop.

The Milkyway, our Galaxy has 1011 Stars approximately with number of planets being an additional 10 times. Estimated number of dwarf planets would be 1000 times the number of planets, say about to 1015. Chunks of planets and asteroids may be a million times the number of planets, say about 1018. All these figures are on the lower side. Hence, about 1019 masses and their positional data is required to simulate a Galaxy. The total number of masses required to simulate would be about 1025 to 1028. 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?

May be 133 masses are too less a number to begin a simulation. However, even 3 body problem is not simple to solve directly with the usual differential equations method. Even if we create a simulation with a million or 10 million masses, it will approximately be 1020 less than what is required for simulating the universe. My resources being limited and having no access to higher computers, the best I can do is testing this SITA algorithm of Dynamic Universe model for the various situations within the available resources and time. I have carried out this work out of my own interest and have not sought any Government or University funding for the same.

I came up with the Dynamic Universe Model after 18 years after much effort and hard work. The Model uses Newtonian Gravitation for calculating the resultant Universal Gravitational force on every mass. No special assumptions have been made for arriving at the Model. In those days I did not think of lower side at all like N=2,3 4..etc. What I was aiming is to accommodate as many numbers of masses as possible. I did not take it in the way of mathematical induction process, i.e., if it is true for n=2, and n=3, then test for n and n+1. I have no way of testing that approach.

People asked me why I worked with only 133 masses. The SITA simulations can be done with higher number of masses on any Supercomputer provided funds and resources are available. I have successfully tested the SITA solution for 2, 3, 4, 133, 25000 point masses. I am sure we can arrive at the same results when tried with higher masses also.

Now I can say, this Dynamic Universe model is no more a fantasy, but it is reality.

Comments:

120 Pages. This Book was published in Germany ISBN 978-3-639-29436-1

Please go to this link below for this book......

https://www.morebooks.de/

.................................

.................................

**Book2. Dynamic Universe Model: SITA singularity free software ---2011 March --- VDM n Germany, March- 2011, ISBN 978-3-639-33501-9,**

Please go to this link below for a FREE copy of this book......

http://viXra.org/abs/1609.0143

The details of the submission were as follows:

request reference: 9014526

request timestamp: 2016-09-11 15:56:10

viXra citation number: 1609.0143

latest version: v1

subject category: Astrophysics

Title: Dynamic Universe Model :SITA singularity free software

Authors: Satyavarapu Naga Parameswara Gupta

Abstract:

In this monograph,all the equations of SITA software are explained for the singularity free solution to N-body problem – Dynamic Universe Model; which is, inter body collision free and dynamically stable are presented. SITA solution can be used in many places like presently unsolved applications like Pioneer anomaly at the Solar system level, Missing mass due to Star circular velocities and Galaxy disk formation at Galaxy level etc.

This is the second book, after the earlier book, “Dynamic Universe Model- a singularity free N-body problem solution” (ISBN 978-3-639-29436-1). Here SITA (Simulation of Inter-intra-Galaxy Tautness and Attraction forces) computer implementation Excel program software and its methodology and all the 21000 equations used there are explained in detail. One COPY OF SITA COPYRIGHTED SOFTWARE WILL SENT FREE OF COST BY CONTACTING THE AUTHOR AT ‘snp.gupta@gmail.com&#

Comments:

268 Pages. This is Book2 is published in Germany ISBN 978-3-639-33501-9

https://www.morebooks.de/

**Book3. Dynamic Universe Model: SITA software simplified[ISBN 978-3-639-36469-9]---Aug-2011----VDM Germany**

This
is the Third book in the series on Dynamic Universe Model, describing
the SITA software in EXCEL in the accompanying CD / DVD emphasizing
mainly HANDS ON usage of a simplified version. It explains 3000
equations for 133 masses [instead of earlier 21000 (Twenty one
thousand)], in 17 different groups with additional 14 Index functions
and 56 single equations. There are 16 ranges, 11 macros & processes
and 18 graphs to view and monitor various parameters. SITA is
singularity-free, inter-body collision free and dynamically stable. Here
basically how to tune, select input values, how to iterate & run to
get the results in EXCEL, how to select time step values, to analyze
data and using Graphs etc., are presented. This SITA solution can be
used by anyone who knows a little about EXCEL and little bit interested
in Physics for solving presently unsolved applications like Pioneer
anomaly, New Horizons satellite trajectory at the Solar system level,
Missing mass due to Star circular velocities and Galaxy disk formation
at Galaxy level etc., that is from the Solar system level, to Cosmology
level via Galaxy level.

https://figshare.com/s/875d033be0ebdbe1d11a

The details of the submission were as follows:

request reference: 9014780

request timestamp: 2016-09-11 20:55:54

viXra citation number: 1609.0150

latest version: v1

subject category: Astrophysics

Title: Dynamic Universe Model: SITA software simplified

Authors: Satyavarapu Naga Parameswara Gupta

Abstract:

With this Book, we have provided a CD or downloadable software in the e-book which has the simplified version of SITA software. Otherwise anyone can contact the author at

snp.gupta@gmail.com

Anyone with very limited knowledge in Physics and Microsoft Excel can try hands on with this software. This SITA software is developed for the singularity free solution to N-body problem – Dynamic Universe Model; which is, inter body collision free and dynamically stable. Basically this is a “how to go about” for using the SITA software. SITA solution can be used in many places like presently unsolved applications like Pioneer anomaly at the Solar system level, Missing mass due to Star circular velocities and Galaxy disk formation at Galaxy level etc.

This is the third book, after the earlier books, 1) “Dynamic Universe Model- a singularity free N-body problem solution” (ISBN 978-3-639-29436-1), and 2) Dynamic Universe Model- SITA singularity free software (978-3-639-33501-9) Here in this book a subset of SITA (Simulation of Inter-intra-Galaxy Tautness and Attraction forces) computer implementation Excel program software about 3000 equations are explained with usage out of all the 21000 equations used in the second book. Provision for a lot of modifications exists in the SITA program to tune to individual needs. This book is prepared in such a way it can be read independently of the first two books.

Comments:

220 Pages. Book3 of Dynamic Universe Model... ISBN 978-3-639-36469-9

..........**Please go to this link below for this FREE Download of book......**

https://figshare.com/s/875d033be0ebdbe1d11a

https://www.morebooks.de/store/fr/book/dynamic-universe-model/isbn/978-3-639-36469-9

http://viXra.org/abs/1609.0150

**Another link for FREE Download of the book....**http://viXra.org/abs/1609.0150

The details of the submission were as follows:

request reference: 9014780

request timestamp: 2016-09-11 20:55:54

viXra citation number: 1609.0150

latest version: v1

subject category: Astrophysics

Title: Dynamic Universe Model: SITA software simplified

Authors: Satyavarapu Naga Parameswara Gupta

Abstract:

With this Book, we have provided a CD or downloadable software in the e-book which has the simplified version of SITA software. Otherwise anyone can contact the author at

snp.gupta@gmail.com

Anyone with very limited knowledge in Physics and Microsoft Excel can try hands on with this software. This SITA software is developed for the singularity free solution to N-body problem – Dynamic Universe Model; which is, inter body collision free and dynamically stable. Basically this is a “how to go about” for using the SITA software. SITA solution can be used in many places like presently unsolved applications like Pioneer anomaly at the Solar system level, Missing mass due to Star circular velocities and Galaxy disk formation at Galaxy level etc.

This is the third book, after the earlier books, 1) “Dynamic Universe Model- a singularity free N-body problem solution” (ISBN 978-3-639-29436-1), and 2) Dynamic Universe Model- SITA singularity free software (978-3-639-33501-9) Here in this book a subset of SITA (Simulation of Inter-intra-Galaxy Tautness and Attraction forces) computer implementation Excel program software about 3000 equations are explained with usage out of all the 21000 equations used in the second book. Provision for a lot of modifications exists in the SITA program to tune to individual needs. This book is prepared in such a way it can be read independently of the first two books.

Comments:

220 Pages. Book3 of Dynamic Universe Model... ISBN 978-3-639-36469-9

...........

### ............

###
**4th Book: SITA: Dynamic Universe Model: Blue Shifted Galaxies Prediction Published (ISBN 978-3-8484-1382-9), 2012**

https://figshare.com/s/01b61b8ce7a4a603f39c

The details of the submission were as follows:

request reference: 9025168

request timestamp: 2016-09-17 04:33:58

viXra citation number: .

latest version:

subject category: Astrophysics

Title: CONTENTS: SITA: Dynamic Universe Model: Blue Shifted Galaxies Prediction …(Quasars, UV Galaxies, X-ray, γ- Ray sources and other Blue Galaxies)

Authors: Satyavarapu Naga Parameswara Gupta

Abstract:

This is the fourth book in the series on Dynamic Universe Model: SITA. These simulations predicted the existence of the large number of Blueshifted Galaxies in 2004, ie., more than about 35 ~ 40 Blueshifted Galaxies known at the time of Astronomer Edwin Hubble in 1930s. The far greater numbers of Blueshifted galaxies was confirmed by the Hubble Space Telescope (HST) observations in the year 2009. Today the known number of Blue shifted Galaxies is more than 7000 scattered all over the sky and the number is increasing day by day. In addition Quasars, UV Galaxies, X-ray, γ- Ray sources and other Blue Galaxies etc., are also Blue shifted Galaxies. Out of a 930,000 Galaxy spectra in the SDSS database, 40% are images for Galaxies; that gives to 558,000 Galaxies. There are 120,000 Quasars, 50,000 brotherhood(X-ray, γ-ray, Blue Galaxies etc.,) of quasars, 7000 blue shifted galaxies. That is more than 31.7% of available Galaxy count are Blue shifted. Just to support Bigbang theory,

we are neglecting such a huge amount Blue shifted Galaxies. It appears to be a Godly Devotion to Bigbang cosmologies!

In the original paper in 2004 (as given in the annexure to this book) there are simulations of the Universe. Here in these simulations the universe is assumed to be heterogeneous and anisotropic. This prediction process was clearly shown in the output data and pictures formed from this Model. These pictures show from the random starting points to final stabilized orbits of the point masses involved. Because of this dynamism built in the model, the universe does not collapse into a lump (due to Newtonian gravitational static forces). This Model depicts the three dimensional orbit formations of involved masses or celestial bodies like in our present universe. From the resulting graphs one can see the orbit formations of the point masses, which were positioned randomly at the start. An orbit formation means that some Galaxies are coming near (Blue shifted) and some are going away (Red shifted) relative to an observer’s viewpoint.

New simulations were conducted about a month before these writings. The resulting data graphs of these simulations with different kinds of input data are shown in this book in the later chapters.

In all these simulations, all point masses will have different distances, masses.

- Simulation 1: All point masses are Galaxies

- Simulation 2: All point masses are Globular Clusters

- Simulation 3: Globular Clusters 34 Galaxies 33 aggregates 33 conglomerations 33

- Simulation 4: Small star systems 10 Globular Clusters 100 Galaxies 8 aggregates 8 conglomerations 7

The problem with such simulations is the overwhelmingly large amounts of data. Each simulation gives 3 dimensional vector data of accelerations, velocities, positions for every point mass in every iteration in addition to many types of derived data. A minimum of 133 x 18 data of 16 decimal digits for each iteration. It is data and data everywhere. It is a huge data mine indeed.

One has to use graphs for visualizing such vast amounts of data. Again the question comes, which data to choose for showing in the graphs? Is it starting? Running? End of iteration? All bodies?Some groups? Single body? Selected bodies? Positions? Velocities? Accelerations? JPEG?GIF? Normal scales? Logarithmic Scales? Thirteen new graphs are being prepared for every iteration for positions.

From all the graphs, I usually handpick some graphs for showing the results.

I don’t know what data to be included as additional files, so I did not include any. I could be directly contacted for any of the data files, should anyone require them.

Hence we may conclude:

The actual ratio of Red shifted to Blue shifted Galaxies will depend on

1. Universal Gravitational Force acting on each Galaxy at that instant of time,

2. The position of the observer in the Universe

3. The actual point mass distribution in the universe in three dimensions at that instant of time. This ratio can never be 50:50.

Newtonian two-body problem used differential equations. Einstein’s general relativity used tensors, which in turn unwrap into differential equations. Dynamic Universe Model uses tensors that give simple equations with interdependencies. Differential equations will not give unique solutions. Whereas Dynamic Universe Model gives a unique solution of positions, velocities and accelerations; for each point mass in the system for every instant of time. This new method of Mathematics in Dynamic Universe Model is different from all earlier methods of solving general N-body problem.

This universe exists now in the present state, it existed earlier, and it will continue to exist in future also in a similar way. All physical laws will work at any time and at any place. Evidences for the three dimensional rotations or the dynamism of the universe can be seen in the streaming motions of local group and local cluster. Here in this dynamic universe, both the red shifted and blue shifted Galaxies co-exist simultaneously.

A point to be noted here is that the Dynamic Universe Model never reduces to General relativity on any condition. It uses a different type of mathematics based on Newtonian physics. This mathematics used here is simple and straightforward. As there are no differential equations present in Dynamic Universe Model, the set of equations give single solution in x y z Cartesian coordinates for every point mass for every time step. All the mathematics and the Excel based software details are explained in the three books published by the author14, 15, 16 In the first book, the solution to N-body problem-called Dynamic Universe Model (SITA) is presented; which is singularity-free, inter-body collision free and dynamically stable. This is the Basic Theory of Dynamic Universe Model published in 2010 14. The second book in the series describes the SITA software in EXCEL emphasizing the singularity free portions. It explains more than 21,000 different equations (2011)15. The third book describes

the SITA software in EXCEL in the accompanying CD / DVD emphasizing mainly HANDS ON usage of a simplified version in an easy way. The third book contains explanation for 3000 equations instead of earlier 21000 (2011)16.

SITA solution can be used in many places like presently unsolved applications like Pioneer anomaly at the Solar system level, Missing mass due to Star circular velocities and Galaxy disk formation at Galaxy level etc. Here we are using it for prediction of blue shifted Galaxies.

Dynamic Universe model does NOT depend on speculation. It is based on hard observed facts. I am writing these sentences especially as cosmology is becoming more and more speculative today.

Comments:

321 Pages. this is Book4 on Dynamic Universe Model.... Published in Germany with ISDN no. 978-3-8484-1382-9

Dynamic Universe model is based on hard observed facts and does NOT

The details of the submission were as follows:

request reference: 9025168

request timestamp: 2016-09-17 04:33:58

viXra citation number: .

latest version:

subject category: Astrophysics

Title: CONTENTS: SITA: Dynamic Universe Model: Blue Shifted Galaxies Prediction …(Quasars, UV Galaxies, X-ray, γ- Ray sources and other Blue Galaxies)

Authors: Satyavarapu Naga Parameswara Gupta

Abstract:

This is the fourth book in the series on Dynamic Universe Model: SITA. These simulations predicted the existence of the large number of Blueshifted Galaxies in 2004, ie., more than about 35 ~ 40 Blueshifted Galaxies known at the time of Astronomer Edwin Hubble in 1930s. The far greater numbers of Blueshifted galaxies was confirmed by the Hubble Space Telescope (HST) observations in the year 2009. Today the known number of Blue shifted Galaxies is more than 7000 scattered all over the sky and the number is increasing day by day. In addition Quasars, UV Galaxies, X-ray, γ- Ray sources and other Blue Galaxies etc., are also Blue shifted Galaxies. Out of a 930,000 Galaxy spectra in the SDSS database, 40% are images for Galaxies; that gives to 558,000 Galaxies. There are 120,000 Quasars, 50,000 brotherhood(X-ray, γ-ray, Blue Galaxies etc.,) of quasars, 7000 blue shifted galaxies. That is more than 31.7% of available Galaxy count are Blue shifted. Just to support Bigbang theory,

we are neglecting such a huge amount Blue shifted Galaxies. It appears to be a Godly Devotion to Bigbang cosmologies!

In the original paper in 2004 (as given in the annexure to this book) there are simulations of the Universe. Here in these simulations the universe is assumed to be heterogeneous and anisotropic. This prediction process was clearly shown in the output data and pictures formed from this Model. These pictures show from the random starting points to final stabilized orbits of the point masses involved. Because of this dynamism built in the model, the universe does not collapse into a lump (due to Newtonian gravitational static forces). This Model depicts the three dimensional orbit formations of involved masses or celestial bodies like in our present universe. From the resulting graphs one can see the orbit formations of the point masses, which were positioned randomly at the start. An orbit formation means that some Galaxies are coming near (Blue shifted) and some are going away (Red shifted) relative to an observer’s viewpoint.

New simulations were conducted about a month before these writings. The resulting data graphs of these simulations with different kinds of input data are shown in this book in the later chapters.

In all these simulations, all point masses will have different distances, masses.

- Simulation 1: All point masses are Galaxies

- Simulation 2: All point masses are Globular Clusters

- Simulation 3: Globular Clusters 34 Galaxies 33 aggregates 33 conglomerations 33

- Simulation 4: Small star systems 10 Globular Clusters 100 Galaxies 8 aggregates 8 conglomerations 7

The problem with such simulations is the overwhelmingly large amounts of data. Each simulation gives 3 dimensional vector data of accelerations, velocities, positions for every point mass in every iteration in addition to many types of derived data. A minimum of 133 x 18 data of 16 decimal digits for each iteration. It is data and data everywhere. It is a huge data mine indeed.

One has to use graphs for visualizing such vast amounts of data. Again the question comes, which data to choose for showing in the graphs? Is it starting? Running? End of iteration? All bodies?Some groups? Single body? Selected bodies? Positions? Velocities? Accelerations? JPEG?GIF? Normal scales? Logarithmic Scales? Thirteen new graphs are being prepared for every iteration for positions.

From all the graphs, I usually handpick some graphs for showing the results.

I don’t know what data to be included as additional files, so I did not include any. I could be directly contacted for any of the data files, should anyone require them.

Hence we may conclude:

The actual ratio of Red shifted to Blue shifted Galaxies will depend on

1. Universal Gravitational Force acting on each Galaxy at that instant of time,

2. The position of the observer in the Universe

3. The actual point mass distribution in the universe in three dimensions at that instant of time. This ratio can never be 50:50.

Newtonian two-body problem used differential equations. Einstein’s general relativity used tensors, which in turn unwrap into differential equations. Dynamic Universe Model uses tensors that give simple equations with interdependencies. Differential equations will not give unique solutions. Whereas Dynamic Universe Model gives a unique solution of positions, velocities and accelerations; for each point mass in the system for every instant of time. This new method of Mathematics in Dynamic Universe Model is different from all earlier methods of solving general N-body problem.

This universe exists now in the present state, it existed earlier, and it will continue to exist in future also in a similar way. All physical laws will work at any time and at any place. Evidences for the three dimensional rotations or the dynamism of the universe can be seen in the streaming motions of local group and local cluster. Here in this dynamic universe, both the red shifted and blue shifted Galaxies co-exist simultaneously.

A point to be noted here is that the Dynamic Universe Model never reduces to General relativity on any condition. It uses a different type of mathematics based on Newtonian physics. This mathematics used here is simple and straightforward. As there are no differential equations present in Dynamic Universe Model, the set of equations give single solution in x y z Cartesian coordinates for every point mass for every time step. All the mathematics and the Excel based software details are explained in the three books published by the author14, 15, 16 In the first book, the solution to N-body problem-called Dynamic Universe Model (SITA) is presented; which is singularity-free, inter-body collision free and dynamically stable. This is the Basic Theory of Dynamic Universe Model published in 2010 14. The second book in the series describes the SITA software in EXCEL emphasizing the singularity free portions. It explains more than 21,000 different equations (2011)15. The third book describes

the SITA software in EXCEL in the accompanying CD / DVD emphasizing mainly HANDS ON usage of a simplified version in an easy way. The third book contains explanation for 3000 equations instead of earlier 21000 (2011)16.

SITA solution can be used in many places like presently unsolved applications like Pioneer anomaly at the Solar system level, Missing mass due to Star circular velocities and Galaxy disk formation at Galaxy level etc. Here we are using it for prediction of blue shifted Galaxies.

Dynamic Universe model does NOT depend on speculation. It is based on hard observed facts. I am writing these sentences especially as cosmology is becoming more and more speculative today.

Comments:

321 Pages. this is Book4 on Dynamic Universe Model.... Published in Germany with ISDN no. 978-3-8484-1382-9

Dynamic Universe model is based on hard observed facts and does NOT

depend on speculation. In this fourth book the simulations predicted the

existnce of the large number of Blue shifted Galaxies, in an expanding

universe, in 2004 itself. It was confirmed by by Hubble Space Teliscope

(HST) observations in the year 2009. This prediction process is clearly shown

in the output pictures formed from this Model from old and new

simulations. These pictures depict the three dimensional orbit formations.

An orbit formation means some Galaxies are coming near (Blue shifted) and

some are going away (Red shifted). This book goes on two main lines. First

is the main line of thinking, to show mathematically that there will be lots

and lots of blue shifted Galaxies mathematically. To support this concept

the question what are the possible blue shifted Galaxies is answered

further. We find that quasars are blue shifted galaxies. The second line of

thinking goes with this finding, that the Quasars are blue shifted

galaxies.Forrest Noble (Pan Theory) in his foreword said “over 7,000

blueshifted galaxies have been discovered extending beyond the Local

Group, first predicted by Mr.Gupta

**Book3. Dynamic Universe Model: SITA software simplified[ISBN 978-3-639-36469-9]---Aug-2011----VDM Germany**

This is the Third book in the series on Dynamic Universe Model, describing the SITA software in EXCEL in the accompanying CD / DVD emphasizing mainly HANDS ON usage of a simplified version. It explains 3000 equations for 133 masses [instead of earlier 21000 (Twenty one thousand)], in 17 different groups with additional 14 Index functions and 56 single equations. There are 16 ranges, 11 macros & processes and 18 graphs to view and monitor various parameters. SITA is singularity-free, inter-body collision free and dynamically stable. Here basically how to tune, select input values, how to iterate & run to get the results in EXCEL, how to select time step values, to analyze data and using Graphs etc., are presented. This SITA solution can be used by anyone who knows a little about EXCEL and little bit interested in Physics for solving presently unsolved applications like Pioneer anomaly, New Horizons satellite trajectory at the Solar system level, Missing mass due to Star circular velocities and Galaxy disk formation at Galaxy level etc., that is from the Solar system level, to Cosmology level via Galaxy level.

Please go to this link below for this FREE Download of book......

https://figshare.com/s/875d033be0ebdbe1d11a

https://figshare.com/s/875d033be0ebdbe1d11a

This is the Second book in the series on Dynamic Universe Model describing the SITA software in EXCEL emphasizing the singularity free portions additionally. It explains more than 21000 (Twenty one thousand) different equations, in 43 different groups with additional 14 Index functions and 69 single equations. There are 16 ranges, 11 macros & processes and 18 graphs to view and monitor various parameters. Here in this, a solution to N-body problem-called Dynamic Universe Model (SITA) is presented; which is singularity-free, inter-body collision free and dynamically stable. The Excel EQUATIONS to all the six cases proving that NO singularity exist in the earlier book are given here with software. Viz., three non-zero cases Angular momentum, Polar moment of Inertia, Internal Distances between all pairs of point masses Stability criteria like specific relative angular momentum is constant, None of the masses are moving towards center, and “Total energy = h= T-V = NEGATIVE”. This SITA solution can be used by anyone who knows EXCEL and little bit interested in Physics for solving presently unsolved applications from the Solar system level, to Cosmology level via Galaxy level.

Please go to this link below for this book......

https://www.morebooks.de/store/gb/book/dynamic-universe-model/isbn/978-3-639-33501-9

**Book1. Dynamic Universe Model: A singularity-free N-body problem solution [ISBN 978-3-639-29436-1]---2010 October----VDM Germany**

Please go to this link below for this book......

https://www.morebooks.de/

Here a solution to N-body problem-called Dynamic Universe Model (SITA) is presented; which is singularity-free, inter-body collision free and dynamically stable. The book talks about history and general introduction and why anisotropic density distributions are to be taken. The book also covers Mathematics and the final tensors formation followed by Numerical Outputs. To prove that no singularities exist in this model: three cases were taken 1. Non-zero Velocity position Vector cross product, 2. The non-zero Polar moment of Inertia 3. The non-zero Internal Distances between all pairs of point masses Their calculation results are shown. Chaotic results with the Earlier Large Astrophysical N-body Problem, and Exponential divergence and the various kinds of errors, like Input and output Errors, are discussed and compared with this model. This N-body problem solution can be used by any person who has a PC for solving presently unsolved applications like Pioneer anomaly, New Horizons satellite trajectory at the Solar system level, Missing mass due to Star circular velocities and Galaxy disk formation at Galaxy level etc.

Please go to this link below for this book......

https://www.morebooks.de/store/gb/book/dynamic-universe-model/isbn/978-3-639-29436-1

Please go to this link below for this book......

https://www.morebooks.de/