ACKNOWLEDGMENTS

The idea to create this site came up with the intention to share with the public the content of a set of studies on the frontier of quantum and astrophysical theory that proved to be somehow instigating, once the used approaches would not be able to correlate these two domains of science so far . These investigations also proved to be strange to my area of formation in the Doctorate and performance in the research lines of the Chemistry Institute of UnB which is Theoretical Chemistry focused on the application of quantum mechanics methods in the study of chemical and biochemical systems. The development of these researches over the 90s and in the first decade of this century was very challenging, requiring courage and dedication on my part to show that the results were convincing and provoked curiosity in the readers of published articles and also in the audience of the lectures. Just as these studies aroused the interest of researchers in the various domains of academia related to the theme, it also led this author to receive harsh manifestations of skepticism, especially in attempts to publish in scientific journals of recognized orthodox character. However, the objective of this author in this text is to express all my gratitude to the valuable support of many colleagues inside and outside Brazil who believed that the results of these studies proved to be consistent and could be promising to encourage future investigations both in the field of quantum mechanics as in the fields of astrophysics and cosmology.

A first version of a manuscript written in Portuguese language during 1993 was brought to the attention of some colleagues, who were also dear friends, and the expressions of support for the studies were very encouraging, namely Professors Carlos V. Speller (IF / UFSC), Paulo M. Bisch (IBCCF / UFRJ), Maristela Rocha (CIC/ UnB), Mário and Myriam Giambiagi (CBPF-RJ) and Dr. Darly Henriques da Silva (Scientific and Technological Development Analyst – CNPq / MCT). These supports were essential to motivate this author to prepare a first version of an article in English language aiming to submit it for publication in the journal Ciência e Cultura (Journal of the Brazilian Association for the Advancement of Science) , accepted for publication in June 1995. This article and related documentation are presented on this website in the Research History section.

All my thanks to the colleagues who have invited me to give lectures at their work institutions and to the audiences present, whose expressions of affection and support were fundamental to consolidate my belief that the ideas and approaches used, the results presented were relevant and encouraging for the continuation of these investigations. It is with great recognition and gratitude that I mention the names of these colleagues who in the 90s were professors at the institutions mentioned below: Luiz Carlos Gomide (IQ / Unicamp), Kleber Mundim (IF / UFBa), Heloiza Schor (ICEx / UFMG), Marcelo Moret (UEFS – Bahia), Nestor Correa (UESCBahia), Henrique Lins de Barros (MAST / CNPq-RJ).

Invitations to internal seminars within the University of Brasília were also made in several academic units of the Institution. To the Institute of Chemistry (IQ / UnB), where I held my position as a professor throughout most of my years at the academy, I manifest all my gratitude to Prof. Elaine Maia, who, for years, was the coordinator of the PET Program for undergraduate courses with great dedication and on several occasions invited me to give warm and fruitful lectures. Equally grateful to Prof. João Batista Lopes Martins for the invitation to give a lecture at the First Symposium on Electronic Structure and Molecular Dynamics of the Federal District in 2006 (I SEEDMOL – DF) and to the Dean of Research and Graduate Studies at UnB to participate as a speaker at the Café com Ciências event in the theme Space Science: Vehicles and Orbital Dynamics in 2005.

Also, all my acknowledgments to Prof. Samuel Simon (Department of Philosophy / UnB), Fernando Oliveira (International Center for Condensed Matter Physics – CIFMC / UnB), to Prof. Ademir Santana coordinator of the group of Physics-Mathematics of the Institute of Physics of UnB for the invitations to give seminars that resulted in highly productive debates.

In September 1998 on the occasion of a lecture at the Physics Institute of the University of Bahia at the invitation of Prof. Kleber Mundim, this author was introduced to Prof. Saulo Carneiro from the Cosmology area of that institution who had already been notified of these investigations by Prof. Marcelo Moret from the State University of Feira de Santana through a copy of the article published in the journal Ciência e Cultura. Prof. Saulo Carneiro kindly offered to send a copy of the article to Prof. Halton Arp of the Max-Planck Institute for Astrophysics in Munich, Germany. In February of 1997, Prof. Arp sent this author a warm letter of encouragement to these investigations where a copy is shown on this website.

The vigorous support of Prof. Arp led this author to extend the study of obtaining the mean planetary distances to the center of the Sun, using an atomic model analogous to Niels Bohr’s semiclassical model for the hydrogen atom, results published in the journal Ciência e Cultura, for a more advanced research. The objective, similar to that used to solve the three-dimensional Schrödinger equation for the hydrogen atom, would be to determine the wave functions resulting from the resolution of the Schrödinger equation for a two-dimensional atomic system. That is, a representative system of the solar system where the planets orbit in a region of approximately planar space. In this sense, wave functions would be used as fundamental pillars to achieve a broader spectrum of effective theoretical results for a complete description of the mean planetary distances of both the rocky and gaseous planets to the center of the Sun, as well as, the Main Asteroid Belt and the Hungarian Asteroid Belt. For the mathematical resolution of the differential equation associated with a Schrödinger wave equation for a planar atomic system, the contribution of Prof. Liliane de Almeida Maia from the Department of Mathematics at UnB was extremely valuable and it is difficult to find words to express my most sincere thanks. All gratitude also to her Scientific Initiation student Ricardo Fragelli, at that time studying Mechanical Engineering, in precious assistance in the use of the Maple program to solve mathematical problems, as well as, in the impeccable organization of the obtained results.

With this set of results in hand and with the valuable participation of Prof. Saulo Carneiro interpreting the results from the rigorous point of view of the fundamentals of Cosmology, a first article was accepted for publication in 2004 in the journal Chaos, Solitons & Fractals with the following bibliographical reference:

OLIVEIRA NETO, Marçal de; CARNEIRO, Saulo; MAIA, Liliane de Almeida. An alternative theoretical approach to describe planetary systems through a Schrodinger-type diffusion equation. Chaos, Solitons and Fractals. v.21, 2004. p. 21–28.

In this article it is important to highlight the theoretical result obtained by predicting distances from celestial bodies at 0.05 AU (Astronomical Units) to the center of a star. At the time when these theoretical studies were being carried out, exoplanets were located in extrasolar planetary systems, where most of them were found precisely at these distances from the centers of the investigated stars, a fact that provided immense satisfaction to these authors, providing security and determination in the purpose of submitting the article for publication.

On the occasion of the lecture given at UFBa in September 1998, Prof. Marcelo Moret invited me to a seminar at the Physics Department of the State University of Feira de Santana (UEFS – Bahia) where I was introduced to Prof. Antônio Delson Conceição de Jesus PhD in Engineering and Space Technologies. The Prof. Antônio Delson promptly put me in contact with Prof. Antônio F. Bertachini de A. Prado PhD in Space Sciences and researcher at the National Institute for Space Research (INPE) in São José dos Campos – São Paulo. In the same year, Prof. Bertachini was coordinating the organization of the IX Brazilian Colloquium on Orbital Dynamics in Águas de Lindóia – São Paulo and kindly suggested that I prepared a summary in order to submit it to the Organizing Committee for the purpose of my participation in this colloquium. It was with a great pleasure that I received the news of the acceptance of the abstract, allowing my presence at that important event. The work presented was published in the book Advances in Space Dynamics mentioned on this website in the publications section. I participated again in this meeting with a presentation of work at the XI Brazilian Colloquium on Orbital Dynamics held in Viçosa- MG in 2002.

I also express my deepest thanks to Prof. B. G. Sidhart of the International Institute for Applicable Mathematics & Information Sciences – Hyderabad (India) and Prof. M. S. El Naschie of the Department of Astrophysics – Cairo University – Egypt, for their constant support and encouragement to carry on with these studies.

All the supports mentioned were essential in order to allow the dissemination of these studies in lectures, articles published and participation in congresses held in Brazil, as well as, abroad. It was with great satisfaction that I had accepted papers to present and participate in the following international events: Conference on Fundamental Interactions In Centro-Oeste Brazil, held in Pirenópolis – Goiás from August 20 to 26, 2000; First Advanced School of Astrophysics on “Extrasolar Planets and Brown Dwarfs” in Santiago – Chile from December 15 to 19, 2003; Sixth International Symposium on Frontiers of Fundamental and Computational Physics in Udine – Italy from 26 to 28 September 2004.

An honorable invitation was made by Prof. Rudy Shild of the Center for Astrophysics, Harvard- Smithsonian – USA to prepare an article to be submitted for publication in the electronic journal Journal of Cosmology, at that time Prof. Rudy was one of the magazine’s editors. The article was written showing the entire set of results obtained for the calculation of the mean planetary distances in accordance with the historical chain of application of the quantum mechanics methodologies starting with the theoretical description of the electronic configurations for atomic systems and also used for planetary orbits in the context of these investigations; then the theoretical aspects involving the formation of simple molecular systems and applied to the description of binary star systems. Finally, the quantum mechanics approach was outlined to describe the formation of chemical bonds and, in this scenario, to obtain a theoretical interpretation for the geometry of protoplanetary disc formation observed around binary star systems as a function of their separation distances. This article has as reference:

OLIVEIRA NETO, Marçal de. Quantum Mechanics Describes Planetary Orbits. Journal of Cosmology. Vol. 13, 2011, pp 3866 – 3874. Available at <http://journalofcosmology.com/Planets100.html>

To end, not least, all my sincere thanks to Mr. Kelson André Venâncio Teixeira, Systems Developer, for all the care and dedication in preparing this site and also for his patience due to our countless exchanges of ideas on line throughout this work.