Vladimir Pletser

Blue Abyss Diving Ltd

Abstract Using Fibonacci polynomials, a general expression of all quadratic irrationals is given such that their continued fraction development has a same integer value for all periodic terms but last. General analytical expressions are then deduced for the fundamental solutions of the associated Pell equation.

During exposure to microgravity in parabolic flights, it has been shown that the control of interaction forces when manipulating an object adapts partially to the lack of gravity, yet evidence indicates that anticipation of gravity's effects persists in the short term. The motivation for these experiments to be performed in long-duration space flig...

Aircraft parabolic flights provide repetitively short periods of reduced gravity and are used to conduct scientific and technology microgravity investigations, to test instrumentation prior to space flights and to train astronauts before a space mission. Since 1997, CNES, DLR and ESA use the Airbus A300 ZERO-G, currently the largest airplane in the...

The Protein Crystallization Diagnostics Facility (PCDF) is an instrument developed by Astrium under an ESA contract to observe and study nucleation and crystallisation processes of molecules from solutions in long duration microgravity experiments on board the International Space Station using advanced diagnostics. The experiment PROTEIN, performed...

In the early fifties, the Belgian Prof. J. de Heinzelin discovered a bone in the region of a fishermen village called Ishango, at one of the farthest sources of the Nile, on the border of Congo and Uganda. The Heinzelin's Ishango bone has notches that seem to form patterns, making it the first tool on which some logic reasoning seems to have been d...

Human long duration exploration missions (LDEMs) raise a number of technological challenges. This paper addresses the question of the crew autonomy: as the distances increase, the communication delays and constraints tend to prevent the astronauts from being monitored and supported by a real time ground control. Eventually, future planetary mission...

This is the first of two papers where we study analytical solutions of a bi-dimensional low-mass gaseous disc slowly rotating around a central mass and submitted to small radial periodic perturbations. Hydrodynamics equations are solved for the equilibrium and perturbed configurations. A wave-like equation for the gas perturbed specific mass is ded...

In the first part of this paper, we considered several theoretical models, a static and four dynamic models without rebounds, of the throw of a fair coin landing on its edge, to demonstrate that the probability of heads or tails is less than 50%, depending on the initial toss conditions, the coin geometry and conditions of the coin and landing surf...

Considering that a fair coin has two sides and a cylindrical edge, the probability that it would fall on its edge is calculated, yielding the probability of heads or tails of less than 50%. In this first part, the theoretical models for a static case and for five dynamic cases, without rebounds, show that there is a small probability that the coin...

The number of astronauts in space will increase exponentially in the coming years as the number of commercial suborbital flights and orbital flights increase, and as human missions to the Moon and Mars become a reality. This new step in space exploration will only be possible if research and training at different gravity levels is actively pursued.

We show that Euler's relation and the Taxi-Cab relation are both solutions of the same equation. General solutions of sums of two consecutive cubes equaling the sum of two other cubes are calculated. There is an infinite number of relations to be found among the sums of two consecutive cubes and the sum of two other cubes, in the form of two famili...

Les vols spatiaux sont une entreprise à haut risque et à gain élevé qui nécessite beaucoup de ressources. Pour ces raisons, les expériences de vol spatial sont rares et la sélection est très compétitive au niveau international. Les critères de sélection des expériences de vol spatial comprennent l'excellence scientifique, l'innovation, la faisabili...

Considering that a fair coin has two sides and a cylindrical edge, the probability that it would fall on its edge is calculated, yielding the probability of heads or tails less than 50%. Theoretical models for a static case and for five dynamic cases, without and with rebounds, show that there is a small probability that the coin does not fall on i...

This preprint is a short paper on the training and preparation of future astronauts at Blue Abyss as a critical element to enable the development and access to space resources on the Moon and Mars.

The number of humans having flown in space will increase dramatically and exponentially in the coming years when first commercial suborbital flights, orbital flights, and human missions to the Moon and Mars will become a reality. This new step in space exploration will only be possible if adequate and professional training is provided, a contention...

More than 500 human beings have flown in space. This number will increase dramatically and exponentially in the coming years with increasing frequency of commercial orbital flights, and with commercial suborbital flights, followed by human missions to the Moon and Mars. This new step in space exploration will only be possible if proficient, profess...

The number of human beings having flown in space will increase dramatically and exponentially in the coming years with increasing frequency of commercial orbital flights, and with commercial suborbital flights, followed by human missions to the Moon and Mars. This new step in space exploration will only be possible if proficient, professional train...

Considering that a fair coin has two sides and a cylindrical edge, the probability that it would fall on its edge is calculated, yielding the probability of heads or tails less than 50%. Theoretical models for a static case and for five dynamic cases, without and with rebounds, show that there is a small probability that the coin does not fall on i...

We show that Euler's relation and the Taxi-Cab relation are both solutions of the same equation. General solutions of sums of two consecutive cubes equaling the sum of two other cubes are calculated. There is an innite number of relations to be found among the sums of two consecutive cubes and the sum of two other cubes, in the form of two families...

This is the first of two papers where we study analytical solutions of a bidimensional low mass gaseous disc rotating around a central mass and submitted to small radial perturbations. Hydrodynamics equations are solved for the equilibrium and perturbed configurations. A wave-like equation for the gas perturbed specific mass is deduced and solved a...

This is the second of two papers where we study additional analytical solutions of a bidimensional low mass gaseous disc rotating around a central mass and submitted to small radial perturbations. In a first Paper, hydrodynamics equations were solved for the equilibrium and perturbed configurations and a wave-like equation for the gas perturbed spe...

This is the second of two papers where we study additional analytical solutions of a bidimensional low mass gaseous disc rotating around a central mass and submitted to small radial perturbations. In a first Paper, hydrodynamics equations were solved for the equilibrium and perturbed configurations and a wave-like equation for the gas perturbed spe...

Aircraft parabolic flights provide repeti¬tively up to 20 seconds of reduced gravity during ballistic flight manoeuvres. They are used to conduct short microgravity investiga¬tions in Physical and Life Sciences, to test instrumentation and to train astronauts be¬fore space flights. As the only earth-based facility for in¬vesti¬gations on human subj...

Abstract on the ESA Parabolic Flight Programme for Physical Sciences.

Abstract of conference paper on the ESA Parabolic Flight Programme for Physical Sciences

Space is a key asset for Europe, providing essential information needed by decision-makers to respond to global challenges. Space provides indispensable technologies and services, and increases our understanding of our planet and the Universe. Since 1975, the European Space Agency (ESA) has been shaping the development of this space capability and...

Commercial orbital spaceflight vehicles are now a reality and are expected to carry passengers in the next year or two. SpaceX and Boeing should begin their commercial flight services to the ISS before or during 2020. Furthermore, companies such as Bigelow, Axiom and Orion Span aim to provide LEO destinations in the years ahead as ISS operations co...

We search for triangular numbers that are multiples of other triangular numbers. For any positive non-square integer multiplier, there is an innity of multiples of triangular numbers that are triangular numbers and recurrent relations are deduced theoretically in function of two parameters. If the multiplier is a squared integer, there is either on...

The paper will present the latest planning for the unique capability to train astronauts at various gravity levels, including 0g and partial g, under development at Blue Abyss.

For any non-square integer multiplier \(k\), there is an infinity of triangular numbers multiple of other triangular numbers. We analyze the congruence properties of indices \(\xi\) of triangular numbers multiple of triangular numbers. Remainders in congruence relations \(\xi\) modulo \(k\) come always in pairs whose sum always equal \((k-1)\), alw...

For all positive non-square integer multipliers, there are infinitely many triangular numbers that are multiples of other triangular numbers. Recurrent relations yielding the triangular numbers and their multiples and indices are given for non-square multipliers between 1 and 102.

For all positive non-square integer multipliers, there are infinitely many triangular numbers that are multiples of other triangular numbers. With a simple change of variables, one obtains a Pell equation, whose odd solutions provide the indices of the many infinitely triangular numbers multiple of other triangular numbers. General algebraic expres...

For all positive non-square integer multiplier, there is an infinity of multiples of triangular numbers which are also triangular numbers. Several searching methods are proposed to find parameters of recurrent equations and analytical expressions of parameters and coefficients of recurrent equations are deduced in some cases. For certain values of...

It is known that, for any positive non-square integer multiplier k, there is an infinity of multiples of triangular numbers which are triangular numbers. We analyze the congruence properties of the indices ξ of triangular numbers that are multiples of other triangular numbers. We show that the remainders in the congruence relations of ξ modulo k co...

For all positive non-square integer multiplier k, there is an infinity of multiples of triangular numbers which are also triangular numbers. With a simple change of variables, these triangular numbers can be found using solutions of Pell equations. With some conditions on parities of fundamental solutions of the simple and generalized Pell equation...

Triangular numbers that are multiple of other triangular numbers are investigated. It is known that for any positive non-square integer multiplier, there is an infinity of multiples of triangular numbers which are triangular numbers. If the multiplier is a squared integer, there is either one or no solution, depending on the multiplier value. Inste...

Une histoire romancée dans le futur d'un voyage d'exploration et de découverte de Mars en 2034.

We search for triangular numbers that are multiples of other triangular numbers. It is found that for any positive non-square integer multiplier, there is an infinity of multiples of triangular numbers that are triangular numbers and recurrent relations are deduced theoretically. If the multiplier is a squared integer, there is either one or no sol...

Access to earthbound weightlessness is critical to many branches of applied sciences. Besides, several space systems require microgravity testing before their launch. Existing solutions (drop towers, parabolic flights, sounding rockets) offer variable durations and qualities of microgravity environment, but their cost and lead times make them unpra...

The aim of the GRIP experiment is to investigate how gravity impacts the kine-matics and dynamics of the upper limb during dexterous manipulation of objects and how the central nervous system adapts to long-term exposure to microgravity and subsequently back to Earth gravity. Hence, we proposed to conduct a set of experiments on healthy human subje...

Microgravity is the state encountered in a vehicle in free fall, whether on Earth, in low Earth orbit or in deep space. Microgravity research has opened up new possibilities for investigations in physical and life sciences that are necessary to enhance our knowledge of how physical systems and the human body, from cells to whole body systems, perfo...

This paper provides an historical perspective of the involvement of Prof. J.C. Legros in microgravity research during aircraft parabolic flights. Prof. Legros conducted 27 experiments during 33 campaign of microgravity research organised by the European Space Agency. Nearly all fields of fluid physics were investigated in microgravity by this indef...

It is shown that orbital period ratios of successive secondaries in the Solar planetary and giant satellite systems and in exoplanetary systems are preferentially closer to irreducible fractions formed with Fibonacci numbers between 1 and 8 than to other fractions, in a ratio of approximately 60% to 40%. Furthermore, if sets of minor planets are ch...

It is shown that orbital period ratios of successive planets in the Solar System, of satellites in giant planet systems and of exoplanets in exoplanetary systems are preferentially closer to irreducible fractions formed with Fibonacci numbers between 1 and 8 than to other fractions, in a ratio of approximately 60% vs 40%. Furthermore, if sets of mi...

Aircraft parabolic flights are a useful tool for performing short duration scientific and technological experiments in reduced gravity, to train astronauts in this new environment and in associated procedures and protocols, and to test experiments and instrumentation prior to future space missions. The principal value of parabolic flights is in the...

Preface of the Book 'Africa and Mathematics' of D Huylebrouck

Preface du livre 'Afrique et Mathématique' de D. Huylebrouck.

Gravity disturbs certain experiments and reduces the field of investigation of some scientific domains. Gravity is omnipresent on Earth. However, gravity can only exist if the gravitational attraction is thwarted by the presence of a solid surface that prevent the gravitational force of continuing its action of attraction. Although gravitation is o...

A body upon which no force other than the force of gravity (or weightiness), is acting is in free-fall state, i.e. that it is falling freely in an external inertial reference frame, while it is weightless, i.e. its weight is null in a non-inertial reference frame attached to the body. This simple concept, sometime difficult to grasp, is introduced...

Perfect weightlessness is an idealized state that is practically impossible to realize in a free-falling vehicle, because of various perturbations. Therefore, one prefers to talk about microweightiness or, as commonly said, microgravity (although this being a language abuse).

The microgravity state as a research environment is also of interest to life sciences, i.e. the whole body of researches in medicine, biology, zoology and botany, studying the influence of gravity on living organisms, including the human being. In this chapter we limit ourselves in giving some general considerations on research in human physiology...

The African scientific community is invited to reflect upon the need to define a set of ethical rules that would apply to scientists in their research and knowledge transfer activities. These ethical rules could be included in a document to be drawn up, called “The Oath of Ishango”, in homage to the rod of Ishango, the earliest man-made object of a...

Yes, the last day. What happened this Saturday 20 April 2002? Well, as announced, it was an extremely busy day. So busy that I did not have time to write anything. I will give you now some recollections of these last two days.

This is the daily diary that I kept during the journey to and my stay in the Desert of Utah. Large excerpts have been published on the web site of ESA, and of the French Chapter of The Mars Society, and daily in the Belgian newspaper ‘La Dernière Heure’. This is the text in its integrality. Dates are indicated and days are counted since the day of...

So, what has happened on Mars in the last 15 years? Where do we stand now? Are we ready to go? This chapter will try to bring some answers to these questions.

We arrived at Grand Junction (GJT), Colorado, in dispersed order last night (Wednesday 28 January). I arrived first from Salt Lake City (SLC), coming from Minneapolis and before that from Amsterdam.

So, what happened afterwards? Well, as for my previous simulations, suddenly, it was time to leave and there was no more time to write down all that happened. But here is an accountant from my memory.

First, that it was possible for a crew to live and work in harmony while in isolation during two weeks. Quite strangely, not one of us really felt isolated. Of course, we were cut off from the world and from what was happening there. But we were so busy with our various research tasks that we did not see the time pass by.

Well, a lot of things. During the two months of the short Arctic summer, six crews took turns in the Hab and numerous experiments were conducted. It would be too long to summarize them all here. The interested reader can find more details in the various daily reports and scientific reports that were published every day on the web site of The Mars S...

This is the daily diary that I kept during my travels and during my stay on Devon Island. Large excerpts were published on the ESA website and in the Belgian newspaper ‘Le Soir’. Here it is in its entirety. Dates are indicated and day 0 corresponds to the planned day of entrance in the Mars Habitat.

One fine morning of January 2002, I received an e-mail from Robert Zubrin. In his characteristic direct and concise style, in less than ten words, he asked me to go again with them, this time in the desert, in the new Hab installed in the middle of the desert of Utah.

One day of December 2000, I ran across an article in Space News on Robert Zubrin and The Mars Society telling about the installation of the first Martian module on Devon Island, an uninhabited island of the Canadian Great North, way beyond the Arctic Circle. This article announced also the beginning of a series of international campaigns of Martian...

Beside how to get to Mars and how to live on Mars (see the last part on this), there is also the question of how to conduct science experiments from the surface of Mars. Like all space agencies in the world, people at ESA start to think also about that aspect and more particularly how to conduct geology, biology and astrophysical experiments from t...

This book introduces the Martian simulations, one installed on Devon Island, an uninhabited island in the Canadian Arctic, well within the polar circle, and two in the desert of Utah, several hundreds of kilometers South of Salt Lake City. The book is based on the diaries during the simulations, held by Vladimir Pletser, a physicist-engineer, who w...

The third chapter covers the first integral and the variational principle. The notions of cyclic coordinates and Poisson brackets are first recalled. The Theorem of Poisson, Euler equation, and the variational principle are then addressed. An application in optics, namely the Fermat principle, is reviewed. Five exercises are then solved, namely on...

Hamilton–Jacobi equations are treated in the fifth chapter. Hamilton–Jacobi equations, their solutions, and the case of a time independent Hamiltonian are first recalled. Thirteen exercises are then solved, namely on a third harmonic oscillator, on a free falling particle, on a projectile ballistic flight, on a particle sliding on an inclined plane...

The first chapter covers Lagrange equations. The notions of generalized coordinates, kinetic energy, and generalized forces are first recalled. Lagrange equations, generalized moments, Lagrange equations for systems with constraints, and for systems with impulse forces are recalled. Five exercises are then solved, namely on a double pendulum, on a...

The phase integral and action-angle variables are the subject of the sixth chapter. The notions of phase integrals, frequency and angular variables are first recalled. Seven exercises are then solved, on a fourth harmonic oscillator, on pendulum small oscillations, on a three-dimensional harmonic oscillator, on energy in a Bohr atom, on Kepler’s cl...

Canonical transformations, also called contact transformations, are addressed in the fourth chapter. Canonical transformations, conditions for a transformation to be canonical and generating functions are first recalled. Eight exercises on canonical transformations are then solved, the last one including a second harmonic oscillator.

Hamilton equations are the subject of the second chapter. The notion of Hamiltonian is first recalled and the Hamilton equations and conservative systems are then reviewed. The expression of the Hamiltonian is given in different coordinate systems. Two exercises are then solved, namely on a particle in a plane with central force and on a harmonic o...

Fibonacci numbers and the golden ratio can be found in nearly all domains of Science, appearing when self-organization processes are at play and/or expressing minimum energy configurations. Several non-exhaustive examples are given in biology (natural and artificial phyllotaxis, genetic code and DNA), physics (hydrogen bonds, chaos, superconductivi...

Since the China Manned Space Program is implemented, the Chinese microgravity research programme is conducted mainly during space missions on board automatic Shijian satellites and manned Shenzhou spaceships and Tiangong space laboratories. There is now a new approach for microgravity research in China. The Zero Gravity Experiment Center (OGEC), af...

The commercial human spaceflight sector is developing at a rapid rate and will grow in size and capacity at an exponential rate once a certain tipping point has been reached. Globally the infrastructure that exists today to support this field is insufficient in scale and has not been established with commercialisation in mind. One of the difficulti...

This list compiles the periods of exo-planets from the European catalogue of exo-planets (Exoplanet TEAM, 2017) as it was when consulted in August 2017 (except for the most recent value of the period of Planet TRAPPIST-1 h, from Luger et al., 2017). The Exoplanet catalogue contained at that date 3652 exoplanets, including 606 multiplanetary systems...

This list compiles the main data of minor planets and of Trans-Neptunian Objects (TNOs) from the catalogue of the Minor Planet Center (MPC) as it was when consulted in August 2017. The MPC catalogue contained at that date 740 419 minor planets, including planetoids, asteroids, Trojans, centaurs, Kuiper belt objects and other trans-Neptunian objects...

Experimental microgravity research has traditionally been dominated by a limited number of solutions: drop towers, parabolic flights, sounding rockets, short-duration orbital platforms (e.g. dedicated Foton flights), and long-duration orbital platforms (e.g. ISS). Over the years, the capabilities, advantages and shortcomings of these different faci...

Aircraft parabolic flights are widely used throughout the world to create microgravity environment for scientific and technology research, experiment rehearsal for space missions, and for astronaut training before space flights. As part of the Space Studies Program 2016 of the International Space University summer session at the Technion-Israel Ins...

Aircraft parabolic flights are widely used throughout the world to create microgravity environment for scientific and technology research, experiment rehearsal for space missions, and astronaut training before space flights. The word aircraft is usually associated to motorized airplanes, either large aircrafts like the Airbus A310 ZERO-G of ESA/CNE...

The usual main objection against any attempt in finding a physical cause for the planet distance distribution is based on the assumption that similar distance distribution could be obtained by sequences of random numbers. This assumption was stated by Lecar in an old paper (1973). We show here how this assumption is incorrect and how his visual com...

One of the usual main objections against attempts in finding a physical cause for the planet distance distribution is based on the assumption that similar distance distribution could be obtained by sequences of random numbers. This assumption was stated by Lecar in a short article of 1973 that is still referred to nowadays. We show here how this as...

http://rdcu.be/pkAb Aircraft parabolic flights are widely used throughout the world to create microgravity environment for scientific and technology research, experiment rehearsal for space missions, and for astronaut training before spaceflights. As part of the Space Studies Program 2016 of the International Space University summer session at the...

We report in this paper a new exponential relation distance of planets in the newly discovered exoplanetary system of the Trappist-1 star, and we comment on near orbital mean motion resonances among the seven planets. We predict that possible smaller planets could be found inside the orbit of the innermost discovered Planet b.

Aircraft parabolic flights repetitively provide up to 23 seconds of reduced gravity during ballistic flight manoeuvres. Parabolic flights are used to conduct short microgravity investigations in Physical and Life Sciences and in Technology, to test instrumentation prior to space flights and to train astronauts before a space mission. The use of par...

Report on the first parabolic flight campaign in the Middle-East for science and student experiments

The Suborbital Research Association (SRA), created in Brussels in June 2013, seeks to raise the awareness of the scientific community to the possibilities for scientific and technological research purposes offered by long suborbital trajectories, yielding several minutes of continuous microgravity at an attractive cost. The SRA, which is open to al...