scholarly journals Kepler´s Ellipse Observed from Newton´s Evolute (1687), Horrebow´s Circle (1717), Hamilton´s Pedal Curve (1847), and Two Contrapedal Curves (28.10.2018)

2018 ◽  
Vol 10 (6) ◽  
pp. 90
Author(s):  
Jiri Stavek
Keyword(s):  
The Other ◽  
Intermediate Step ◽  
The Sun ◽  
Isaac Newton ◽  
Additional Information ◽  
Johannes Kepler ◽  
The Moment ◽  
Area Law ◽  
Pedal Curve ◽  
Normal Momentum

Johannes Kepler discovered the very elegant elliptical path of planets with the Sun in one focus of that ellipse in 1605. Kepler inspired generations of researchers to study properties hidden in those elliptical paths. The visible elliptical paths belong to the Aristotelian World. On the other side there are invisible mathematical objects in the Plato´s Realm that might describe the mechanism behind those elliptical paths. One such curve belonging to the Plato´s Realm discovered Isaac Newton in 1687 - the locus of radii of curvature of that ellipse (the evolute of the ellipse). Are there more curves in the Plato´s Realm that could reveal to us additional information about Kepler´s ellipse? W.R. Hamilton in 1847 discovered the hodograph of the Kepler´s ellipse using the pedal curve with pedal points in both foci (the auxiliary circle of that ellipse). This hodograph depicts the moment of the tangent momentum of orbiting planets. Inspired by the hodograph model we propose newly to use two contrapedal curves of the Kepler´s ellipse with contrapedal points in both the Kepler´s occupied and Ptolemy´s empty foci. Observers travelling along those contrapedal curves might bring new valuable experimental data about the orbital angular velocity of planets and a new version of the Kepler´s area law. Based on these contrapedal curves we have defined the moment of the normal momentum. The first derivation of the moment of the normal momentum reveals the torque of the ellipse. This torque of ellipse should contribute to the precession of the Kepler´s ellipse. In the Library of forgotten works of Old Masters we have re-discovered the Horrebow´s circle (1717) and the Colwell´s anomaly H (1993) that might serve as an intermediate step in the solving of the Kepler´s Equation (KE). Have we found the Arriadne´s Thread leading out of the Labyrinth or are we still lost in the Labyrinth?

scholarly journals Newton’s Hyperbola Observed from Newton’s Evolute (1687), Gudermann’s Circle (1833), the Auxiliary Circle (Pedal Curve and Inversion Curve), the Lemniscate of Bernoulli (1694) (Pedal Curve and Inversion Curve) (09.01.2019)

2019 ◽  
Vol 11 (1) ◽  
pp. 65
Author(s):  
Jiri Stavek
Keyword(s):  
The Sun ◽  
Conic Sections ◽  
Isaac Newton ◽  
Lemniscate Of Bernoulli ◽  
Johannes Kepler ◽  
New Information ◽  
Inversion Curve ◽  
And Inversion ◽  
Pedal Curve ◽  
Normal Momentum

Johannes Kepler and Isaac Newton inspired generations of researchers to study properties of elliptic, hyperbolic, and parabolic paths of planets orbiting around the Sun. After the intensive study of those conic sections during the last four hundred years it is believed that this topic is practically closed and the 21st Century cannot bring anything new to this subject. Can we add to those visible orbits from the Aristotelian World some curves from the Plato’s Realm that might bring to us new information about those conic sections? Isaac Newton in 1687 discovered one such curve - the evolute of the hyperbola - behind his famous gravitation law. In our model we have been working with Newton’s Hyperbola in a more complex way. We have found that the interplay of the empty focus M (= Menaechmus - the discoverer of hyperbola), the center of the hyperbola A (= Apollonius of Perga - the Great Geometer), and the occupied focus N (= Isaac Newton - the Great Mathematician) together form the MAN Hyperbola with several interesting hidden properties of those hyperbolic paths. We have found that the auxiliary circle of the MAN Hyperbola could be used as a new hodograph and we will get the tangent velocity of planets around the Sun and their moment of tangent momentum. We can use the lemniscate of Bernoulli as the pedal curve of that hyperbola and we will get the normal velocities of those orbiting planets and their moment of normal momentum. The first derivation of this moment of normal momentum will reveal the torque of that hyperbola and we can estimate the precession of hyperbolic paths and to test this model for the case of the flyby anomalies. The auxiliary circle might be used as the inversion curve of that hyperbola and the Lemniscate of Bernoulli could help us to describe the Kepler’s Equation (KE) for the hyperbolic paths. Have we found the Arriadne’s Thread leading out of the Labyrinth or are we still lost in the Labyrinth?

scholarly journals Newton’s Parabola Observed from Pappus’ Directrix, Apollonius’ Pedal Curve (Line), Newton’s Evolute, Leibniz’s Subtangent and Subnormal, Castillon’s Cardioid, and Ptolemy’s Circle (Hodograph) (09.02.2019)

2019 ◽  
Vol 11 (2) ◽  
pp. 30
Author(s):  
Jiri Stavek
Keyword(s):  
Gottfried Wilhelm Leibniz ◽  
Future Research ◽  
Isaac Newton ◽  
Johannes Kepler ◽  
Parabolic Orbit ◽  
Curve Line ◽  
Old Masters ◽  
Parabolic Orbits ◽  
The Moment ◽  
Pedal Curve

Johannes Kepler and Isaac Newton inspired generations of researchers to study properties of elliptic, hyperbolic, and parabolic paths of planets and other astronomical objects orbiting around the Sun. The books of these two Old Masters “Astronomia Nova” and “Principia…” were originally written in the geometrical language. However, the following generations of researchers translated the geometrical language of these Old Masters into the infinitesimal calculus independently discovered by Newton and Leibniz. In our attempt we will try to return back to the original geometrical language and to present several figures with possible hidden properties of parabolic orbits. For the description of events on parabolic orbits we will employ the interplay of the directrix of parabola discovered by Pappus of Alexandria, the pedal curve with the pedal point in the focus discovered by Apollonius of Perga (The Great Geometer), and the focus occupied by our Sun discovered in several stages by Aristarchus, Copernicus, Kepler and Isaac Newton (The Great Mathematician). We will study properties of this PAN Parabola with the aim to extract some hidden parameters behind that visible parabolic orbit in the Aristotelian World. In the Plato’s Realm some curves carrying hidden information might be waiting for our research. One such curve - the evolute of parabola - discovered Newton behind his famous gravitational law. We have used the Castillon’s cardioid as the curve describing the tangent velocity of objects on the parabolic orbit. In the PAN Parabola we have newly used six parameters introduced by Gottfried Wilhelm Leibniz - abscissa, ordinate, length of tangent, subtangent, length of normal, and subnormal. We have obtained formulae both for the tangent and normal velocities for objects on the parabolic orbit. We have also obtained the moment of tangent momentum and the moment of normal momentum. Both moments are constant on the whole parabolic orbit and that is why we should not observe the precession of parabolic orbit. We have discovered the Ptolemy’s Circle with the diameter a (distance between the vertex of parabola and its focus) where we see both the tangent and normal velocities of orbiting objects. In this case the Ptolemy’s Circle plays a role of the hodograph rotating on the parabolic orbit without sliding. In the Plato’s Realm some other curves might be hidden and have been waiting for our future research. Have we found the Arriadne’s Thread leading out of the Labyrinth or are we still lost in the Labyrinth?

La riflessione impossibile e il rispecchiamento nel mondo. Dall’esperienza infantile alla surréflexion

2020 ◽  
Vol 22 ◽  
pp. 135-151
Author(s):  
Prisca Amoroso ◽  
Keyword(s):  
The Body ◽  
The Other ◽  
The Sun ◽  
The Earth ◽  
Way Of Knowing ◽  
The Moment

This essay builds on two questions: the relation of the child with the other and the child’s way of knowing, in which the resistance of the unreflected is not yet problematized. Through a reconstruction of Merleau-Ponty’s critique of Piaget’s idea of the child’s linear intellectual progression toward reflexive abstraction, I highlight the moment of unreflection by taking up the notion of ultra-thing, which Merleau-Ponty borrows from Henry Wallon. These ultra-things are entities with which the child entertains a vague relation and which always remain at the horizon of her perception without yet being possessed in a representation or grasped in a concept. They include, for example, the sun, the sky, the Earth, the body as an object, existence before the birth of the child – uninhabitable dimensions or, to the contrary, ones that are necessarily inhabited. The concept of ultra-thing has not been sufficiently explored in Merleau-Pontian studies and its importance remains underappreciated. This essay thus formulates a hypothesis about the relation between ultra-things and hyper-reflection.

scholarly journals Kepler’s Ellipse Generated by the Trigonometrically Organized Gravitons

2018 ◽  
Vol 10 (4) ◽  
pp. 26
Author(s):  
Jiri Stavek
Keyword(s):  
Albert Einstein ◽  
Elliptical Orbit ◽  
Future Research ◽  
The Sun ◽  
Fermat Principle ◽  
Geometrical Properties ◽  
Isaac Newton ◽  
Johannes Kepler ◽  
Guiding Principle ◽  
Repulsive Forces

Johannes Kepler made his great breakthrough when he discovered the elliptical path of the planet Mars around the Sun located in one focus of that ellipse (on the 11th October in 1605 in a letter to Fabricius). The first generation of researchers in the 17th century intensively discussed about the possible mechanism needed for the generation of that elliptical orbit and about the function of the empty focus of that ellipse. First generations of researchers proposed an interplay between attractive and repulsive forces that might guide the planet on its elliptical orbit. Isaac Newton made a giant mathematical progress in his Principia and introduced the concept of the attractive gravitational force between the Sun and planets. However, Newton did not propose a possible mechanism behind this attractive force. Albert Einstein in 1915 left the concept of attractive and repulsive forces and introduced his Theory based on the elastic spacetime. In his concept gravity itself became fictitious force and the attraction is explained via the elastic spacetime. In our proposed model we try to re-open the discussion of Old Masters on the existence of attractive and repulsive forces. The guiding principle for our trigonometrical model is the generation of the ellipse discovered by one of the last ancient Greek mathematicians – Anthemius of Tralles – who generated the ellipse by the so-called gardener’s method (one string and two pins fixed to the foci of that ellipse). Frans van Schooten in 1657 invented a series of original simple mechanisms for generating ellipses, hyperbolas, and parabolas. Schooten’s antiparallelogram might simulate the interplay of attractive and repulsive forces creating the elliptical path. We propose a model with trigonometrically organized Solar and planet gravitons. In this model the Solar and planet gravitons are reflected and refracted in predetermined directions so that their joint momentum transferred on the planet atoms guides the planet on an elliptical path around the Sun. At this stage we cannot directly measure the gravitons but we can use the analogy with behavior of photons. We propose to observe paths of photons emitted from one focus of the ellipse towards the QUARTER-silvered elliptical mirror. 1/4 of photons will be reflected towards to the second empty focus and the ¾ of photons might be reflected and refracted into the trigonometrically expected directions. (Until now we have experimental data only for the FULLY–silvered elliptical mirrors). The observed behavior of photons with the quarter-silvered elliptic mirror might support this concept or to exclude this model as a wrong model. The quantitative values of attractive and repulsive forces could be found from the well-known geometrical properties of the ellipse. The characteristic lengths of distances will be inserted into the great formula of Isaac Newton - the inverse square law. (In order to explain some orbit anomalies, we can use Paul Gerber’s formula derived for the Pierre Fermat principle). We have found that the Kant’s ellipse rotating on the Keppler’s ellipse might express the co-operation of attractive and repulsive forces to guide the planet on its elliptic path. Finally, we have derived a new formula inspired by Bradwardine - Newton - Tan - Milgrom that might contribute to the MOND gravitational model. We have found that the Kepler ellipse is the very elegant curve that might still keep some hidden secrets waiting for our future research.

II. On the precession of the equinoxes

1807 ◽  
Vol 97 ◽  
pp. 57-82
Keyword(s):  
Natural Philosophy ◽  
The Other ◽  
The Sun ◽  
Sir Isaac Newton ◽  
Isaac Newton ◽  
The Third ◽  
The Earth ◽  
Figure Of The Earth ◽  
The Subject ◽  
Theory Of Gravity

Perhaps the solution of no other problem, in natural philo­sophy, has so often baffled the attempts of mathematicians as that of determining the precession of the equinoxes, by the theory of gravity. The phenomenon itself was observed about one hundred and fifty years before the Christian æra, but Sir Isaac Newton was the first who endeavoured to estimate its magnitude by the true principles of motion, combined with the attractive influence of the sun and moon on the spheroidal figure of the earth. It has always been allowed, by those competent to judge, that his investigations relating to the subject evince the same transcendent abilities as are displayed in the other parts of his immortal work, the mathematical Principles of natural Philosophy, but, for more than half a century past, it has been justly asserted that he made a mistake in his process, which rendered his conclusions erro­neous. Since the detection of this error, some of the most eminent mathematicians in Europe have attempted solutions of the problem. Their success has been various; but their investi­gations may be arranged under three general heads. Under the first of these may be placed such as lead to a wrong conclusion, in consequence of a mistake committed in some part of the proceedings. The second head may be allotted to those in which the conclusions may be admitted as just, but rendered so by the counteraction of opposite errors. Such may be ranked under the third head as are conducted without error fatal to the conclusion, and in which the result is as near the truth as the subject seems to admit.

The Final ‘Thank You’

Derrida Today ◽  
2010 ◽  
Vol 3 (1) ◽  
pp. 21-36
Author(s):  
Grant Farred
Keyword(s):  
South Africa ◽  
South African ◽  
Jacques Derrida ◽  
Political Transition ◽  
The Other ◽  
World Cup ◽  
The Core ◽  
Nelson Mandela ◽  
Black President ◽  
The Moment

‘The Final “Thank You”’ uses the work of Jacques Derrida and Friedrich Nietzsche to think the occasion of the 1995 rugby World Cup, hosted by the newly democratic South Africa. This paper deploys Nietzsche's Zarathustra to critique how a figure such as Nelson Mandela is understood as a ‘Superman’ or an ‘Overhuman’ in the moment of political transition. The philosophical focus of the paper, however, turns on the ‘thank yous’ exchanged by the white South African rugby captain, François Pienaar, and the black president at the event of the Springbok victory. It is the value, and the proximity and negation, of the ‘thank yous’ – the relation of one to the other – that constitutes the core of the article. 1

Macaronics as What Eludes Translation

Paragraph ◽  
2015 ◽  
Vol 38 (2) ◽  
pp. 214-230
Author(s):  
Haun Saussy
Keyword(s):  
Print Culture ◽  
The Other ◽  
Digital Code ◽  
Avant Garde ◽  
The Moment

‘Translation’ is one of our all-purpose metaphors for almost any kind of mediation or connection: we ask of a principle how it ‘translates’ into practice, we announce initiatives to ‘translate’ the genome into predictions, and so forth. But the metaphor of translation — of the discovery of equivalents and their mutual substitution — so attracts our attention that we forget the other kinds of inter-linguistic contact, such as transcription, mimicry, borrowing or calque. In a curious echo of the macaronic writings of the era of the dawn of print, the twentieth century's avant-garde, already foreseeing the end of print culture, experimented with hybrid languages. Their untranslatability under the usual definitions of ‘translation’ suggests a revival of this avant-garde practice, as the mainstream aesthetic of the moment invests in ‘convergence’ and the subsumption of all media into digital code.

Computational and experimental studies of the strength of full-scale samples of pipes with defects "metal loss" and "dent with groove"

2020 ◽  
Vol 10 (3) ◽  
pp. 226-233
Author(s):  
Dmitry A. Neganov ◽  
◽  
Victor M. Varshitsky ◽  
Andrey A. Belkin ◽  
◽  
...  
Keyword(s):  
Internal Pressure ◽  
Experimental Studies ◽  
Full Scale ◽  
The Other ◽  
Metal Loss ◽  
Calculation Methods ◽  
Reliable Operation ◽  
Sufficient Stability ◽  
Comparative Results ◽  
The Moment

The article contains the comparative results of the experimental and calculated research of the strength of a pipeline with such defects as “metal loss” and “dent with groove”. Two coils with diameter of 820 mm and the thickness of 9 mm of 19G steel were used for full-scale pipe sample production. One of the coils was intentionally damaged by machining, which resulted in “metal loss” defect, the other one was dented (by press machine) and got groove mark (by chisel). The testing of pipe samples was performed by applying static internal pressure to the moment of collapse. The calculation of deterioration pressure was carried out with the use of national and foreign methodical approaches. The calculated values of collapsing pressure for the pipe with loss of metal mainly coincided with the calculation experiment results based on Russian method and ASME B31G. In case of pipe with dent and groove the calculated value of collapsing pressure demonstrated greater coincidence with Russian method and to a lesser extent with API 579/ASME FFS-1. In whole, all calculation methods demonstrate sufficient stability of results, which provides reliable operation of pipelines with defects.

The Curious Eye

2020 ◽  
Author(s):  
Erin Webster
Keyword(s):  
Seventeenth Century ◽  
Human Vision ◽  
Francis Bacon ◽  
Robert Hooke ◽  
Robert Boyle ◽  
Isaac Newton ◽  
Johannes Kepler ◽  
The Social ◽  
The Subject ◽  
Historical Moment

The Curious Eye explores early modern debates over two related questions: what are the limits of human vision, and to what extent can these limits be overcome by technological enhancement? Today, in our everyday lives we rely on optical technology to provide us with information about visually remote spaces even as we question the efficacy and ethics of such pursuits. But the debates surrounding the subject of technologically mediated vision have their roots in a much older literary tradition in which the ability to see beyond the limits of natural human vision is associated with philosophical and spiritual insight as well as social and political control. The Curious Eye provides insight into the subject of optically mediated vision by returning to the literature of the seventeenth century, the historical moment in which human visual capacity in the West was first extended through the application of optical technologies to the eye. Bringing imaginative literary works by Francis Bacon, John Milton, Margaret Cavendish, and Aphra Behn together with optical and philosophical treatises by Johannes Kepler, René Descartes, Robert Hooke, Robert Boyle, and Isaac Newton, The Curious Eye explores the social and intellectual impact of the new optical technologies of the seventeenth century on its literature. At the same time, it demonstrates that social, political, and literary concerns are not peripheral to the optical science of the period but rather an integral part of it, the legacy of which we continue to experience.

The Starry Universe of Jacques Cassini: Century-old Echoes of Kepler

2021 ◽  
Vol 52 (2) ◽  
pp. 147-167
Author(s):  
Christopher M. Graney
Keyword(s):  
18Th Century ◽  
The Sun ◽  
Johannes Kepler ◽  
Apparent Diameter ◽  
Early 18Th Century ◽  
Made In

This paper discusses measurements of the apparent diameter and parallax of the star Sirius, made in the early 18th century by Jacques Cassini, and how those measurements were discussed by other writers. Of particular interest is how other writers accepted Cassini’s measurements, but then discussed Sirius and other stars as though they were all the same size as the sun. Cassini’s measurements, by contrast, required Sirius and other stars to dwarf the sun—something Cassini explicitly noted, and something that echoed the ideas of Johannes Kepler more than a century earlier.

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