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Interesse spielt beim Lernprozess eine wichtige Rolle. Im Zuge der vorliegenden Arbeit wurden daher geometrische Konzepte anhand astronomischer Anwendungen für Schüler:innen aufgearbeitet, mit dem Ziel, Interesse und Freude am Lernen zu wecken. So werden durch den Blick in die Vergangenheit Überlegungen zu Distanzen zwischen Erde, Sonne und Mond angestellt. Auch mit den Namensgebern der Astronomie, den Sternen, wird Geometrie in Verbindung gesetzt. Beispielsweise hilft sphärische Trigonometrie dabei, den Lauf des erdnächsten Sterns, der Sonne, zu beschreiben. Der Supermond und der schiefe Mond sind Phänomene, die in den Medien Präsenz zeigen. Jene Erscheinungen unseres Erdmondes werden anhand geometrischer Erläuterungen kritisch untersucht. Auch unser Lebensraum, der Planet Erde, dient als mathematisches Objekt Kugel. Seine Bahn, und die der anderen Planeten unseres Sonnensystems, wird durch Keplers Gesetze beschrieben., Interest plays an important role in the learning process. In the course of this work, geometric concepts were therefore worked through using astronomical applications for students with the aim of arousing interest and enjoyment in learning. For example, by looking into the past, considerations are made about distances between the earth, sun and moon. Geometry is also linked to the namesakes of astronomy, the stars. For example, spherical trigonometry helps to describe the path of the closest star to the earth, the sun. The supermoon and the tilted moon are phenomena that have been featured in the media. These phenomena of our Earth's moon are critically examined using geometric explanations. Our habitat, the planet Earth, also acts as the mathematical object sphere. Its orbit, and that of the other planets in our solar system, is described by Kepler's laws., Sabrina Obrist, BEd, in englischer Sprache, Masterarbeit Universität Innsbruck 2024

Discovered in 1900 in an ancient Greek shipwreck, the Antikythera mechanism was supposedly capable of tracking the solar, lunar, eclipse, constellation, and planetary orbital calendars, in addition to the major athletic games in Greece (such as the Olympics). The device contained more than thirty gears that controlled all of these functions, and is considered to be the world's first functioning computer. One of the most complex and fascinating artifacts recovered to date from the ancient world, the Antikythera is simultaneously one of the most continuously studied and the most enigmatic devices ever to be constructed. The device was truly ahead of its time, and proves that the Greeks were capable of a technological prowess not witnessed again until the end of the Medieval Ages, nearly one and a half millennia after its invention.

The planetary orbits in our solar system have been successfully described by an approach similar to the Bohr atomic model [1-3]. A Schrödinger-type diffusion equation has shown that quantum states associated to the asteroid belt are in very good agreement with the observed mean radii of the asteroids which perform the internal and external orbits in the belt. According to these results, a model of quantum states condensation was proposed in order to infer the orbits of the planets in our solar system [4]. In this paper, the use of the Schrödinger-type diffusion equation reproduces the observed mean distances for the 101 extra-solar planets discovered up to now. A considerable number of these planets were found at the planetary mean distance of 0.05 AU from their stars, which is the fundamental radius obtained by this approach. Planets with mean distances of 2.0 AU were also predicted by the model., Pages: 113-121

The planetary orbits in our solar system have been successfully described by an approach similar to the Bohr atomic model [1-3]. A Schrödinger-type diffusion equation has shown that quantum states associated to the asteroid belt are in very good agreement with the observed mean radii of the asteroids which perform the internal and external orbits in the belt. According to these results, a model of quantum states condensation was proposed in order to infer the orbits of the planets in our solar system [4]. In this paper, the use of the Schrödinger-type diffusion equation reproduces the observed mean distances for the 101 extra-solar planets discovered up to now. A considerable number of these planets were found at the planetary mean distance of 0.05 AU from their stars, which is the fundamental radius obtained by this approach. Planets with mean distances of 2.0 AU were also predicted by the model., Pages: 113-121

The planetary orbits in our solar system have been successfully described by an approach similar to the Bohr atomic model [1-3]. A Schrödinger-type diffusion equation has shown that quantum states associated to the asteroid belt are in very good agreement with the observed mean radii of the asteroids which perform the internal and external orbits in the belt. According to these results, a model of quantum states condensation was proposed in order to infer the orbits of the planets in our solar system [4]. In this paper, the use of the Schrödinger-type diffusion equation reproduces the observed mean distances for the 101 extra-solar planets discovered up to now. A considerable number of these planets were found at the planetary mean distance of 0.05 AU from their stars, which is the fundamental radius obtained by this approach. Planets with mean distances of 2.0 AU were also predicted by the model., Pages: 113-121

The planetary orbits in our solar system have been successfully described by an approach similar to the Bohr atomic model [1-3]. A Schrödinger-type diffusion equation has shown that quantum states associated to the asteroid belt are in very good agreement with the observed mean radii of the asteroids which perform the internal and external orbits in the belt. According to these results, a model of quantum states condensation was proposed in order to infer the orbits of the planets in our solar system [4]. In this paper, the use of the Schrödinger-type diffusion equation reproduces the observed mean distances for the 101 extra-solar planets discovered up to now. A considerable number of these planets were found at the planetary mean distance of 0.05 AU from their stars, which is the fundamental radius obtained by this approach. Planets with mean distances of 2.0 AU were also predicted by the model., Pages: 113-121

The planetary orbits in our solar system have been successfully described by an approach similar to the Bohr atomic model [1-3]. A Schrödinger-type diffusion equation has shown that quantum states associated to the asteroid belt are in very good agreement with the observed mean radii of the asteroids which perform the internal and external orbits in the belt. According to these results, a model of quantum states condensation was proposed in order to infer the orbits of the planets in our solar system [4]. In this paper, the use of the Schrödinger-type diffusion equation reproduces the observed mean distances for the 101 extra-solar planets discovered up to now. A considerable number of these planets were found at the planetary mean distance of 0.05 AU from their stars, which is the fundamental radius obtained by this approach. Planets with mean distances of 2.0 AU were also predicted by the model., Pages: 113-121

The planetary orbits in our solar system have been successfully described by an approach similar to the Bohr atomic model [1-3]. A Schrödinger-type diffusion equation has shown that quantum states associated to the asteroid belt are in very good agreement with the observed mean radii of the asteroids which perform the internal and external orbits in the belt. According to these results, a model of quantum states condensation was proposed in order to infer the orbits of the planets in our solar system [4]. In this paper, the use of the Schrödinger-type diffusion equation reproduces the observed mean distances for the 101 extra-solar planets discovered up to now. A considerable number of these planets were found at the planetary mean distance of 0.05 AU from their stars, which is the fundamental radius obtained by this approach. Planets with mean distances of 2.0 AU were also predicted by the model., Pages: 113-121

The planetary orbits in our solar system have been successfully described by an approach similar to the Bohr atomic model [1-3]. A Schrödinger-type diffusion equation has shown that quantum states associated to the asteroid belt are in very good agreement with the observed mean radii of the asteroids which perform the internal and external orbits in the belt. According to these results, a model of quantum states condensation was proposed in order to infer the orbits of the planets in our solar system [4]. In this paper, the use of the Schrödinger-type diffusion equation reproduces the observed mean distances for the 101 extra-solar planets discovered up to now. A considerable number of these planets were found at the planetary mean distance of 0.05 AU from their stars, which is the fundamental radius obtained by this approach. Planets with mean distances of 2.0 AU were also predicted by the model., Pages: 113-121

The report describes results of an investigation of the propellant economies of using the gravitational attraction of Jupiter's four large moons to effect the transfer of a spacecraft into orbit around that planet. Use of a simplified model to approximate the maximum possible energy change as a function of the approach energy shows that the maximum energy loss from a flyby of Ganymede, the largest moon, is less than half that required to transfer from a high-thrust approach trajectory to an acceptable elliptical orbit. Thus, chemical retro-thrust is necessary to effect the transfer, and a moon swingby may not be justified. With a low-thrust trajectory approach, however, economical gravity assist from a moon is more promising. The lower approach energies of optimal low-thrust trajectories can be further reduced by retrothrusting, and guidance problems are more easily handled. A no-impulse capture could result in a final orbit with a one-year orbital period. Moreover, the relaxation of the required velocity endpoint conditions for low-thrust trajectories may allow significantly increased payloads or shorter flight times.

The classical Kepler Problem consists in the determination of the relative orbital motion of a secondary body (planet) with respect to the primary body (Sun), for a given time. However, any natural system tends to have minimum energy and is subjected to differential gravitational or tidal forces (called into play mainly due to the finite size and deformability of the secondary body). We formulate the Kepler Problem taking into account the finite size of the secondary body and consider an approximation which tends towards minimum energy orbits, by increasing the dimensionality of the problem. This formulation leads to a conceivable natural explanation of the fact that the planetary orbits are characterized by small eccentricities. © 1997 Kluwer Academic Publishers.

Diplomová práca sa zameriava na návrh a vytvorenie programu pre výpočet vzájomnej pozície planét Zem a Mars v solárnom systéme. Cieľom tejto záverečnej práce je preštudovať a predstaviť súčasné a v budúcnosti plánované možnosti optickej a laserovej komunikácie na trase Zem Mars. Následne je v práci predstavený návrh programu, ktorý je doplnený o teoretický výpočet vzájomných pozícii najmä planét Zem Mars v solárnom systéme. Tento program ďalej vykresľuje samotné planéty v solárnom systéme s obežnými dráhami. Ďalším smerovaním práce je návrh optického bezkáblového spoja a následná analýza energetickej bilancie optického spoja medzi planétami Zem a Mars., The master’s thesis is focused on the design and development of a program for calculating the relative positions of the planets Earth and Mars in the solar system. The aim of this thesis was to study and present the current and planned possibilities of optical and laser communication between Earth and Mars. Subsequently, the thesis presents the design of the program, which is complemented by the theoretical calculation of the relative positions of the planets Earth – Mars in the solar system. This program further plots the planets themselves in the solar system with their orbits. Another focus of the thesis is the design of an optical link and the subsequent analysis of the optical link budget between the planets Earth and Mars.