Astrodynamics

Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of motion and the law of universal gravitation. Orbital mechanics is a core discipline within space-mission design and control. Celestial mechanics treats more broadly the orbital dynamics of systems under the influence of gravity, including both spacecraft and natural astronomical bodies such as star systems, planets, moons, and comets. Orbital mechanics focuses on spacecraft trajectories, including orbital maneuvers, orbital plane changes, and interplanetary transfers, and is used by mission planners to predict the results of propulsive maneuvers. General relativity is a more exact theory than Newton's laws for calculating orbits, and it is sometimes necessary to use it for greater accuracy or in high-gravity situations (e.g. orbits near the Sun). Until the rise of space travel in the twentieth century, there was little distinction between orbital and celestial mechanics. At the time of Sputnik, the field was termed 'space dynamics'. The fundamental techniques, such as those used to solve the Keplerian problem (determining position as a function of time), are therefore the same in both fields. Furthermore, the history of the fields is almost entirely shared. Johannes Kepler was the first to successfully model planetary orbits to a high degree of accuracy, publishing his laws in 1605. Isaac Newton published more general laws of celestial motion in the first edition of Philosophiæ Naturalis Principia Mathematica (1687), which gave a method for finding the orbit of a body following a parabolic path from three observations. This was used by Edmund Halley to establish the orbits of various comets, including that which bears his name. Newton's method of successive approximation was formalised into an analytic method by Leonhard Euler in 1744, whose work was in turn generalised to elliptical and hyperbolic orbits by Johann Lambert in 1761–1777.

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PHYS-100: Advanced physics I (mechanics)

La Physique Générale I (avancée) couvre la mécanique du point et du solide indéformable. Apprendre la mécanique, c'est apprendre à mettre sous forme mathématique un phénomène physique, en modélisant l

PHYS-101(g): General physics : mechanics

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Space Mission Design and Operations

Learn the concepts used in the design of space missions, manned or unmanned, and operations, based on the professional experience of the lecturer.

Space Mission Design and Operations

Learn the concepts used in the design of space missions, manned or unmanned, and operations, based on the professional experience of the lecturer.

Vis-viva equation

In astrodynamics, the vis-viva equation, also referred to as orbital-energy-invariance law or Burgas formula, is one of the equations that model the motion of orbiting bodies. It is the direct result of the principle of conservation of mechanical energy which applies when the only force acting on an object is its own weight which is the gravitational force determined by the product of the mass of the object and the strength of the surrounding gravitational field.

Mantle (geology)

A mantle is a layer inside a planetary body bounded below by a core and above by a crust. Mantles are made of rock or ices, and are generally the largest and most massive layer of the planetary body. Mantles are characteristic of planetary bodies that have undergone differentiation by density. All terrestrial planets (including Earth), a number of asteroids, and some planetary moons have mantles. Earth's mantle The Earth's mantle is a layer of silicate rock between the crust and the outer core. Its mass of 4.

Halo orbit

A halo orbit is a periodic, three-dimensional orbit near one of the L1, L2 or L3 Lagrange points in the three-body problem of orbital mechanics. Although a Lagrange point is just a point in empty space, its peculiar characteristic is that it can be orbited by a Lissajous orbit or by a halo orbit. These can be thought of as resulting from an interaction between the gravitational pull of the two planetary bodies and the Coriolis and centrifugal force on a spacecraft. Halo orbits exist in any three-body system, e.

Doppler-based positioning using LEO augmented satellite constellation - Simulations of perspectives

Alice Andreetti

The Global Navigation Satellite System (GNSS) refers to a constellation of satellites emitting signals from space, used to provide Position, Navigation and Timing (PNT) services to the receivers on Earth. Nowadays, the GNSS is exploited in a wide range of applications among which ground mapping, transportation, machine control, timing, surveying, defense, or aerial photogrammetry [1]. However, as we become more dependent on GNSS technology, we also become more vulnerable to its limitations [2]. The GNSS operates with satellites orbiting in Medium Earth Orbits (MEO, approximately 20200 [km] in altitude). On one hand, this great distance allows to have a large footprint of the satellite signal on Earth, but on the other hand, it requires the signal to cross a wide path in the atmosphere before reaching the receiver. This results in a decrease of signal strength, which is not an issue in open-sky condition, but becomes a limitation in deep attenuation environments, with little or no service in urban canyon, in dense cities or indoors [3]. In this contribution, a possible strategy to cope with this issue is proposed and evaluated through a simulation process. It implies the use of Low Earth Orbits (LEO) satellites as a support for the GNSS PNT service. Since nowadays no broadband big LEO constellation broadcasting navigation messages exist, in this project various LEO constellation setups have been simulated and tested. Because LEOs are much closer to Earth (200 to 1500 [km]), they move faster in the sky, passing overhead in minutes instead of hours like MEOs. This gives rise to the possibility to exploit the Doppler effect to accurately locate the user. Therefore, three different PNT algorithms, employing the Kalman filter, are implemented and the evaluation of the localization quality is made at four distinct locations on the globe. The results show that, for most of the cases, compared to the standard GPS pseudorange only PNT, the addition of LEO pseudoranges already improve the localization quality. The performance of the PNT algorithm increases even more with the exploitation of both pseudoranges and pseudorangerates (Doppler) measurements. Nevertheless, the choice of constellation parameters such as satellites altitude, total number of satellites, orbit inclination or the frequency of the emitted signal, has a great impact on the magnitude of the improvement in the localization quality. The factor that has the most significant influence seems to be the signal frequency and for that reason it must be carefully chosen: the higher the better. Moreover, it has been demonstrated that at high elevation cut-off angles (denied environments), the addition of LEO constellation is a valid option and allows us to obtain an accurate position even when the GNSS only can not provide a solution. Finally, the LEO only system seems to be a promising alternative to cope with GNSS jamming or spoofing. However, the optimal LEO parameters providing an accurate solution for all the location on the globe has not yet been identified. In conclusion, the result of this effort is the awareness that, once the optimal parameters for the LEO system have been found, it is a valid option to augment the GNSS, or even as a standalone backup, especially when the Doppler-based positioning is applied. Nevertheless, we are still far from that end and much more research needs to be done.

2020

Improved pivot-slide model of the motion of a curling rock

Laurent De Schoulepnikoff

The pivot-slide model (Shegelski and Lozowski) successfully predicts the slide and curl distances of a curling rock. However, in this model, there is no dependence of the curl distance on the initial velocity, because the ratio between the pivot to sliding times is constant. A refined model is presented, in which the ratio of the pivot to sliding times depends on the stone velocity via two parameters. Confidence limits for these parameters are deduced from experimental data, which show that the pivot-slide ratio depends on the stone velocity. However, precise values of these parameters could not be obtained with this study, as more precise experiment data are needed. The refined model allows one to qualitatively explain two characteristics of the stone trajectory observed in a curling game, namely the bigger final curl with lower initial velocity and the lower curl with the effect of sweeping the ice.

CANADIAN SCIENCE PUBLISHING2019

Kepler's Laws and Orbital Mechanics

Explores Kepler's laws, orbital mechanics, energy of motion, flight path angles, orbital maneuvers, Hohmann transfers, geostationary orbits, and Lagrange points.

Elliptical Orbits: Examples and Formulas MOOC: Space Mission Design and Operations

Covers examples and formulas related to elliptical orbits and how to determine parameters of an elliptical orbit using known points.

Space Mission Design and Operations EE-585: Space mission design and operations

Covers space mission design, spacecraft energy, orbits, and maneuvers, including gravity effects, tethers, and interplanetary trajectories.

Topics in astrodynamics

Atmosphere

An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosphere is the outer region of a star, which includes the layers above the opaque photosphere; stars of low temperature might have outer atmospheres containing compound molecules. The atmosphere of Earth is composed of nitrogen (78 %), oxygen (21 %), argon (0.

Meteorology

Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not begin until the 18th century. The 19th century saw modest progress in the field after weather observation networks were formed across broad regions. Prior attempts at prediction of weather depended on historical data.