scholarly journals Mapping Orbits regarding Perturbations due to the Gravitational Field of a Cube

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Flaviane C. F. Venditti ◽  
Antonio F. B. A. Prado
Keyword(s):  
Gravitational Field ◽  
Three Dimensional ◽  
Orbital Dynamics ◽  
Keplerian Orbits ◽  
The Earth ◽  
Celestial Bodies ◽  
Good Potential ◽  
Exact Shape ◽  
Nonspherical Shape ◽  
Irregular Body

The orbital dynamics around irregular shaped bodies is an actual topic in astrodynamics, because celestial bodies are not perfect spheres. When it comes to small celestial bodies, like asteroids and comets, it is even more import to consider the nonspherical shape. The gravitational field around them may generate trajectories that are different from Keplerian orbits. Modeling an irregular body can be a hard task, especially because it is difficult to know the exact shape when observing it from the Earth, due to their small sizes and long distances. Some asteroids have been observed, but it is still a small amount compared to all existing asteroids in the Solar System. An approximation of their shape can be made as a sum of several known geometric shapes. Some three-dimensional figures have closed equations for the potential and, in this work, the formulation of a cube is considered. The results give the mappings showing the orbits that are less perturbed and then have a good potential to be used by spacecrafts that need to minimize station-keeping maneuvers. Points in the orbit that minimizes the perturbations are found and they can be used for constellations of nanosatellites.

scholarly journals DYNAMICS AROUND AN ASTEROID MODELED AS A MASS TRIPOLE

2020 ◽  
Vol 56 (2) ◽  
pp. 269-286
Author(s):  
L. B. T. dos Santos ◽  
L. Marchi ◽  
P. A. Sousa-Silva ◽  
D. M. Sanchez ◽  
S. Aljbaae ◽  
...  
Keyword(s):  
Orbital Dynamics ◽  
Challenging Problem ◽  
Simplified Models ◽  
Poor Knowledge ◽  
The Poor ◽  
The Earth ◽  
Celestial Bodies ◽  
Exact Shape ◽  
Qualitative Dynamics ◽  
Natural Satellites

The orbital dynamics of a spacecraft orbiting around irregular small celestial bodies is a challenging problem. Diffculties to model the gravity field of these bodies arise from the poor knowledge of the exact shape as observed from the Earth. In order to understand the complex dynamical environment in the vicinity of irregular asteroids, several studies have been conducted using simplified models. In this work, we investigate the qualitative dynamics in the vicinity of an asteroid with an arched shape using a tripole model based on the existence of three mass points linked to each other by rods with given lengths and negligible masses. We applied our results to some real systems, namely, asteroids 8567, 243 Ida and 433 Eros and also Phobos, one of the natural satellites of Mars.

scholarly journals Accurate Time Calculations of Falling Bodies in the Earth's Gravitational Field and Comparisons with Newton's Laws of Vertical Motion

2021 ◽  
pp. 44-53
Author(s):  
A. Ebaid ◽  
Shorouq M. S. Al-Qahtani ◽  
Afaf A. A. Al-Jaber ◽  
Wejdan S. S. Alatwai ◽  
Wafaa T. M. Alharbi
Keyword(s):  
Gravitational Field ◽  
Real Life ◽  
Vertical Motion ◽  
Exact Form ◽  
Potential Danger ◽  
Accurate Calculation ◽  
The Earth ◽  
Earth’S Gravitational Field ◽  
Celestial Bodies ◽  
Newton’S Laws

The Earth is exposed annually to the fall of some meteorites and probably other celestial bodies which cause a potential danger to vital areas in several countries. Consequently, the accurate calculation of the falling time of such bodies is useful in order to take the necessary procedures for protecting these areas. In this paper, Newton’s law of general gravitation is applied to analyze the vertical motion in the Earth’s gravitational field. The falling time is obtained in exact form. The results are applied on several objects in real life.

scholarly journals Development of Tactile Globe by Additive Manufacturing

2020 ◽  
pp. 419-426
Author(s):  
Yoshinori Teshima ◽  
Yohsuke Hosoya ◽  
Kazuma Sakai ◽  
Tsukasa Nakano ◽  
Akiko Tanaka ◽  
...  
Keyword(s):  
Visually Impaired ◽  
Three Dimensional ◽  
3D Models ◽  
The North ◽  
The Earth ◽  
Spherical Surfaces ◽  
Tactile Learning ◽  
Exact Shape ◽  
Prime Meridian ◽  
Topography Data

AbstractTo understand geographical positions, globes adapted for tactile learning is needed for people with visual impairments. Therefore, we created three-dimensional (3D) tactile models of the earth for the visually impaired, utilizing the exact topography data obtained by planetary explorations. Additively manufactured 3D models of the earth can impart an exact shape of relief on their spherical surfaces. In this study, we made improvements to existing models to satisfy the requirements of tactile learning. These improvements were the addition of the equator, prime meridian, and two poles to a basis model. Hence, eight types of model were proposed. The equator and the prime meridian were expressed by the belt on four models (i.e., B1, B2, B3, and B4). The height of their belt was pro-vided in four stages. The equator and the prime meridian were expressed by the gutter on four models (i.e., C1, C2, C3, and C4). The width of their gutter was provided in four stages. The north pole was expressed by a cone, while the south pole was expressed by a cylinder. The two poles have a common shape in all of the eight models. Evaluation experiments revealed that the Earth models developed in this study were useful for tactile learning of the visually impaired.

scholarly journals Synchronism of the Events on the Sun and the Earth - A Sign of External Influence on the Solar System

2019 ◽  
Vol 2 (3) ◽  
Keyword(s):  
Gravitational Field ◽  
Solar System ◽  
The Sun ◽  
Additional Energy ◽  
Gravitational Effects ◽  
External Influences ◽  
The Earth ◽  
The Galaxy ◽  
Celestial Bodies ◽  
Endogenous Activity

To solve fundamental and applied problems, it is useful to detect signs of external influences on the Solar system from the synchronous responses of the Earth’s shells, using a systemic and interdisciplinary analysis of solar-terrestrial relations - taking into account, along with solar activity and GCR fluxes, the endogenous activity of the Earth due to gravitational effects on the Earth with the sides of the Moon, the Sun and other celestial bodies of the Solar system during its barycentric motion in the gravitational field of the Galaxy, as well as the effects of perturbations on the Solar system as a whole. At the same time, the mechanism, energy, cyclicity, synchronism, change in the shape of the Earth and gravity, polar asymmetry and jump-like manifestations of solar-terrestrial relations, instability of the Earth’s daily rotation become explainable. The Solar system is subject to external influences of gravity of the heavy planets of Jupiter and Saturn in the course of its barycentric motion in the gravitational field of the Galaxy, as well as the bringing in solar system of additional energy when exposed to a heterogeneous interstellar environment.

Structure of the terrain and gravitational field of the planets: Kaula’s rule as a consequence of the probability laws by A.N. Kolmogorov and his school

2019 ◽  
Vol 485 (4) ◽  
pp. 493-496
Author(s):  
E. B. Gledzer ◽  
G. S. Golitsyn
Keyword(s):  
Random Walk ◽  
Gravitational Field ◽  
Spherical Harmonics ◽  
Empirical Data ◽  
The Moon ◽  
Linear Coefficient ◽  
Water Flows ◽  
The Earth ◽  
Order Of Magnitude ◽  
Celestial Bodies

Kaula’s empirical rule has been known for more than 50 years: the coefficients of expansion over spherical harmonics for the fluctuations of the gravitational field and terrain of the planets decrease as the number of the harmonic squared. This was found for Venus, the Moon, Mars, the asteroid Vesta, and very small celestial bodies. The inverse-square line spectra were also found for various types of the Earth’s surface on a scale of up to a hundred kilometers. From this it follows that the spectra of the terrain slope angles are constant, i.e., “white noise”. This, they are delta-correlated horizontally. These are the assumptions under which the random walk laws were derived by A.N. Kolmogorov in 1934. Using them, the equation of the horizontal probability diffusion of the terrain with the linear coefficient diffusion D is derived. Based on the empirical data, D = 1.3 ± 0.3 m for the Earth, while for Venus it is almost an order of magnitude less. The slopes resist the wind; the rock crumbles, and the water flows down the slopes as well. This consideration turns Kaula’s rule into the random walk laws (over terrain) developed by Kolmogorov in 1934.

scholarly journals Gravitational Field Intensity and Shifting of Waves

2020 ◽  
Vol 10 (4) ◽  
pp. 55-57
Author(s):  
Sankar Palchoudhury
Keyword(s):  
Gravitational Field ◽  
Field Intensity ◽  
Single Frequency ◽  
The Sun ◽  
The Earth ◽  
Celestial Bodies

The celestial bodies like the sun, stars, etc., are the owner of higher gravitational field intensity areas and the ‎source of various ‎kinds of waves. Waves rush from higher gravitational field intensity areas like the sun to lower ‎gravitational field intensity ‎areas like the earth. This paper, finding out that the wave exchanges some ‎force during traveling from the sun to the ground. ‎Every wave has a frequency and each frequency of a wave ‎has two parts, crest and trough and both together is a complete ‎single frequency.‎

The analysis is geometrically stable orbits of spacecraft remote sensing of the Еarth

2018 ◽  
Vol 15 (1) ◽  
pp. 12-22
Author(s):  
V. M. Artyushenko ◽  
D. Y. Vinogradov
Keyword(s):  
Remote Sensing ◽  
Gravitational Field ◽  
State Vector ◽  
Semimajor Axis ◽  
The State ◽  
Zonal Harmonics ◽  
The Earth ◽  
Conditions Of Stability

The article reviewed and analyzed the class of geometrically stable orbits (GUO). The conditions of stability in the model of the geopotential, taking into account the zonal harmonics. The sequence of calculation of the state vector of GUO in the osculating value of the argument of the latitude with the famous Ascoli-royski longitude of the ascending node, inclination and semimajor axis. The simulation is obtained the altitude profiles of SEE regarding the all-earth ellipsoid model of the gravitational field of the Earth given 7 and 32 zonal harmonics.

Spheric radial basis functions in Mahalanobis measuring for displaying local field features

2019 ◽  
Vol 952 (10) ◽  
pp. 2-9
Author(s):  
Yu.M. Neiman ◽  
L.S. Sugaipova ◽  
V.V. Popadyev
Keyword(s):  
Gravitational Field ◽  
Quadratic Form ◽  
Local Field ◽  
Euclidean Distance ◽  
Basis Functions ◽  
Spherical Functions ◽  
Local Models ◽  
Stationary Field ◽  
Modeling Process ◽  
The Earth

As we know the spherical functions are traditionally used in geodesy for modeling the gravitational field of the Earth. But the gravitational field is not stationary either in space or in time (but the latter is beyond the scope of this article) and can change quite strongly in various directions. By its nature, the spherical functions do not fully display the local features of the field. With this in mind it is advisable to use spatially localized basis functions. So it is convenient to divide the region under consideration into segments with a nearly stationary field. The complexity of the field in each segment can be characterized by means of an anisotropic matrix resulting from the covariance analysis of the field. If we approach the modeling in this way there can arise a problem of poor coherence of local models on segments’ borders. To solve the above mentioned problem it is proposed in this article to use new basis functions with Mahalanobis metric instead of the usual Euclidean distance. The Mahalanobis metric and the quadratic form generalizing this metric enables us to take into account the structure of the field when determining the distance between the points and to make the modeling process continuous.

scholarly journals III. On the nature and construction of the sun and fixed stars

1795 ◽  
Vol 85 ◽  
pp. 46-72 ◽  
Keyword(s):  
Central Body ◽  
Planetary System ◽  
Considerable Progress ◽  
The Sun ◽  
Great Satisfaction ◽  
The Earth ◽  
The World ◽  
Celestial Bodies ◽  
The Universe ◽  
Made In

Among the celestial bodies the sun is certainly the first which should attract our notice. It is a fountain of light that illuminates the world! it is the cause of that heat which main­tains the productive power of nature, and makes the earth a fit habitation for man! it is the central body of the planetary system; and what renders a knowledge of its nature still more interesting to us is, that the numberless stars which compose the universe, appear, by the strictest analogy, to be similar bodies. Their innate light is so intense, that it reaches the eye of the observer from the remotest regions of space, and forcibly claims his notice. Now, if we are convinced that an inquiry into the nature and properties of the sun is highly worthy of our notice, we may also with great satisfaction reflect on the considerable progress that has already been made in our knowledge of this eminent body. It would require a long detail to enumerate all the various discoveries which have been made on this subject; I shall, therefore, content myself with giving only the most capital of them.

Gravity assists maneuver in the problem of extension accessible landing areas on the Venus surface

2021 ◽  
Vol 30 (1) ◽  
pp. 103-109
Author(s):  
Natan A. Eismont ◽  
Vladislav A. Zubko ◽  
Andrey A. Belyaev ◽  
Ludmila V. Zasova ◽  
Dmitriy A. Gorinov ◽  
...  
Keyword(s):  
Gravitational Field ◽  
Entry Angle ◽  
Gravity Assist ◽  
Flight Duration ◽  
The Earth ◽  
Gravity Assists ◽  
Primary Basis ◽  
Venusian Surface ◽  
Research Show

Abstract This study discusses the usage of Venus gravity assist in order to choose and reaching any point on Venusian surface. The launch of a spacecraft to Venus during the launch windows of 2029 to 2031 is considered for this purpose. The constraints for the method are the re-entry angle and the maximum possible overload. The primary basis of the proposed strategy is to use the gravitational field of Venus to transfer the spacecraft to an orbit resonant to the Venusian one – with the aim of expanding accessible landing areas. Results of the current research show that this strategy provides an essential increase in accessible landing areas and, moreover, may provide an access to any point on the surface of Venus with a small increase in ∆V required for launch from the Earth and in the flight duration. The comparison with the landing without using gravity assist near planet is also given.

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