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 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.

Gravitational acceleration of a weakly relativistic electron in a conducting drift tube

2018 ◽  
Vol 33 (33) ◽  
pp. 1850192 ◽  
Author(s):  
V. I. Denisov ◽  
I. P. Denisova ◽  
M. G. Gapochka ◽  
A. F. Korolev ◽  
N. N. Koshelev
Keyword(s):  
Gravitational Field ◽  
Relativistic Electron ◽  
Horizontal Plane ◽  
Drift Tube ◽  
Gravitational Force ◽  
Vertical Direction ◽  
Gravitational Acceleration ◽  
The Earth ◽  
Earth’S Gravitational Field

We propose the idea of method for observing the effect of the Earth’s gravitational field on the motion of an electron. Earlier attempts to measure such an effect proved unsuccessful due to the fact that under the conductive sheath, the gravitational force acting on the non-relativistic electron is completely compensated by Barnhill–Schiff force. Therefore, experiments of this kind were unable to measure the effect of the Earth’s gravitational field on the motion of electrons. In this paper, we propose to use electrons moving with relativistic speeds in the horizontal plane, and with non-relativistic speeds in the vertical direction, in which case the gravitational force on these electrons is not fully compensated by the Barnhill–Schiff force. Calculations showed that in this case, it is possible to measure the force exerted on an electron by the gravitational field of the Earth.

scholarly journals Satellite Gravimetry: A Review of Its Realization

2021 ◽  
Author(s):  
Frank Flechtner ◽  
Christoph Reigber ◽  
Reiner Rummel ◽  
Georges Balmino
Keyword(s):  
Gravitational Field ◽  
Gravity Field ◽  
Water Cycle ◽  
Temporal Changes ◽  
Sensor Technology ◽  
Satellite Gravimetry ◽  
The Earth ◽  
Earth’S Gravitational Field ◽  
Gravity Field Determination ◽  
Space Age

AbstractSince Kepler, Newton and Huygens in the seventeenth century, geodesy has been concerned with determining the figure, orientation and gravitational field of the Earth. With the beginning of the space age in 1957, a new branch of geodesy was created, satellite geodesy. Only with satellites did geodesy become truly global. Oceans were no longer obstacles and the Earth as a whole could be observed and measured in consistent series of measurements. Of particular interest is the determination of the spatial structures and finally the temporal changes of the Earth's gravitational field. The knowledge of the gravitational field represents the natural bridge to the study of the physics of the Earth's interior, the circulation of our oceans and, more recently, the climate. Today, key findings on climate change are derived from the temporal changes in the gravitational field: on ice mass loss in Greenland and Antarctica, sea level rise and generally on changes in the global water cycle. This has only become possible with dedicated gravity satellite missions opening a method known as satellite gravimetry. In the first forty years of space age, satellite gravimetry was based on the analysis of the orbital motion of satellites. Due to the uneven distribution of observatories over the globe, the initially inaccurate measuring methods and the inadequacies of the evaluation models, the reconstruction of global models of the Earth's gravitational field was a great challenge. The transition from passive satellites for gravity field determination to satellites equipped with special sensor technology, which was initiated in the last decade of the twentieth century, brought decisive progress. In the chronological sequence of the launch of such new satellites, the history, mission objectives and measuring principles of the missions CHAMP, GRACE and GOCE flown since 2000 are outlined and essential scientific results of the individual missions are highlighted. The special features of the GRACE Follow-On Mission, which was launched in 2018, and the plans for a next generation of gravity field missions are also discussed.

scholarly journals Constants related to the Earth and Moon

1965 ◽  
Vol 21 ◽  
pp. 67-79
Author(s):  
Harold Jeffreys
Keyword(s):  
Gravitational Field ◽  
The Moon ◽  
The Earth ◽  
Earth’S Gravitational Field ◽  
Tesseral Harmonics

The author discusses various determinations of zonal and tesseral harmonics of the Earth's gravitational field, the values of the solar parallax, and the constants related to the figure of the Moon and its motion.

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.

The effect of atmospheric rotation on the orbital plane of a near-earth satellite

1960 ◽  
Vol 258 (1295) ◽  
pp. 516-528 ◽  
Keyword(s):  
Gravitational Field ◽  
Orbital Plane ◽  
Earth Satellite ◽  
Theoretical Curve ◽  
Orbital Inclination ◽  
Small Eccentricity ◽  
Earth’S Atmosphere ◽  
The Earth ◽  
Earth’S Gravitational Field ◽  
Good Agreement

Besides the perturbations due to the gravitational field of the earth, the rotation of the earth’s atmosphere produces a perturbing force on a satellite which affects the motion of its orbital plane. Theoretical formulae are derived for the rotation of the orbital plane about the earth’s axis and the change in orbital inclination of a near-earth satellite of small eccentricity (< 0.2) due to the influence of the atmosphere. It is assumed that the atmosphere is spherically symmetrical and has a density which varies exponentially with altitude. Comparison of the theoretical changes in orbital inclination show reasonably good agreement with those estimated from kinetheodolite observations, although the need for a slightly steeper theoretical curve is indicated. Although the rotation of the orbital plane is small, allowance must be made for it when making estimates of the harmonics of the earth's gravitational field.

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.

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