A study on numerical methods for modelling the viscoelastic deformation of the earth due to surface loading

2018 ◽  
Author(s):  
Ching-kit Wong
Keyword(s):  
Numerical Methods ◽  
Viscoelastic Deformation ◽  
Surface Loading ◽  
The Earth

Mapping exomoon trajectories around Earth-like exoplanets

2021 ◽  
Vol 502 (4) ◽  
pp. 5292-5301
Author(s):  
Euaggelos E Zotos ◽  
Konstantinos E Papadakis ◽  
S Wageh
Keyword(s):  
Phase Space ◽  
Numerical Methods ◽  
Periodic Solutions ◽  
Linear Stability ◽  
Grid Method ◽  
Regular Motion ◽  
The Earth ◽  
Classification Technique ◽  
Predictor Corrector ◽  
Parent Star

ABSTRACT We consider a system in which both the parent star and the Earth-like exoplanet move on circular orbits. Using numerical methods, such as the orbit classification technique, we study all types of trajectories of possible exomoons around the exoplanet. In particular, we scan the phase space around the exoplanet and we distinguish between bounded, collisional, and escaping trajectories, considering both retrograde and prograde types of motion. In the case of bounded regular motion, we also use the grid method and a standard predictor-corrector procedure for revealing the corresponding network of symmetric periodic solutions, while we also compute their linear stability.

The restrictions on the assumption about conservation of parameters of orbit for submicron particles in the Earth’s plasmasphere in light of the corotational electric field

2018 ◽  
Vol 84 (6) ◽  
Author(s):  
A. B. Yakovlev ◽  
E. K. Kolesnikov ◽  
S. V. Chernov
Keyword(s):  
Magnetic Field ◽  
Numerical Methods ◽  
Electric Field ◽  
Submicron Particles ◽  
Quasi Equilibrium ◽  
Micro Particles ◽  
Equilibrium Charge ◽  
The Earth ◽  
Elliptic Orbits ◽  
The Magnetic Field

The influence of the corotational electric field on the possibility of long holding of micro-particles with radii of the order of some hundredths of micrometers and quasi-equilibrium charge moving along weakly elliptic orbits in the plasmasphere of the Earth is considered by analytical and numerical methods. It is shown that, unlike the magnetic field, the corotational electric field causes a slow change in the shape of the orbit.

scholarly journals Analytical and numerical methods of converting Cartesian to ellipsoidal coordinates

2021 ◽  
Vol 11 (1) ◽  
pp. 111-121
Author(s):  
G. Panou ◽  
R. Korakitis
Keyword(s):  
Numerical Methods ◽  
Analytical Method ◽  
Oblate Spheroid ◽  
Comparative Assessment ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
The Earth ◽  
Ellipsoidal Coordinates ◽  
Set Of Points ◽  
Exact Analytical Method

Abstract In this work, two analytical and two numerical methods of converting Cartesian to ellipsoidal coordinates of a point in space are presented. After slightly modifying a well-known exact analytical method, a new exact analytical method is developed. Also, two well-known numerical methods, which were developed for points exactly on the surface of a triaxial ellipsoid, are generalized for points in space. The four methods are validated with numerical experiments using an extensive set of points for the case of the Earth. Then, a theoretical and a numerical comparative assessment of the four methods is made. Furthermore, the new exact analytical method is applied for an almost oblate spheroid and for the case of the Moon and the results are compared. We conclude that, the generalized Panou and Korakitis’ numerical method, starting with approximate values from the new exact analytical method, is the best choice in terms of accuracy of the resulting ellipsoidal coordinates.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Formation of Lunar Craters and Bright Rays as a Result of Meteorite Impacts

1962 ◽  
Vol 14 ◽  
pp. 415-418
Author(s):  
K. P. Stanyukovich ◽  
V. A. Bronshten
Keyword(s):  
Explosive Charge ◽  
The Moon ◽  
Meteorite Impacts ◽  
The Earth ◽  
Lunar Craters ◽  
The Impact

The phenomena accompanying the impact of large meteorites on the surface of the Moon or of the Earth can be examined on the basis of the theory of explosive phenomena if we assume that, instead of an exploding meteorite moving inside the rock, we have an explosive charge (equivalent in energy), situated at a certain distance under the surface.

The Origin of the Moon

1962 ◽  
Vol 14 ◽  
pp. 149-155 ◽  
Author(s):  
E. L. Ruskol
Keyword(s):  
Chemical Composition ◽  
Solar System ◽  
The Moon ◽  
The Earth ◽  
The Difference ◽  
Origin Of The Moon

The difference between average densities of the Moon and Earth was interpreted in the preceding report by Professor H. Urey as indicating a difference in their chemical composition. Therefore, Urey assumes the Moon's formation to have taken place far away from the Earth, under conditions differing substantially from the conditions of Earth's formation. In such a case, the Earth should have captured the Moon. As is admitted by Professor Urey himself, such a capture is a very improbable event. In addition, an assumption that the “lunar” dimensions were representative of protoplanetary bodies in the entire solar system encounters great difficulties.

The Origin of the Moon and its Relationship to the Origin of the Solar System

1962 ◽  
Vol 14 ◽  
pp. 133-148 ◽  
Author(s):  
Harold C. Urey
Keyword(s):  
Solar System ◽  
The Moon ◽  
The Past ◽  
The Earth ◽  
Short Period ◽  
Origin Of The Moon

During the last 10 years, the writer has presented evidence indicating that the Moon was captured by the Earth and that the large collisions with its surface occurred within a surprisingly short period of time. These observations have been a continuous preoccupation during the past years and some explanation that seemed physically possible and reasonably probable has been sought.

Probable Structure and Nature of the Formations on the Reverse Side of the Moon According to Photometric Measurements of Lunar Photographs

1962 ◽  
Vol 14 ◽  
pp. 39-44
Author(s):  
A. V. Markov
Keyword(s):  
The Moon ◽  
Probable Structure ◽  
The Earth ◽  
Interplanetary Station ◽  
Photometric Measurements ◽  
Automatic Interplanetary Station

Notwithstanding the fact that a number of defects and distortions, introduced in transmission of the images of the latter to the Earth, mar the negatives of the reverse side of the Moon, indirectly obtained on 7 October 1959 by the automatic interplanetary station (AIS), it was possible to use the photometric measurements of the secondary (terrestrial) positives of the reverse side of the Moon in the experiment of the first comparison of the characteristics of the surfaces of the visible and invisible hemispheres of the Moon.

Seti Space Missions

1997 ◽  
Vol 161 ◽  
pp. 761-776 ◽  
Author(s):  
Claudio Maccone
Keyword(s):  
Electromagnetic Waves ◽  
Space Missions ◽  
Gravitational Lens ◽  
The Sun ◽  
Space Antenna ◽  
Focal Distance ◽  
Large Space ◽  
The Earth ◽  
Space Antennas ◽  
New Space

AbstractSETI from space is currently envisaged in three ways: i) by large space antennas orbiting the Earth that could be used for both VLBI and SETI (VSOP and RadioAstron missions), ii) by a radiotelescope inside the Saha far side Moon crater and an Earth-link antenna on the Mare Smythii near side plain. Such SETIMOON mission would require no astronaut work since a Tether, deployed in Moon orbit until the two antennas landed softly, would also be the cable connecting them. Alternatively, a data relay satellite orbiting the Earth-Moon Lagrangian pointL2would avoid the Earthlink antenna, iii) by a large space antenna put at the foci of the Sun gravitational lens: 1) for electromagnetic waves, the minimal focal distance is 550 Astronomical Units (AU) or 14 times beyond Pluto. One could use the huge radio magnifications of sources aligned to the Sun and spacecraft; 2) for gravitational waves and neutrinos, the focus lies between 22.45 and 29.59 AU (Uranus and Neptune orbits), with a flight time of less than 30 years. Two new space missions, of SETI interest if ET’s use neutrinos for communications, are proposed.

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