scholarly journals The Planetary Theories and The Precession of the Ecliptic

1998 ◽  
Vol 11 (1) ◽  
pp. 158-162
Author(s):  
P. Bretagnon
Keyword(s):  
Present State ◽  
Secular Variation ◽  
Major Axis ◽  
High Accuracy ◽  
Reference Systems ◽  
Semi Major Axis ◽  
The Mean ◽  
Over Time ◽  
Planetary Theories

In this paper, I give the present state of the analytical planetary theories by describing the general theories and the secular variation theories, the variations of the ecliptic with respect to the ecliptic J2000, the utilization of the analytical planetary theories in the calculation of the precession-nutation of the equator and in the calculation of the expressions of transformation between the barycentric and geocentric reference systems. At last, I describe the construction of new planetary theories undertaken at the Bureau des longitudes. The analytical planetary theories arise in two forms: the general theories give, with a low accuracy, the variations of the elements of the planets over several million years; the secular variation theories reach a high accuracy over time spans of a few thousands of years. In all these solutions, the motion of the planets is represented with 6 elements: a, the semi major axis, λ, the mean longitude and the variables k = e cos ϖ, h = e sin ϖ, q = sin ½ cos Ω, p = sin ½ sin Ω where e represents the eccentricity of the orbit, w the longitude of the perihelion, i the inclination of the orbit about the ecliptic J2000 and Ω the longitude of the node.

Influence of some resonances on the inclination of a satellite

2020 ◽  
Author(s):  
Timothée Vaillant ◽  
Alexandre C. M. Correia
Keyword(s):  
Major Axis ◽  
The Moon ◽  
Semi Major Axis ◽  
Tidal Dissipation ◽  
The Earth ◽  
Hamiltonian Model ◽  
The Future ◽  
The Mean ◽  
Over Time ◽  
Probability Of Capture

<p align="justify">Knowing if the inclination of a satellite with respect to the equator of its planet is primordial can give hints on its origin and its formation. However, several mechanisms are able to modify its inclination during its evolution. The orbit of a satellite evolves over time and because of the tidal dissipation its semi-major axis can notably decrease or increase. Therefore the satellite can encounter several resonances in which it can potentially be captured. Some resonances are able to modify the equatorial inclination of a satellite. Touma and Wisdom (1998) noted that a resonance called ‘eviction’ between the mean motion of the Earth and the ascending node frequency of the Moon could increase by several degrees the equatorial inclination of the early Moon and could explain the present orientation of its orbit. Yokoyama (2002) studied these resonances for Phobos and Triton and observed that several resonances of this type can increase the equatorial inclination of Phobos in the future.</p> <p align="justify"> </p> <p align="justify">In this work, we study the different existing ‘eviction’ resonances to determine their possible influence on the equatorial inclination of a satellite. When a satellite goes through such a resonance, the capture is not certain and as noted by Yokoyama (2002), the probability of capture depends on several parameters as the obliquity of the planet and the interaction between other resonances. We consider the case of Phobos where we search to estimate the probability of a capture in an ‘eviction’ resonance by using an analytical Hamiltonian model and numerical simulations. This work will then notably estimate the probability that Phobos will be captured in the future in an ‘eviction’ resonance able to modify significantly its inclination and will measure the influence of the different parameters over the probability of capture.</p> <p align="justify"> </p> <p align="justify"><span lang="en-US">Acknowledgments: </span>The authors acknowledge support from project POCI-01-0145-FEDER-029932 (PTDC/FIS-AST/29932/2017), funded by FEDER through COMPETE 2020 (POCI) and FCT.</p> <p align="justify"> </p> <p align="justify">References:</p> <p align="justify"> </p> <p align="justify">Touma J. and Wisdom J., Resonances in the Early Evolution of the Earth-Moon System. <em>The Astronomical Journal</em>, 115:1653–1663, 1998.</p> <p align="justify">Yokoyama T., Possible effects of secular resonances in Phobos and Triton. <em>Planetary and Space Science</em>, 50:63–77, 2002.</p>

scholarly journals Some Special Types of Orbits around Jupiter

Aerospace ◽  
2021 ◽  
Vol 8 (7) ◽  
pp. 183
Author(s):  
Yongjie Liu ◽  
Yu Jiang ◽  
Hengnian Li ◽  
Hui Zhang
Keyword(s):  
Gravity Model ◽  
Small Perturbation ◽  
Equilibrium Points ◽  
Major Axis ◽  
Semi Major Axis ◽  
Ground Track ◽  
The Earth ◽  
Degenerate Equilibrium ◽  
The Mean ◽  
Element Theory

This paper intends to show some special types of orbits around Jupiter based on the mean element theory, including stationary orbits, sun-synchronous orbits, orbits at the critical inclination, and repeating ground track orbits. A gravity model concerning only the perturbations of J2 and J4 terms is used here. Compared with special orbits around the Earth, the orbit dynamics differ greatly: (1) There do not exist longitude drifts on stationary orbits due to non-spherical gravity since only J2 and J4 terms are taken into account in the gravity model. All points on stationary orbits are degenerate equilibrium points. Moreover, the satellite will oscillate in the radial and North-South directions after a sufficiently small perturbation of stationary orbits. (2) The inclinations of sun-synchronous orbits are always bigger than 90 degrees, but smaller than those for satellites around the Earth. (3) The critical inclinations are no-longer independent of the semi-major axis and eccentricity of the orbits. The results show that if the eccentricity is small, the critical inclinations will decrease as the altitudes of orbits increase; if the eccentricity is larger, the critical inclinations will increase as the altitudes of orbits increase. (4) The inclinations of repeating ground track orbits are monotonically increasing rapidly with respect to the altitudes of orbits.

scholarly journals Creation/destruction of ultra-wide binaries in tidal streams

2020 ◽  
Author(s):  
Jorge Peñarrubia
Keyword(s):  
Globular Clusters ◽  
Galactic Halo ◽  
Local Density ◽  
Formation Rate ◽  
Semimajor Axis ◽  
Major Axis ◽  
Binding Energies ◽  
Semi Major Axis ◽  
The Mean ◽  
Tidal Streams

Abstract This paper uses statistical and N-body methods to explore a new mechanism to form binary stars with extremely large separations (≳ 0.1 pc), whose origin is poorly understood. Here, ultra-wide binaries arise via chance entrapment of unrelated stars in tidal streams of disrupting clusters. It is shown that (i) the formation of ultra-wide binaries is not limited to the lifetime of a cluster, but continues after the progenitor is fully disrupted, (ii) the formation rate is proportional to the local phase-space density of the tidal tails, (iii) the semimajor axis distribution scales as p(a)da ∼ a1/2da at a ≪ D, where D is the mean interstellar distance, and (vi) the eccentricity distribution is close to thermal, p(e)de = 2ede. Owing to their low binding energies, ultra-wide binaries can be disrupted by both the smooth tidal field and passing substructures. The time-scale on which tidal fluctuations dominate over the mean field is inversely proportional to the local density of compact substructures. Monte-Carlo experiments show that binaries subject to tidal evaporation follow p(a)da ∼ a−1da at a ≳ apeak, known as Öpik’s law, with a peak semi-major axis that contracts with time as apeak ∼ t−3/4. In contrast, a smooth Galactic potential introduces a sharp truncation at the tidal radius, p(a) ∼ 0 at a ≳ rt. The scaling relations of young clusters suggest that most ultra-wide binaries arise from the disruption of low-mass systems. Streams of globular clusters may be the birthplace of hundreds of ultra-wide binaries, making them ideal laboratories to probe clumpiness in the Galactic halo.

scholarly journals Report of Special Commission 3 of IAG

2000 ◽  
Vol 180 ◽  
pp. 337-352 ◽  
Author(s):  
Erwin Groten
Keyword(s):  
Reference Frames ◽  
Major Axis ◽  
General Assembly ◽  
Specific Reference ◽  
Reference Systems ◽  
Semi Major Axis ◽  
Zonal Harmonic ◽  
Mean Values ◽  
Basic Parameters ◽  
New System

AbstractSince the last presentation of SC-3 on numerical values of fundamental geodetic parameters at the IAU General Assembly at Kyoto in 1997 there were some conceptual as well as fundamental numerical changes. The four basic parameters of geodetic (ellipsoidal) reference systems (GRS) can no longer be considered as constant with time:J2,a, ω, and GM have to be replaced by clearly (±10−8or better) specified mean values or have to be associated with a specific epoch or, in case of GM, with specific reference frames (a= semi-major axis of Earth ellipsoid,J2= second degree zonal harmonic of geopotential,ω= spin of Earth rotation). In case of (a, J2....) associated tidal reductions must be specifically defined in view of particular applications and significant differences between different tidal reduction types. Or we may replace “a” by a quantity which is independent of tides like the geopotential at the geoid, W0, where, however, also temporal changes are now discussed. The official geodetic reference systems such as GRS 80 and WGS 84 (revised in 97-form) are also no longer truly representing reality; a new system GRS 2000 is desired. We are, meanwhile, able to define and determine tidal and non-tidal (secular, periodic, aperiodic) variatipns of some fundamental geodetic parameters. Others are under investigation. New precession and/or nutation formulas to be adopted by IAU in 2000 or later would imply, again, changes in geodetic parameters such asH= hydrostatic flattening. Those and related other consequences are considered.

scholarly journals High Order Resonances in the Evolution of the Lunar Orbit

1983 ◽  
Vol 74 ◽  
pp. 3-17
Author(s):  
J. Kovalevsky
Keyword(s):  
Major Axis ◽  
Lunar Theory ◽  
The Moon ◽  
Tidal Effects ◽  
Semi Major Axis ◽  
Natural Satellite ◽  
Variation Of Constants ◽  
The Mean ◽  
Mean Elements

AbstractThis paper deals with the long term evolution of the motion of the Moon or any other natural satellite under the combined influence of gravitational forces (lunar theory) and the tidal effects. We study the equations that are left when all the periodic non-resonant terms are eliminated. They describe the evolution of the-mean elements of the Moon. Only the equations involving the variation of the semi-major axis are considered here. Simplified equations, preserving the Hamiltonian form of the lunar theory are first considered and solved. It is shown that librations exist only for those terms which have a coefficient in the lunar theory larger than a quantity A which is function of the magnitude of the tidal effects. The solution of the general case can be derived from a Hamiltonian solution by a method of variation of constants. The crossing of a libration region causes a retardation in the increase of the semi-major axis. These results are confirmed by numerical integration and orders of magnitude of this retardation are given.

The system of short period meteor streams

1974 ◽  
Vol 22 ◽  
pp. 269-281 ◽  
Author(s):  
B. A. Lindblad
Keyword(s):  
Major Axis ◽  
Progressive Increase ◽  
Orbital Energy ◽  
The Sun ◽  
Meteor Stream ◽  
Semi Major Axis ◽  
Meteor Streams ◽  
Short Period ◽  
The Mean ◽  
Orbital Periods

AbstractThe orbital characteristics of precisely reduced photographic meteors were studied. Most photographic meteors move in short period, direct orbits with orbital periods inbetween those of Jupiter and Mars. Practically no meteors have (Orbital periods coincident with those of the planets Jupiter, Mars and Earth.A search among all precisely reduced, photographic meteors revealed a number of new – or previously not well studied – meteor streams. For 18 short period meteor streams the scatter in the orbital elements 1/a,πand Ω was studied. An almost linear relation was found between the mean orbital energy of a meteor stream (– 1/a) and the standard deviation σ(1/a), indicating a progressive increase in the orbital scatter with decreasing mean distance to the sun. An index of mean meteoroid density was computed for 11 of the short period streams. The mean density increases with decreasing semi-major axis.The results are interpreted as indicating that the short period meteor streams are initially formed in orbits with periods slightly shorter than Jupiter’s. As the streams gradually drift inwards towards the sun under the influence of various drag forces the individual stream members spread out and only the high density, resistant meteors still remain, or can be recognized, as stream members.

The Apollo Group Asteroid 2008 OS9: Discovery, Orbit, Rotation and the Yarkovsky/YORP Effects

2010 ◽  
Vol 19 (3-4) ◽  
Author(s):  
K. Černis ◽  
I. Eglitis ◽  
I. Wlodarczyk ◽  
J. Zdanavičius ◽  
K. Zdanavičius
Keyword(s):  
Rotation Period ◽  
Major Axis ◽  
Brightness Variation ◽  
Semi Major Axis ◽  
Mean Values ◽  
Secular Changes ◽  
Photometric Observations ◽  
The Mean ◽  
The Difference

AbstractA project for astrometric and photometric observations of asteroids at the Baldone Observatory is described. One of the most important results of the project is the discovery of 2008 OS9, a 600 meter asteroid of the NEO Apollo group. The results of its astrometric and photometric observations at the Molėtai and Baldone observatories are presented. From the brightness variation with the 0.27 mag amplitude, a rotation period of 8.430 ± 0.005 h is determined. Close approaches of the asteroid to Earth and Venus during the next millenium are predicted. The mean values of secular changes in the semi-major axis, eccentricity and inclination are computed with and without the Yarkovsky and YORP effects. A negative value of the difference between the value of semi-major axis computed with the Yarkovsky and YORP effects and without them, da/dt, may indicate retrograde rotation of the asteroid.

Contraction of satellite orbits in an oblate atmosphere with a diurnal density variation

1982 ◽  
Vol 383 (1784) ◽  
pp. 127-145 ◽  
Keyword(s):  
Major Axis ◽  
Density Variation ◽  
Scale Height ◽  
Satellite Orbits ◽  
Semi Major Axis ◽  
Third Order ◽  
Small Eccentricity ◽  
Air Density ◽  
The Mean ◽  
Density Scale

The effect of air drag on satellite orbits of small eccentricity, e < 0.2, is considered. A model of the atmosphere that allows for oblateness is adopted, in which the density behaviour approximates to the observed diurnal variation. The equations governing the changes due to drag in the semi-major axis a , and in x = ae , during one revolution of the satellite are integrated, the density scale-height H being assumed constant. The resulting expressions for ∆ a and ∆ x are presented to third order in e . Compact expressions for the gradient d a /d x , and for the mean air density at perigee altitude ρ 1 are obtained, when H is allowed to vary with altitude. An equivalence between the variable- H and the constant- H equations is demonstrated, provided that the value of H used in the latter is chosen appropriately.

scholarly journals Analytical solution of the motion of the planets over several thousands of years

1996 ◽  
Vol 172 ◽  
pp. 17-28 ◽  
Author(s):  
P. Bretagnon
Keyword(s):  
Analytical Solution ◽  
Secular Variation ◽  
Barycentric Coordinates ◽  
Planetary Theory ◽  
Great Precision ◽  
The Mean ◽  
Rigid Earth ◽  
Mean Elements ◽  
Planetary Theories

The results of a planetary theory built by an iterative method are given here in order to show the relation with the secular variation theories and the meaning of the mean elements in these latter theories. The general theories have a validity span of several millions years but a weak precision; on the contrary, the secular variation theories reach a great precision over several thousand years. Two applications of the analytical planetary theories are presented: the relation between the barycentric coordinates and the geocentric ones; the determination of the terms of precession and nutation for the rigid Earth.

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