scholarly journals Third-Body Perturbation Using a Single Averaged Model: Application in Nonsingular Variables

2007 ◽  
Vol 2007 ◽  
pp. 1-14 ◽  
Author(s):  
Carlos Renato Huaura Solórzano ◽  
Antonio Fernando Bertachini de Almeida Prado
Keyword(s):  
Semimajor Axis ◽  
The Moon ◽  
Orbital Elements ◽  
Third Body ◽  
Short Period ◽  
Time Histories ◽  
Physical Reasons ◽  
Averaged Model ◽  
The Mathematical Model ◽  
Third Body Perturbation

The Lagrange's planetary equations written in terms of the classical orbital elements have the disadvantage of singularities in eccentricity and inclination. These singularities are due to the mathematical model used and do not have physical reasons. In this paper, we studied the third-body perturbation using a single averaged model in nonsingular variables. The goal is to develop a semianalytical study of the perturbation caused in a spacecraft by a third body using a single averaged model to eliminate short-period terms caused by the motion of the spacecraft. This is valid if no resonance occurs with the moon or the sun. Several plots show the time histories of the Keplerian elements of equatorial and circular orbits, which are the situations with singularities. In this paper, the expansions are limited only to second order in eccentricity and for the ratio of the semimajor axis of the perturbing and perturbed bodies and to the fourth order for the inclination.

scholarly journals A Comparison of Averaged and Full Models to Study the Third-Body Perturbation

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Carlos Renato Huaura Solórzano ◽  
Antonio Fernando Bertachini de Almeida Prado
Keyword(s):  
Initial Conditions ◽  
Artificial Satellite ◽  
Main Body ◽  
Long Term Effects ◽  
Third Body ◽  
Mean Motion ◽  
Short Period ◽  
The Mean ◽  
Averaged Models ◽  
Averaged Model

The effects of a third-body travelling in a circular orbit around a main body on a massless satellite that is orbiting the same main body are studied under two averaged models, single and double, where expansions of the disturbing function are made, and the full restricted circular three-body problem. The goal is to compare the behavior of these two averaged models against the full problem for long-term effects, in order to have some knowledge of their differences. The single averaged model eliminates the terms due to the short period of the spacecraft. The double average is taken over the mean motion of the satellite and the mean motion of the disturbing body, so removing both short period terms. As an example of the methods, an artificial satellite around the Earth perturbed by the Moon is used. A detailed study of the effects of different initial conditions in the orbit of the spacecraft is made.

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.

Models of comets with strongly variable nongravitational effects

1999 ◽  
Vol 173 ◽  
pp. 381-387
Author(s):  
M. Królikowska ◽  
G. Sitarski ◽  
S. Szutowicz
Keyword(s):  
Cometary Nucleus ◽  
Spin Axis ◽  
Reactive Force ◽  
Orbital Elements ◽  
Cometary Nuclei ◽  
Short Period ◽  
Basic Parameters ◽  
Polar Radius ◽  
Cometary Activity ◽  
Nongravitational Effects

AbstractThe nongravitational motion of five “erratic” short-period comets is studied on the basis of published astrometric observations. We present the precession models which successfully link all the observed apparitions of the comets: 21P/Giacobini-Zinner, 31P/Schwassmann-Wachmann 2, 32P/Comas Solá, 37P/Forbes, and 43P/Wolf-Harrington. We used the Sekanina's forced precession model of the rotating cometary nucleus to include the nongravitational terms into equations of the comet's motion. Values of six basic parameters (four connected with the rotating comet nucleus and two describing the precession of spin-axis of the nucleus) have been determined along the orbital elements from positional observations of the comets. The solutions were derived with additional assumptions which introduce instantaneous changes of modulus of reactive force,Aand of maximum of cometary activity with respect to perihelion time. The present precession models impose some contraints on sizes and rotational periods of cometary nuclei. According to our solutions the nucleus of 21P/Giacobini-Zinner with oblateness along the spin-axis of about 0.32 (equatorial to polar radius of 1.46) is the most oblate among five investigated comets.

scholarly journals Extended analytical formulae for the perturbed Keplerian motion under low-thrust acceleration and orbital perturbations

2021 ◽  
Vol 133 (3) ◽  
Author(s):  
Marilena Di Carlo ◽  
Simão da Graça Marto ◽  
Massimiliano Vasile
Keyword(s):  
Gravitational Perturbation ◽  
Low Thrust ◽  
Orbital Elements ◽  
Third Body ◽  
The Third ◽  
Orbital Perturbations ◽  
Analytical Formulae ◽  
Numerical Orbit ◽  
Body Potential

AbstractThis paper presents a collection of analytical formulae that can be used in the long-term propagation of the motion of a spacecraft subject to low-thrust acceleration and orbital perturbations. The paper considers accelerations due to: a low-thrust profile following an inverse square law, gravity perturbations due to the central body gravity field and the third-body gravitational perturbation. The analytical formulae are expressed in terms of non-singular equinoctial elements. The formulae for the third-body gravitational perturbation have been obtained starting from equations for the third-body potential already available in the literature. However, the final analytical formulae for the variation of the equinoctial orbital elements are a novel derivation. The results are validated, for different orbital regimes, using high-precision numerical orbit propagators.

scholarly journals On the 2PN Pericentre Precession in the General Theory of Relativity and the Recently Discovered Fast-Orbiting S-Stars in Sgr A*

Universe ◽  
2021 ◽  
Vol 7 (2) ◽  
pp. 37
Author(s):  
Lorenzo Iorio
Keyword(s):  
General Theory ◽  
Present Author ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Orbital Elements ◽  
Analytical Expression ◽  
Potential Interest ◽  
Short Period ◽  
The Future ◽  
Sgr A

Recently, the secular pericentre precession was analytically computed to the second post-Newtonian (2PN) order by the present author with the Gauss equations in terms of the osculating Keplerian orbital elements in order to obtain closer contact with the observations in astronomical and astrophysical scenarios of potential interest. A discrepancy in previous results from other authors was found. Moreover, some of such findings by the same authors were deemed as mutually inconsistent. In this paper, it is demonstrated that, in fact, some calculation errors plagued the most recent calculations by the present author. They are explicitly disclosed and corrected. As a result, all of the examined approaches mutually agree, yielding the same analytical expression for the total 2PN pericentre precession once the appropriate conversions from the adopted parameterisations are made. It is also shown that, in the future, it may become measurable, at least in principle, for some of the recently discovered short-period S-stars in Sgr A*, such as S62 and S4714.

scholarly journals LOWER BOUNDS OF CHARACTERISTIC SCALE OF TOPOLOGICAL MODIFICATION OF THE NEWTONIAN GRAVITATION

2012 ◽  
Vol 21 (05) ◽  
pp. 1250048
Author(s):  
L. IORIO
Keyword(s):  
Semimajor Axis ◽  
Data Sets ◽  
Orbital Elements ◽  
Dynamical Models ◽  
Spatial Direction ◽  
Newtonian Gravitation ◽  
Complementary Approach ◽  
Local Modification

We analytically work out the long-term orbital perturbations induced by the leading order of perturbing potential arising from the local modification of the Newton's inverse square law due to a topology ℝ2 × 𝕊1 with a compactified dimension of radius R recently proposed by Floratos and Leontaris. We neither restrict to any specific spatial direction [Formula: see text] for the asymmetry axis nor to particular orbital configurations of the test particle. Thus, our results are quite general. Nonvanishing long-term variations occur for all the usual osculating Keplerian orbital elements, apart from the semimajor axis which is left unaffected. By using recent improvements in the determination of the orbital motion of Saturn from Cassini data, we preliminarily inferred R ≳ 4-6 kau . As a complementary approach, the putative topological effects should be explicitly modeled and solved-for with a modified version of the ephemerides dynamical models with which the same data sets should be reprocessed.

scholarly journals Wolf-Rayet binaries: old friends and new acquaintances

1999 ◽  
Vol 193 ◽  
pp. 26-37 ◽  
Author(s):  
Virpi S. Niemela ◽  
Roberto Gamen ◽  
Nidia I. Morrell ◽  
Sixto Giménez Benítez
Keyword(s):  
Radial Velocity ◽  
Binary Systems ◽  
Magellanic Cloud ◽  
Elliptic Orbit ◽  
Spectral Lines ◽  
Small Magellanic Cloud ◽  
Orbital Elements ◽  
Spectroscopic Observations ◽  
Short Period ◽  
Old Friends

Observations of WR stars in binary systems are discussed, emphasizing constraints on our knowledge of the binary frequency of WR stars, and of WR stars as a distinctive class of objects. Radial velocity orbits of newly discovered binaries, e.g., WR 29, a short period WN7+OB binary in our Galaxy, and SMC/AB 7, a massive WN+O7 binary in the Small Magellanic Cloud, are presented. New spectroscopic observations of binary systems with previously known orbits are also reported, showing in the case of WR 21 evidence of change of the orbital elements as derived from different spectral lines. An elliptic orbit for CV Ser is also illustrated.

scholarly journals Recent Dynamical History of the Six Short-Period Comets Discovered in 1975

1979 ◽  
Vol 81 ◽  
pp. 293-298 ◽  
Author(s):  
Hans Rickman
Keyword(s):  
Orbital Elements ◽  
Close Encounters ◽  
Short Period ◽  
History Of

In 1975 a remarkably large number of short-period comets were discovered - only the most recent number from 1977 is comparable. While the average discovery rate has been 0.8-1.0 new short-period comets per year (Kresák 1974), in 1975 there were six discoveries. In five of the cases IAU Circulars soon afterwards contained indications that close encounters with Jupiter had recently taken place (Marsden 1975, Kastel' 1975). For two of the comets, P/Kohoutek and P/Smirnova-Chernykh, also pre-encounter orbital elements were outlined, suggesting that substantial reductions of the perihelion distances had occurred.

A high-mass-ratio red-dwarf contact binary with an extremely cool close-in red dwarf

2019 ◽  
Author(s):  
Xiao-Hui Fang ◽  
Shengbang Qian ◽  
Miloslav Zejda ◽  
Soonthornthum Boonrucksar ◽  
Xiao Zhou ◽  
...  
Keyword(s):  
Orbital Period ◽  
Light Curves ◽  
High Mass ◽  
Mass Ratio ◽  
Third Body ◽  
Dynamical Interaction ◽  
The Third ◽  
Short Period ◽  
Contact Binaries ◽  
Mass Component

Abstract 1SWASP J161335.80$-$284722.2 (hereafter J161335) is an eclipsing red-dwarf binary with an orbital period of $0.229778\:$d, which is around the short-period limit for contact binaries. Three sets of multi-color light curves of J161335 were obtained from different telescopes in 2015 and 2016 and are analyzed using the Wilson–Devinney method. We discovered that the system is a W-type contact system with a contact degree of 19% and a high mass ratio of 0.91. By using all available eclipse times, we found that the observed $-$ calculated $(O-C)$ diagram displays a cyclic oscillation with an amplitude of 0.00196($\pm 0.00006)\:$d and a period of 4.79($\pm 0.14)\:$yr while it undergoes a downward parabolic change. This downward variation corresponds to a continuous decrease in the orbital period at a rate of $dP/dt = -4.26(\pm$0.01) $\times$ 10$^{-7}\:$d$\:$yr$^{-1}$. The small-amplitude oscillation is explained as the light travel-time effect from the gravitational influence of a third body with a lowest mass of $M _{3}$ = 0.15($\pm 0.01)M_{\,\odot }$. In solving the light curves, we found that the third light is increasing, with the wavelength suggesting that the third body may be a cool red dwarf. This is in agreement with the results obtained by analyzing the $O-C$ diagram. The tertiary red dwarf is orbiting the central red-dwarf binary at an orbital separation of 2.8($\pm 0.2$) au. These results suggest that the J161335 system may be formed through early dynamical interaction where the original low-mass component was replaced by a higher-mass third body and the lower-mass component was kicked out to a wider orbit. In this way, a hierarchical triple system similar to J161335 with a high-mass-ratio binary and a small close-in third body is formed.

scholarly journals Searching for Orbits with Minimum Fuel Consumption for Station-Keeping Maneuvers: An Application to Lunisolar Perturbations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Antonio Fernando Bertachini de Almeida Prado
Keyword(s):  
Numerical Simulations ◽  
Fuel Consumption ◽  
Total Variation ◽  
The Sun ◽  
The Moon ◽  
Station Keeping ◽  
Third Body ◽  
Lunisolar Perturbations ◽  
The Earth ◽  
New Criterion

The present paper has the goal of developing a new criterion to search for orbits that minimize the fuel consumption for station-keeping maneuvers. This approach is based on the integral over the time of the perturbing forces. This integral measures the total variation of velocity caused by the perturbations in the spacecraft, which corresponds to the equivalent variation of velocity that an engine should deliver to the spacecraft to compensate the perturbations and to keep its orbit Keplerian all the time. This integral is a characteristic of the orbit and the set of perturbations considered and does not depend on the type of engine used. In this sense, this integral can be seen as a criterion to select the orbit of the spacecraft. When this value becomes larger, more consumption of fuel is required for the station keeping, and, in this sense, less interesting is the orbit. This concept can be applied to any perturbation. In the present research, as an example, the perturbation caused by a third body is considered. Then, numerical simulations considering the effects of the Sun and the Moon in a satellite around the Earth are shown to exemplify the method.

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