TIME VARIATION OF THE GRAVITATIONAL CONSTANT AND SECULAR EVOLUTION OF THE ORBIT OF BINARY STARS

2009 ◽  
Vol 18 (08) ◽  
pp. 1243-1256 ◽  
Author(s):  
LIN-SEN LI
Keyword(s):  
Secular Variation ◽  
Time Variation ◽  
Binary Stars ◽  
Gravitational Constant ◽  
Semimajor Axis ◽  
Periodic Variation ◽  
Numerical Results ◽  
Orbital Elements ◽  
Secular Evolution ◽  
Theoretical Results

The author of this paper examines the influence of time variation of the gravitational constant on the evolution of the orbital elements of binary stars. The theoretical results show that the semimajor axis, eccentricity and mean longitude exhibit periodic, secular and mixed periodic variation, but the longitude of the periastron exists in periodic and mixed periodic variation, but not secular variation. The inclination and ascending node exhibit no variation. In addition, the limits of the secular evolution of the orbit of six binary stars due to time variation of the gravitational constant are estimated. The numerical results are given. The theoretical results are discussed and conclusions drawn.

The study of short orbital period of delta scuti pulsating variable stars

2019 ◽  
Vol 15 (S356) ◽  
pp. 407-407
Author(s):  
Abduselam Mohammed
Keyword(s):  
Time Delay ◽  
Orbital Period ◽  
Binary Stars ◽  
Arrival Time ◽  
Periodic Variation ◽  
Variable Stars ◽  
Orbital Elements ◽  
Pulsating Stars ◽  
Delta Scuti ◽  
Arrival Time Delay

AbstractAs a pulsating star moves in its binary orbit, the path length of the light between us and the star varies, leading to the periodic variation in the arrival time of the signal from the star to us (earth). With the consideration of pulsators light arrival time delay effects several new methods which allows using Kepler photometric data (light curves) alone to find binary stars have been recently developed. Among these modern techniques we used binarogram method and we identified that several δSct pulsating stars have companions. The application of these method on detecting long periods(i.e. longer than about 50 d) δSct pulsating stars is not new, but the uniqueness of this study is we verified that it is also applicable to detect and determine the orbital elements of short periods (i.e short orbital period) δSct pulsating stars. With this investigation, we identified the possible way to overcome effects of fictious peaks, even, on the maximum peaks helpful to verify weather the star has companion or not depend up on the existence of the time-delay. Then, we applied the technique on known binary stars and their orbital elements are previously published. Finally, we identified some new short orbital period δSct pulsating stars and obtained their orbital frequency and period with the same procedures. Because of with our attempts we succeeded and verified the applicability of the method (the Binarogram method) on these stars (i.e short orbital period) for the first time, we expect that our present study will play a great role for similar study and to improve our binary statistics.

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 The number of lattice rules having given invariants

1992 ◽  
Vol 46 (3) ◽  
pp. 479-495 ◽  
Author(s):  
Stephen Joe ◽  
David C. Hunt
Keyword(s):  
Normal Form ◽  
Quadrature Rule ◽  
Unit Cube ◽  
Numerical Results ◽  
Smith Normal Form ◽  
Lattice Rules ◽  
Dimensional Unit ◽  
Lattice Rule ◽  
Positive Integers ◽  
Theoretical Results

A lattice rule is a quadrature rule used for the approximation of integrals over the s-dimensional unit cube. Every lattice rule may be characterised by an integer r called the rank of the rule and a set of r positive integers called the invariants. By exploiting the group-theoretic structure of lattice rules we determine the number of distinct lattice rules having given invariants. Some numerical results supporting the theoretical results are included. These numerical results are obtained by calculating the Smith normal form of certain integer matrices.

scholarly journals Long Periodic Variation of Orbital Elements of A Satellite Perturbed by Discrete Gravity Anomalies

1978 ◽  
Vol 41 ◽  
pp. 240-240
Author(s):  
M.P. Ananda
Keyword(s):  
Gravity Field ◽  
Gravity Anomalies ◽  
Large Data ◽  
Periodic Variation ◽  
Static Case ◽  
Orbital Elements ◽  
Disturbing Potential ◽  
Data Set ◽  
Simple Matrix ◽  
Derivatives Of

AbstractA method for generating long periodic variations in satellite orbital elements when perturbed by discrete gravity anomalies is presented. The method consists of developing a disturbing potential as a function of orbital and gravity anomaly parameters, and generating partial derivatives of the potential with respect to the orbital elements. The partials are averaged over the period of the satellite to eliminate the short periodic variations. The averaged partials are substituted into the variation of parameter equations to give the mean orbital rates. Classically orbital elements are used in generating gravity field and thus the method is dynamic in nature. The problem is extremely cumbersome and complex when multi-state parameters have to be estimated from a considerably large data set. However, when mean orbital rates are used, the problem reduces to a simple linear static case, where only the gravity parameters have to be estimated, and it is a simple matrix inversion problem. Thus the method developed here was utilized in reducing Appolo 15 and 16 subsatellite radio tracking data to produce a lunar gravity field represented by point masses.

scholarly journals Masses of the components of SB2 binaries observed with Gaia – V. Accurate SB2 orbits for 10 binaries and masses of the components of 5 binaries

2020 ◽  
Vol 496 (2) ◽  
pp. 1355-1368
Author(s):  
J-L Halbwachs ◽  
F Kiefer ◽  
Y Lebreton ◽  
H M J Boffin ◽  
F Arenou ◽  
...  
Keyword(s):  
Radial Velocity ◽  
Binary Stars ◽  
Main Sequence ◽  
Spectroscopic Binaries ◽  
Orbital Elements ◽  
Evolved Stars ◽  
The Individual ◽  
The Masses ◽  
Stellar Masses ◽  
Selection Of

ABSTRACT Double-lined spectroscopic binaries (SB2s) are one of the main sources of stellar masses, as additional observations are only needed to give the inclinations of the orbital planes in order to obtain the individual masses of the components. For this reason, we are observing a selection of SB2s using the SOPHIE spectrograph at the Haute-Provence observatory in order to precisely determine their orbital elements. Our objective is to finally obtain masses with an accuracy of the order of one per cent by combining our radial velocity (RV) measurements and the astrometric measurements that will come from the Gaia satellite. We present here the RVs and the re-determined orbits of 10 SB2s. In order to verify the masses, we will derive from Gaia, we obtained interferometric measurements of the ESO VLTI for one of these SB2s. Adding the interferometric or speckle measurements already published by us or by others for four other stars, we finally obtain the masses of the components of five binary stars, with masses ranging from 0.51 to 2.2 solar masses, including main-sequence dwarfs and some more evolved stars whose location in the HR diagram has been estimated.

Design equation for stress concentration factors of notched strips and grooved shafts

1992 ◽  
Vol 27 (1) ◽  
pp. 21-28 ◽  
Author(s):  
A Kato
Keyword(s):  
Stress Concentration ◽  
Empirical Equation ◽  
Numerical Results ◽  
Design Equation ◽  
Loading Conditions ◽  
Use Values ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Theoretical Results

A new design equation for stress concentration factors is presented in this paper. This equation is an empirical equation and has been derived based on theoretical results of semi-infinite plates with a notch under tension and also numerical results of strips and shafts with finite notches under tension or bending. It gives stress concentration factors of notched strips and grooved shafts under tension or bending with one expression. This equation can be applied to various shapes of notches and loading conditions and is very convenient for a practical use. Values calculated by this equation are found to be closer to the numerical results recently published than those calculated by Neuber's formula.

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.

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