scholarly journals Analytical and Semi-Analytical Treatment of the Satellite Motion in a Resisting Medium

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
S. E. Abd El-Bar ◽  
F. A. Abd El-Salam
Keyword(s):  
Fourth Order ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Orbital Dynamics ◽  
Atmospheric Drag ◽  
Satellite Motion ◽  
Orbital Elements ◽  
Analytical Treatment ◽  
First Order ◽  
Resisting Medium

The orbital dynamics of an artificial satellite in the Earth's atmosphere is considered. An analytic first-order atmospheric drag theory is developed using Lagrange's planetary equations. The short periodic perturbations due to the geopotential of all orbital elements are evaluated. And to construct a second-order analytical theory, the equations of motion become very complicated to be integrated analytically; thus we are forced to integrate them numerically using the method of Runge-Kutta of fourth order. The validity of the theory is checked on the already decayed Indian satellite ROHINI where its data are available.

scholarly journals Third-Order Solution of An Artificial-Satellite Theory

1978 ◽  
Vol 41 ◽  
pp. 241-257
Author(s):  
Hiroshi Kinoshita
Keyword(s):  
Fourth Order ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Earth Satellite ◽  
Artificial Satellites ◽  
Artificial Satellite Theory ◽  
Third Order ◽  
Small Eccentricity ◽  
Order Solution ◽  
Better Than

AbstractA third-order solution is developed for the motions of artificial satellites moving in the gravitational field of the Earth, whose potential includes the second-, third-, and fourth-order zonal harmonics. Third-order periodic perturbations with fourth-order secular perturbations are derived by Hori’s perturbations method. All quantities are expanded into power series of the eccentricity, but the solution is obtained so as to be closed with respect to the inclination. A comparison with the results of numerical integration of the equations of motion indicates that the solution can predict the position of a close-earth satellite with a small eccentricity with an accuracy of better than 1 cm over 1 month.

scholarly journals Post-Newtonian direct and mixed orbital effects due to the oblateness of the central body

2015 ◽  
Vol 24 (08) ◽  
pp. 1550067 ◽  
Author(s):  
L. Iorio
Keyword(s):  
Test Particle ◽  
Central Body ◽  
Symmetry Axis ◽  
Equations Of Motion ◽  
Mixed Effects ◽  
Orbital Dynamics ◽  
Artificial Satellites ◽  
Orbital Elements ◽  
Zonal Harmonic ◽  
Orbital Configuration

The orbital dynamics of a test particle moving in the nonspherically symmetric field of a rotating oblate primary is impacted also by certain indirect, mixed effects arising from the interplay of the different Newtonian and post-Newtonian accelerations which induce known direct perturbations. We systematically calculate the indirect gravitoelectromagnetic shifts per orbit of the Keplerian orbital elements of the test particle arising from the crossing among the first even zonal harmonic J2 of the central body and the post-Newtonian static and stationary components of its gravitational field. We also work out the Newtonian shifts per orbit of order [Formula: see text], and the direct post-Newtonian gravitoelectric effects of order J2c-2 arising from the equations of motion. In the case of both the indirect and direct gravitoelectric J2c-2 shifts, our calculation holds for an arbitrary orientation of the symmetry axis of the central body. We yield numerical estimates of their relative magnitudes for systems ranging from Earth's artificial satellites to stars orbiting supermassive black holes. As far as their measurability is concerned, highly elliptical orbital configuration are desirable.

scholarly journals Dynamics of Artificial Satellites around Europa

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jean Paulo dos Santos Carvalho ◽  
Rodolpho Vilhena de Moraes ◽  
Antônio Fernando Bertachini de Almeida Prado
Keyword(s):  
Closed Form ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Maintenance Cost ◽  
Artificial Satellites ◽  
Present Moment ◽  
Orbital Elements ◽  
Disturbing Potential ◽  
Planetary Satellite ◽  
Nonspherical Shape

A planetary satellite of interest at the present moment for the scientific community is Europa, one of the four largest moons of Jupiter. There are some missions planned to visit Europa in the next years, for example, Jupiter Europa Orbiter (JEO, NASA) and Jupiter Icy Moon Explorer (JUICE, ESA). In this paper, we search for orbits around Europa with long lifetimes. Here, we develop the disturbing potential in closed form up to the second order to analyze the effects caused on the orbital elements of an artificial satellite around Europa. The equations of motion are developed in closed form to avoid expansions in power series of the eccentricity and inclination. We found polar orbits with long lifetimes. This type of orbits reduces considerably the maintenance cost of the orbit. We show a formula to calculate the critical inclination of orbits around Europa taking into account the disturbing potential due to the nonspherical shape of the central body and the perturbation of the third body.

scholarly journals Post-Newtonian Kozai–Lidov mechanism and its effect on cumulative shift of periastron time of binary pulsar

2020 ◽  
Vol 500 (2) ◽  
pp. 1645-1665 ◽  
Author(s):  
Haruka Suzuki ◽  
Priti Gupta ◽  
Hirotada Okawa ◽  
Kei-ichi Maeda
Keyword(s):  
Gravitational Waves ◽  
Triple System ◽  
Averaging Method ◽  
Equations Of Motion ◽  
Radio Observation ◽  
Orbital Elements ◽  
Binary Pulsar ◽  
First Order ◽  
Double Averaging ◽  
Wave Emission

ABSTRACT We study the Kozai–Lidov mechanism in a hierarchical triple system in detail by the direct integration of the first-order post-Newtonian equations of motion. We analyse a variety of models with a pulsar to evaluate the cumulative shift of the periastron time of a binary pulsar caused by the gravitational wave emission in a hierarchical triple system with Kozai–Lidov mechanism. We compare our results with those by the double-averaging method. The deviation in the eccentricity, even if small, is important in the evaluation of the emission of the gravitational waves. We also calculate the cumulative shift of the periastron time by using obtained osculating orbital elements. If Kozai–Lidov oscillations occur, the cumulative shift curve will bend differently from that of the isolated binary. If such a bending is detected through the radio observation, it will be the first indirect observation of gravitational waves from a triple system.

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.

Artificial satellite orbit computations

1966 ◽  
Vol 25 ◽  
pp. 363-371
Author(s):  
P. Sconzo
Keyword(s):  
Artificial Satellite ◽  
Satellite Orbit ◽  
Artificial Satellites ◽  
Orbital Elements ◽  
Differential Correction ◽  
Gravitational Effects ◽  
Short Intervals ◽  
The Subject ◽  
Introductory Discussion ◽  
Orbit Computation

In this paper an orbit computation program for artificial satellites is presented. This program is operational and it has already been used to compute the orbits of several satellites.After an introductory discussion on the subject of artificial satellite orbit computations, the features of this program are thoroughly explained. In order to achieve the representation of the orbital elements over short intervals of time a drag-free perturbation theory coupled with a differential correction procedure is used, while the long range behavior is obtained empirically. The empirical treatment of the non-gravitational effects upon the satellite motion seems to be very satisfactory. Numerical analysis procedures supporting this treatment and experience gained in using our program are also objects of discussion.

Onboard Real-time Estimation of Mean Orbital Elements with Atmospheric Drag

2013 ◽  
Vol 39 (10) ◽  
pp. 1722
Author(s):  
Zhao-Wei SUN ◽  
Wei-Chao ZHONG ◽  
Shi-Jie ZHANG ◽  
Jian ZHANG
Keyword(s):  
Real Time ◽  
Time Estimation ◽  
Atmospheric Drag ◽  
Orbital Elements ◽  
Real Time Estimation

Kinetic theory

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Distribution Function ◽  
Kinetic Theory ◽  
Liouville Equation ◽  
Vlasov Equation ◽  
Particle Distribution ◽  
Equations Of Motion ◽  
Poisson Brackets ◽  
Hamiltonian Form ◽  
First Order ◽  
Number Of Particles

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.

scholarly journals Derivative-Free King’s Scheme for Multiple Zeros of Nonlinear Functions

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1242
Author(s):  
Ramandeep Behl ◽  
Sonia Bhalla ◽  
Eulalia Martínez ◽  
Majed Aali Alsulami
Keyword(s):  
Iterative Methods ◽  
Fourth Order ◽  
Order Of Convergence ◽  
Real Life ◽  
Multiple Roots ◽  
Computational Results ◽  
Nonlinear Functions ◽  
First Order ◽  
Life Problems ◽  
Derivative Free

There is no doubt that the fourth-order King’s family is one of the important ones among its counterparts. However, it has two major problems: the first one is the calculation of the first-order derivative; secondly, it has a linear order of convergence in the case of multiple roots. In order to improve these complications, we suggested a new King’s family of iterative methods. The main features of our scheme are the optimal convergence order, being free from derivatives, and working for multiple roots (m≥2). In addition, we proposed a main theorem that illustrated the fourth order of convergence. It also satisfied the optimal Kung–Traub conjecture of iterative methods without memory. We compared our scheme with the latest iterative methods of the same order of convergence on several real-life problems. In accordance with the computational results, we concluded that our method showed superior behavior compared to the existing methods.

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