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 Transient Annular Structures in Exploding Galaxies

1972 ◽  
Vol 44 ◽  
pp. 313-313
Author(s):  
J. L. Sěrsic
Keyword(s):  
Gravitational Field ◽  
Test Particle ◽  
Relative Velocity ◽  
Symmetry Axis ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Physical Space ◽  
Space Time ◽  
High Mass ◽  
New Variables

The explosive events going on in the central parts of some galaxies are related to a very high mass concentration. As an explosion is actually a drastic rearrangement of the concerned masses with energy release, the binding energy of the central core will change and, correspondingly, its effective gravitational mass. A test particle far from the nuclear region, although within the galaxy, will be moving accordingly in a variable-mass Newtonian gravitational field.On the other hand the observations suggest that explosions in galaxies have axial symmetry, so we are concerned with the global properties of the motion of a particle in a variable mass axisymmetric gravitational field. In order to get rid of the mass variation a space-time conformal transformation is made, which, after imposing some not very restrictive conditions, leads to a conservative potential in the new variables. This new potential has additional terms due to the elimination of the variable mass. The equations of motion in the new variables provide the motion of the test particle relative to an expanding or contracting background which depends on the choice of the transformation and the law of the mass variability. The problem is, at this point, formally similar to Hill's. It is possible to write an equation for the relative energy (a generalization of Jacobi's integral) and also to define surfaces of zero relative velocity for the infinitesimal particle. The general topological properties of these surfaces require singular points along the symmetry axis (analogous to the collinear Eulerian points) and also a dense set in a circumference on a plane perpendicular to the symmetry axis (analogous to the Lagrangian points). The latter one is the main feature characterizing the topology of the zero relative velocity surfaces. Even when we lift some of the restrictive conditions, the Lagrangian ring preserves its properties, as for example, the one of being the only region where zero-velocity curves and equi-potentials coincide when the configuration evolves in time (in the transformed space-time).It is easy to understand that the topology of the surfaces is kept when we reverse the transformation and go back to physical space-time. If the dust, gas or stars in the system has definite upper limits for its Jacobian constants, spatial segregation of them will arise, as is the case in radio-galaxies such as NGC 5128, NGC 1316, etc. where ringlike dust structures are observed.

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 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.

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.

Variable mass motion in the Hénon–Heiles system

2021 ◽  
pp. 2150150
Author(s):  
Abdullah A. Ansari ◽  
Elbaz I. Abouelmagd
Keyword(s):  
Test Particle ◽  
Equations Of Motion ◽  
Variable Mass ◽  
Stationary Points ◽  
Mass Motion ◽  
Jacobi Integral

In this work, we analyze the motion properties of the test particle, that has a variable mass within the frame of Hénon–Heiles system. We derive the equations of motion of the test particle which varies its mass according to Jean’s law. We also determine the quasi-Jacobi integral which shows the effective variation due to variable mass parameters. Further, we studied the locations of stationary points and their stability, after using Meshcherskii spacetime inverse transformations.

Motion of a satellite in the earth’s gravitational field

1960 ◽  
Vol 254 (1276) ◽  
pp. 48-65 ◽  
Keyword(s):  
Gravitational Field ◽  
Spherical Harmonics ◽  
Main Part ◽  
Equations Of Motion ◽  
Orbital Elements ◽  
Partial Derivatives ◽  
Rates Of Change ◽  
Zonal Harmonics ◽  
The Earth ◽  
Secular Terms

The equations of motion of a satellite are given in a general form, account being taken of the precession and nutation of the earth. The main part of the paper deals with the motion arising from the gravitational field of the earth, expressed as a general expansion in spherical harmonics. By evaluating the partial derivatives in Lagrange’s planetary equations, • expressions are obtained for the rates of change of the orbital elements. Particular consideration is given to the form of the expressions for the secular terms arising from the first four zonal harmonics.

scholarly journals Planetary perturbation equations based on relativistic Keplerian motion

1986 ◽  
Vol 114 ◽  
pp. 41-52
Author(s):  
Neil Ashby
Keyword(s):  
Test Particle ◽  
Particle Motion ◽  
Elliptic Functions ◽  
Orbital Elements ◽  
Keplerian Motion ◽  
Jacobian Elliptic Functions ◽  
Planetary Perturbation ◽  
Geodesic Equations ◽  
Bound Test ◽  
Perturbation Equations

Solutions of the geodesic equations for bound test particle motion in a Schwarzschild field are expressed using Jacobian elliptic functions. Keplerian orbital elements are identified and related to a set of canonical constants. Relativistic Lagrange planetary perturbation equations are derived.

scholarly journals Long-Term Predictions for Highly Eccentric Orbits

1993 ◽  
Vol 132 ◽  
pp. 353-363
Author(s):  
José M. Ferrándiz ◽  
M. Eugenia Sansaturio ◽  
Jesús Vigo
Keyword(s):  
Equations Of Motion ◽  
Analytical Techniques ◽  
Artificial Satellites ◽  
Numerical Techniques ◽  
Dynamical Models ◽  
Eccentric Orbits

AbstractPredictability in orbital behaviour of artificial satellites depends on several factors: the accuracy required, the particular dynamical models formulated, the sets of variables chosen to describe them, the numerical or analytical techniques used and, specially, the specific trajectories to be established. In this paper we address the problem of predictability for highly eccentric satellites with (J2 + J22)-perturbation, by using numerical techniques to integrate the equations of motion when expressed in different sets of regular variables.

scholarly journals On J2 short-term orbit predictions in terms of KS elements

2017 ◽  
Vol 5 (1) ◽  
pp. 7 ◽  
Author(s):  
Sharon Sara Saji ◽  
Harishkumar Sellamuthu ◽  
Ram Krishan Sharma
Keyword(s):  
Radial Distance ◽  
Single Step ◽  
Test Cases ◽  
Orbital Elements ◽  
Short Term ◽  
Zonal Harmonic ◽  
Numerical Experimentation ◽  
Earth Orbits ◽  
Analytical Expressions ◽  
Mean Elements

Sharma’s singularity-free analytical theory for the short-term orbital motion of satellites in terms of KS elements in closed form in eccentricity with Earth’s zonal harmonic term J2, is improved by using King-Hele’s expression for the radial distance ‘r’ which includes the effect of J2, and is suitable for low eccentricity orbits. Numerical experimentation with four test cases with perigee altitude of 200 km and eccentricity varying from 0.01 to 0.3 for different inclinations is carried out. It is found that the orbital elements computed with the analytical expressions in a single step during half a revolution match very well with numerically integrated values and show significant improvement over the earlier theory. The solution can be effectively used for computation of mean elements for near-Earth orbits, where the short-term orbit perturbations due to J2 play most important role. The theory will be very useful in computing the state vectors during the coast phase of rocket trajectories and flight algorithms for on-board implementation.

scholarly journals On the mean anomaly and the mean longitude in tests of post-Newtonian gravity

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Lorenzo Iorio
Keyword(s):  
Binary Systems ◽  
Central Body ◽  
Semimajor Axis ◽  
Newtonian Gravity ◽  
Atmospheric Drag ◽  
Tests Of General Relativity ◽  
Orbital Configuration ◽  
The Mean ◽  
Tests Of Gravity ◽  
Linear Trends

Abstract The distinction between the mean anomaly $${\mathcal {M}}(t)$$M(t) and the mean anomaly at epoch $$\eta $$η, and the mean longitude l(t) and the mean longitude at epoch $$\epsilon $$ϵ is clarified in the context of a their possible use in post-Keplerian tests of gravity, both Newtonian and post-Newtonian. In particular, the perturbations induced on $${\mathcal {M}}(t),\,\eta ,\,l(t),\,\epsilon $$M(t),η,l(t),ϵ by the post-Newtonian Schwarzschild and Lense–Thirring fields, and the classical accelerations due to the atmospheric drag and the oblateness $$J_2$$J2 of the central body are calculated for an arbitrary orbital configuration of the test particle and a generic orientation of the primary’s spin axis $$\varvec{{\hat{S}}}$$S^. They provide us with further observables which could be fruitfully used, e.g., in better characterizing astrophysical binary systems and in more accurate satellite-based tests around major bodies of the Solar System. Some erroneous claims by Ciufolini and Pavlis appeared in the literature are confuted. In particular, it is shown that there are no net perturbations of the Lense–Thirring acceleration on either the semimajor axis a and the mean motion $$n_{\mathrm{b}}$$nb. Furthermore, the quadratic signatures on $${\mathcal {M}}(t)$$M(t) and l(t) due to certain disturbing non-gravitational accelerations like the atmospheric drag can be effectively disentangled from the post-Newtonian linear trends of interest provided that a sufficiently long temporal interval for the data analysis is assumed. A possible use of $$\eta $$η along with the longitudes of the ascending node $$\Omega $$Ω in tests of general relativity with the existing LAGEOS and LAGEOS II satellites is suggested.

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