scholarly journals Analytical and Semianalytical Treatment of the Collinear Points in the Photogravitational Relativistic RTBP

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
S. E. Abd El-Bar ◽  
F. A. Abd El-Salam
Keyword(s):  
Mass Ratio ◽  
Gravitational Effects ◽  
Relativistic Corrections ◽  
Newtonian Approximation

The problem of restricted three bodies is considered. The treatment is carried out within the framework of the post-Newtonian approximation. The primaries also are assumed to be radiant sources. The locations of the collinear points are computed. Series forms of these locations are obtained as new results. A Mathematica program is constructed so as to draw the locations of collinear points versus the whole range of the mass ratioμtaking into account the photo-gravitational effects and/or the relativistic corrections. Analyses of these figures are addressed.

scholarly journals Realization of the Local Inertial Geocentric Frame in Relativity

1990 ◽  
Vol 141 ◽  
pp. 430-430
Author(s):  
He Miao-Fu ◽  
Huang Cheng
Keyword(s):  
Solar System ◽  
Inertial Frame ◽  
The Sun ◽  
Gravitational Effects ◽  
Local Inertial Frame ◽  
Relativistic Corrections ◽  
Tidal Forces ◽  
The Earth

There are two kinds of geocentric frames: local inertial and non-inertial geocentric frames. Ashby et al successfully constructed a local inertial geocentric frame in the neighborhood of the gravitating Earth. In the frame with origin at the Earth's center, the gravitational effects of the sun and of planets other than the Earth are basically reduced to their tidal forces, with very small relativistic corrections.However, the spatial base vectors of the local inertial frame essentially experience the geodesic (or deSitter) precession with respect to the solar system barycentric frame. Hence the realization of the local inertial frame requires that the general precession should exclude the geodesic precession. This requirement is inconsistent with the convention that the amount of geodesic precession is included in that of the general precession given by Lieske et al.

scholarly journals Note on accuracy of the post-Newtonian approximation for extreme-mass ratio inspirals: retrograde orbits

2017 ◽  
Vol 35 (2) ◽  
pp. 027001 ◽  
Author(s):  
Ryuichi Fujita ◽  
Norichika Sago ◽  
Hiroyuki Nakano
Keyword(s):  
Mass Ratio ◽  
Newtonian Approximation

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.

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