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 Dynamics of an Artificial Satellite in an Earth-Fixed Reference Frame: Effects of Polar Motions

1980 ◽  
Vol 56 ◽  
pp. 271-274
Author(s):  
P. Farinella ◽  
A. Milani ◽  
A.M. Nobili ◽  
F. Sacerdote
Keyword(s):  
Reference Frame ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Earth Satellite ◽  
Unknown Parameters ◽  
Fixed Frame ◽  
Long Period ◽  
Fixed Reference ◽  
Orbital Data ◽  
Free Nutation

AbstractIn an Earth-fixed reference frame, polar motions (precession, lunisolar nutation, free nutation) introduce small apparent forces in the equations of motion of an Earth satellite. We discuss the possibilities (a) of integrating the orbit in an Earth-fixed frame when tracking data are used for geophysical applications, and (b) of determining from orbital data a set of unknown parameters describing the long-period wandering of the pole.

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 Further Acceleration of the Simpson Method for Solving Nonlinear Equations

2018 ◽  
Vol 14 (2) ◽  
pp. 7631-7639
Author(s):  
Rajinder Thukral
Keyword(s):  
Nonlinear Equation ◽  
Fourth Order ◽  
Efficiency Index ◽  
New Method ◽  
Order Method ◽  
Third Order ◽  
Type Method ◽  
New Formula ◽  
Order Four ◽  
Better Than

There are two aims of this paper, firstly, we present an improvement of the classical Simpson third-order method for finding zeros a nonlinear equation and secondly, we introduce a new formula for approximating second-order derivative. The new Simpson-type method is shown to converge of the order four.  Per iteration the new method requires same amount of evaluations of the function and therefore the new method has an efficiency index better than the classical Simpson method.  We examine the effectiveness of the new fourth-order Simpson-type method by approximating the simple root of a given nonlinear equation. Numerical comparisons is made with classical Simpson method to show the performance of the presented method.

scholarly journals 6th and 8th Order Hermite Integrator Using Snap and Crackle

2007 ◽  
Vol 3 (S246) ◽  
pp. 473-474
Author(s):  
Keigo Nitadori ◽  
Masaki Iwasawa ◽  
Junichiro Makino
Keyword(s):  
Fourth Order ◽  
Sixth Order ◽  
Floating Point ◽  
Eighth Order ◽  
Third Order ◽  
Order Scheme ◽  
Force Calculation ◽  
Derivatives Of ◽  
Very High ◽  
Better Than

AbstractWe present sixth- and eighth-order Hermite integrators for astrophysical N-body simulations, which use the derivatives of accelerations up to second order (snap) and third order (crackle). These schemes do not require previous values for the corrector, and require only one previous value to construct the predictor. Thus, they are fairly easy to be implemented. The additional cost of the calculation of the higher order derivatives is not very high. Even for the eighth-order scheme, the number of floating-point operations for force calculation is only about two times larger than that for traditional fourth-order Hermite scheme. The sixth order scheme is better than the traditional fourth order scheme for most cases. When the required accuracy is very high, the eighth-order one is the best.

scholarly journals Effects of radiation pressure and earth’s oblatness on high altitude artificial satellite orbit

10.4081/708 ◽  
2011 ◽  
Vol 1 (1) ◽  
pp. e2
Author(s):  
Khalil I. Khalil ◽  
Mohamed N.S. Ismail
Keyword(s):  
High Altitude ◽  
Radiation Pressure ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Satellite Orbit ◽  
Artificial Satellites ◽  
Runge Kutta Method ◽  
Ks Variables ◽  
Effects Of Radiation ◽  
Earth’S Oblateness

This paper is devoted to study the effects of radiation pressure together with tesseral and zonal harmonics on the high altitude artificial satellites orbits. The equations of motion were regularized by using the KS variables and the problem was solved numerically using the fourth order of Runge Kutta method. A numerical testing was performed on Lageos-1 satellite in order to analyze its orbital changes due to effects of both radiation pressure and Earth's oblateness.

scholarly journals Effects of radiation pressure and earth’s oblatness on high altitude artificial satellite orbit

2011 ◽  
Vol 1 (1) ◽  
pp. 2
Author(s):  
Khalil I. Khalil ◽  
Mohamed N.S. Ismail
Keyword(s):  
High Altitude ◽  
Radiation Pressure ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Satellite Orbit ◽  
Artificial Satellites ◽  
Runge Kutta Method ◽  
Ks Variables ◽  
Effects Of Radiation ◽  
Earth’S Oblateness

This paper is devoted to study the effects of radiation pressure together with tesseral and zonal harmonics on the high altitude artificial satellites orbits. The equations of motion were regularized by using the KS variables and the problem was solved numerically using the fourth order of Runge Kutta method. A numerical testing was performed on Lageos-1 satellite in order to analyze its orbital changes due to effects of both radiation pressure and Earth's oblateness.

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