The Taylor series is defined by the f and g series. The solution to the satellite's equation of motion is expanding to generate Taylor series through the coefficients f and g. In this study, the orbit equation in a perifocal system is solved using the Taylor series, which is based on time changing. A program in matlab is designed to apply the results for a geocentric satellite in low orbit (height from perigee, hp= 622 km). The input parameters were the initial distance from perigee, the initial time, eccentricity, true anomaly, position, and finally the velocity. The output parameters were the final distance from perigee and the final time values. The results of radial distance as opposed to time were plotted for dissimilar times in seconds and their comparison with the exact solution, with the aim of selecting an optimized reference orbit at a height of 622 km. The results indicated that the two series diverged excessively as the time increased from the exact solution, excluding the time of 850 sec. The f and g series had a little shift. Besides, the root mean square error (rmse) is computed for 750 sec. It was about 5 for the two series before diverging at about 180 sec and rapidly growing with time. For 850 sec, the (rmse) is approaching 10 for the two series and increasing quickly over time. So, the (rmse) is directly proportional to time, which means that as time increases, the diverging behavior and the value of the (rmse) will also increase. If more terms (Δt) are used for the two series and more time is included, the two series will deviate from the exact solution. The program's results are compared to other published studies in this field; they demonstrated high convergence.
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Both the double-differenced and zero-differenced GNSS positioning strategies have been widely used by the geodesists for different geodetic applications which are demanded for reliable and precise positions. A closer inspection of the requirements of these two GNSS positioning techniques, the zero-differenced positioning, which is known as Precise Point Positioning (PPP), has gained a special importance due to three main reasons. Firstly, the effective applications of PPP for geodetic purposes and precise applications depend entirely on the availability of the precise satellite products which consist of precise satellite orbital elements, precise satellite clock corrections, and Earth orientation parameters. Secondly, th
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The major goal of this research was to use the Euler method to determine the best starting value for eccentricity. Various heights were chosen for satellites that were affected by atmospheric drag. It was explained how to turn the position and velocity components into orbital elements. Also, Euler integration method was explained. The results indicated that the drag is deviated the satellite trajectory from a keplerian orbit. As a result, the Keplerian orbital elements alter throughout time. Additionally, the current analysis showed that Euler method could only be used for low Earth orbits between (100 and 500) km and very small eccentricity (e = 0.001).
The effects of solar radiation pressure at several satellite (near Earth orbit satellite, low Earth orbit satellite, medium Earth orbit satellite and high Earth orbit satellite ) have been investigated. Computer simulation of the equation of motion with perturbations using step-by-step integration (Cowell's method) designed by matlab a 7.4 where using Jacobian matrix method to increase the accuracy of result.
In this study, the first kind Bessel function was used to solve Kepler equation for an elliptical orbiting satellite. It is a classical method that gives a direct solution for calculation of the eccentric anomaly. It was solved for one period from (M=0-360)° with an eccentricity of (e=0-1) and the number of terms from (N=1-10). Also, the error in the representation of the first kind Bessel function was calculated. The results indicated that for eccentricity of (0.1-0.4) and (N = 1-10), the values of eccentric anomaly gave a good result as compared with the exact solution. Besides, the obtained eccentric anomaly values were unaffected by increasing the number of terms (N = 6-10) for eccentricities (0.8 and 0.9). The Bessel
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The optimum separators operating pressure is determined by using flash calculations and equilibrium ratios. In this study, the optimum separator size for Jambur field is calculated by using equations introduced by Arnold and Stewart and API12J Specification [1]. Because Jambur field has a high production rate two conditions are taken in the study to determine separator size, first based on production rate 80,000 bbl/day and second based on split the production between two banks A and B (40,000 bbl/day for each bank). The calculation resulted in optimum separator pressure for the first stage of 700 psi, and the second stage of 300 psi, and the third stage of 120 psi. The results show that as the number of stages increased above three-stag
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The optimum separators operating pressure is determined by using flash calculations and equilibrium ratios. In this study, the optimum separator size for Jambur field is calculated by using equations introduced by Arnold and Stewart and API12J Specification [1]. Because Jambur field has a high production rate two conditions are taken in the study to determine separator size, first based on production rate 80,000 bbl/day and second based on split the production between two banks A and B (40,000 bbl/day for each bank). The calculation resulted in optimum separator pressure for the first stage of 700 psi, and the second stage of 300 psi, and the third stage of 120 psi. The results show that as the number of stages increased above three
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Researchers have increased interest in recent years in determining the optimum sample size to obtain sufficient accuracy and estimation and to obtain high-precision parameters in order to evaluate a large number of tests in the field of diagnosis at the same time. In this research, two methods were used to determine the optimum sample size to estimate the parameters of high-dimensional data. These methods are the Bennett inequality method and the regression method. The nonlinear logistic regression model is estimated by the size of each sampling method in high-dimensional data using artificial intelligence, which is the method of artificial neural network (ANN) as it gives a high-precision estimate commensurate with the dat
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The equation of Kepler is used to solve different problems associated with celestial mechanics and the dynamics of the orbit. It is an exact explanation for the movement of any two bodies in space under the effect of gravity. This equation represents the body in space in terms of polar coordinates; thus, it can also specify the time required for the body to complete its period along the orbit around another body. This paper is a review for previously published papers related to solve Kepler’s equation and eccentric anomaly. It aims to collect and assess changed iterative initial values for eccentric anomaly for forty previous years. Those initial values are tested to select the finest one based on the number of iterations, as well as the
... Show MoreFuzzy orbit topological space is a new structure very recently given by [1]. This new space is based on the notion of open fuzzy orbit sets. The aim of this paper is to provide applications of open fuzzy orbit sets. We introduce the notions of fuzzy orbit irresolute mappings and fuzzy orbit open (resp. irresolute open) mappings and studied some of their properties. .