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

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

To transfer a satellite or a spacecraft from a low parking orbit to a geosynchronous  orbit, one of the many transition methods is used. All these methods need to identify some orbital elements of the initial and final orbits as perigee and apogee distances. These methods compete to achieve the transition with minimal consumption of energy, transfer time and mass ratio consumed ), as well as highest accuracy of transition. The ten methods of transition used in this project required designing programs to perform the calculations and comparisons among them.

     The results showed that the evaluation must depend on the initial conditions of the initial orbit and the satellite mechanical exception as well as

The transition from low Earth orbit 200-1500 (km) to geostationary Earth orbit 42162 (km) was studied in this work by many methods of transfer. The delta-v requirement (Δv), the time of flight (Δt), the mass ratio of propellant consume (Δm/m) and total mass was calculated for many values altitude in the same plane also when the plane is change. The results from work show that (Δv) that required for transfer when the plane of orbit change is large than (Δv) required when the transfer in coplanar maneuvers while the bi-elliptical transfer method need time of transfer longer than a Hohmann transfer method. The most energy efficiency was determined when the transfer in coaxial between elliptical orbits

An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.

An approximate solution of the liner system of ntegral cquations fot both fredholm(SFIEs)and Volterra(SIES)types has been derived using taylor series expansion.The solusion is essentailly

In this paper, by using the Banach fixed point theorem, we prove the existence and uniqueness theorem of a fractional Volterra integral equation in the space of Lebesgue integrable 𝐿1(𝑅+) on unbounded interval [0,∞).

The method of solving volterra integral equation by using numerical solution is a simple operation but to require many memory space to compute and save the operation. The importance of this equation appeares new direction to solve the equation by using new methods to avoid obstacles. One of these methods employ neural network for obtaining the solution.

This paper presents a proposed method by using cascade-forward neural network to simulate volterra integral equations solutions. This method depends on training cascade-forward neural network by inputs which represent the mean of volterra integral equations solutions, the target of cascade-forward neural network is to get the desired output of this network. Cascade-forward neural