Orbital maneuver transfer time is traditionally accomplished using direct numerical sampling to find the mission design with the lowest delta-ʋ requirements. The availability of explicit time series solutions to the Lambert orbit determination problem allows for the total delta-ʋ of a series of orbital maneuvers to be expressed as an algebraic function of only the individual transfer times. Series solution was applied for Hohmann transfer and Bi-elliptic transfer and comparing between Hohmann transfer and Bi-elliptic transfer for long distance. It has been concluded that Hohmann transfer is more appropriate when the ratio of radius of final orbit to initial orbit () is less than 11.94. The purpose of this work is to minimize total full requirements, as well known that no refueling station in space, then using the computed ∆ʋ for determining the mass propellant consumed , at different specific impulse of the propellants, help us to carefully plane a mission to minimize the propellant mass carried on the rocket.

The main objective of this paper is to calculate the perturbations of tide effect on LEO's satellites . In order to achieve this goal, the changes in the orbital elements which include the semi major axis (a) eccentricity (e) inclination , right ascension of ascending nodes ( ), and fifth element argument of perigee ( ) must be employed. In the absence of perturbations, these element remain constant. The results show that the effect of tidal perturbation on the orbital elements depends on the inclination of the satellite orbit. The variation in the ratio  decreases with increasing the inclination of satellite, while it increases with increasing the time.

The main point of this paper is to evaluate the change in the inclination (i) and semi-major axis (a) due to tidal perturbation in orbital elements of a low Earth orbiting satellite LEO's. The orbital elements in the sense of Keplerian motion are affect perturbation in a satellite motion and change in the orbital elements must be employed to study the perturbations of the tidal effect on these satellites. These elements remain constant in the absence of perturbation where perturbed equation of motion was numerically integrated using Lagrange's formulas where numerical analysis is the most suitable method to analyze disturbances. The findings demonstrate that the tidal disruption of the orbital elements relies on the satellite's inclination the variation in the ratio (∆𝒊/𝒊) and (∆𝒂/𝒂) decreases with increasing the inclination of satellite, while it increases with increasing the time and the difference in inclination reduces as the satellite's inclination rises, and the difference in semi major axis increases as time increases.