Coplanar Maneuvers Transfer for Mission Design with Lowest Δʋ using Series Solution

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 (R) 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 Δʋ for determining the mass propellant consumed Δm, at different specific impulse of the propellants, help us to carefully plane a mission to minimize the propellant mass carried on the rocket.