Trajectories with velocity corrections in the impulsive transfer orbits

The main goal of this paper is to acquire the precise final elliptic orbit stemming from an initial orbit via an optimal transfer orbit, by applying small tangential impulses at peri-apse and apoapse. We consider two systems; the generalized Hohmann and the generalized bi-elliptic transfer orbits. For the first system, we obtain the four relationships connecting the increments in major axes and eccentricities with the correctional increments in velocities delta vA and delta vB at points A, B. For the second system, we derive the three relationships, connecting slight changes in major axes with small increments in velocities at points A, B and C due to motor thrusts. Forminimum fuel consumption, we consider the initial impulse applied at periapse of initial orbit

Solution for the lambert's problem

In this work, we have formulated and solved the well known Lambert problem, one of the most important topics in celestial mechanics. As Lambert stated, the transfer time depends only on the unknown parameter a [semi major axis], the two radii and the chord length are already known from the definition of the problem. It should be possible to write the transfer time as a function of the semi major axis only [t[2] -t[1]=delta t =f[a]]. Also the transfer time can be written as a function of some other parameter such as AE, this allows for a well-behaved iteration, and is the chosen method for the universal variable formulation. We solve Lambert problem by using this method, for two cases, elliptic orbits and hyperbolic orbits. Parabolic orbits are of no practical importance. We consider the Earth - Mars trajectory case, as a numerical example