Optimization of the launch profile of geostationary spacecraft with electric propulsion system using Falcon-9 launch vehicle

Abstract

A combined flight profile is being considered, in which the Falcon 9 launch vehicle launches the spacecraft into elliptical intermediate orbit from the Cape Canaveral launch site. In the process of analyzing the problem, the value of the height of the perigee and the inclination of the intermediate orbit are fixed, and the height of the apogee of the intermediate orbit varies. After separation from the last stage of the launch vehicle, the spacecraft carries out transfer to geostationary orbit using electric propulsion system. At the stage of insertion spacecraft from intermediate orbit to geostationary orbit using electric propulsion system, the problem of minimizing the mass of the propellant, multi-revolutionary transfer is considered. The number of revolution and the height of the apogee of the intermediate orbit vary in order to analyze the effect of these parameters on the duration of the transfer and the delivered mass of the spacecraft into geostationary orbit. The main purpose of this paper is to calculate the optimal values of the apogee height of the intermediate orbit and the optimal number of revolution that ensure the delivery of the maximum mass of the spacecraft to the geostationary orbit in a given time delta(t)*. To solve the optimization problem, the Pontryagin maximum principle is applied. After apply ing the maximum principle, the optimization problem is reduced to solving the boundary value problem, which is solved by the continuation method by parameter. The paper presents the results of the optimization problem of multi-revolutionary transfer and analysis of the energy characteristics of combined flight profile for insertion of spacecraft into geostationary orbit.

Keywords

• limited power
• limited thrust
• auxiliary longitude
• pontryagin maximum principle
• continuation method by parameter