A new indirect measurement method of the electron temperature for the Protosphera's pinch plasma

This article presents a new method for estimating the electron temperature of the Protosphera's screw pinch. The temperature radial profile is obtained by a self-consistent modeling of a 1D MHD equilibrium along with a 0D power balance of the plasma column, given measurements and estimates of the axial pinch plasma current, of the plasma rotational frequency and, at the equatorial plane, of the electron density radial profile, of the edge poloidal magnetic field, of the edge electron temperature and of the neutrals pressure in the vacuum vessel. The plasma is considered in equilibrium with its neutral phase and in constant rotation. A MATLAB code has been developed with the aim of estimating the MHD radial equilibrium profiles, the thermodynamic plasma state and the neutrals profile. The numerical estimates are compared with available experimental data showing a good agreement.Comment: 4 pages, 6 figures, 1 table, research presented to the "6th ICFDT

A paper and pencil method of evaluating trajectories of space launchers

The determination of the trajectory of a space launcher is a complex optimization problem with boundary and path constraints. In particular the trajectory is initially constrained to a vertical launch, then it has to keep a zero incidence angle, the so called gravity turn phase, while several other path constraints can be active, such as: avoiding the flying over inhabited areas, controlling the fall of exhausted stages within safe regions, ensuring the launcher visibility from selected ground stations, etc. In this paper analytic formulas are developed for the gravity turn trajectory of a multistage space launcher. Formulas are given for relative velocity, flight path angle, altitude and range. All the trajectories start from the same initial conditions: vertical launch with zero relative velocity and they differ by the final value of the last stage flight path angle. It is proved in the paper that from these formulas it is possible to derive: i) a good estimate of the gravitational and aerodynamic losses of a space launcher ii) sub-optimal trajectories providing approximate evaluation of launcher performances iii) determination of the pitch manoeuvre to rotate the launcher from the vertical to the gravity turn trajectory iv) characterization of the attitude manoeuvres that the launcher control system has to implement during the atmospheric phase of the flight The two stage launcher Falcon 1 and the four stage Scout launcher are considered as test case to show effectiveness and criticalities of the analytic solutions proposed her

ON THE BELETSKY EQUATION

This paper was presented at the Beletsky Session of the 4th IAA Conference on University Satellite Missions and CubeSat Workshop held in Rome and dedicated to the memory of the great Russian mathematician and pioneer scientist of Astrodynamics. The paper is concentrated to the so called Beletsky equation, concerning the attitude motion of a satellite under gravity gradient torque. In fact Professor Beletsky dealt with many aspects of astrodynamics giving deep and useful contributions and establishing some theoretical basis for the development of the space activity in USSR, then it looks like disappointing that his name is so strictly linked to a simple equation such as(1 + e cos theta)theta '' - 2e sin theta ' + alpha sin theta = 4e sin thetadescribing the planar attitude motion of a satellite in elliptic orbit: The reason of the enormous success of the Beletsky equation is just in its simplicity and in the interesting characteristics of its phase space, where regular and periodic solutions are merged together with unstable and chaotic solutions. This is not unusual for a non linear differential equation, but in the Beletsky equation these characteristics can be understood in deep and the transition to chaos can be checked by various indices, so many researchers were attracted by the results that can be achieved from the abstract point of view of dynamical system theory while obtaining output of concrete interest in space applications. Most of the content presented in this paper is derived from my PhD thesis "Chaos in Astrodymanics" presented at the School of Aerospace Engineering of Rome in 1991 and developed under the supervision of Professor Filippo Graziani

Deployment strategies of a satellite constellation for polar ice monitoring

This research considers a constellation of 16 satellites equipped with SAR sensors and tailored to monitoring the polar ice evolution, with a suitable revisit time over the regions of interest. Satellite deployment includes three phases: (i) orbit injection, performed by the upper stage of the launch vehicle, (ii) orbit plane selection, and (iii) orbit phasing. This work is primarily focused on phase (ii). Carrier spacecraft are proposed as a valuable option to place the majority of satellites in their orbits. Two distinct strategies are proposed to complete this task. The first strategy is based on the use of chemical propulsion, combined with the perturbing action due to Earth oblateness. The second strategy considers the use of low-thrust electric propulsion, in conjunction with nonlinear orbit control. A comparison between these two approaches is drawn, in terms of deployment time and final mass ratio of the carrier. Orbit phasing concludes the constellation deployment, and is carried out by each satellite. A tradeoff is proven to exist between phasing time and propellant expenditure