Minimax model of transport operations of emergency on-orbit servicing in heliosynchronous orbits

Heliosynchronous orbits are attractive for space system construction. As a result, the number of spacecraft operating therein is constantly increasing. To increase their efficiency, timely on-orbit servicing (both scheduled and emergency) is needed. Emergency on-orbit servicing of spacecraft is needed in the case of unforeseen, emergency situations with them. According to available statistical estimates, emergency situations with serviced spacecraft are not frequent. Because of this, serviced spacecraft must be within the reach of a service spacecraft for a long time. In planning emergency on-orbit servicing, the following limitations must be met: the time it takes the service spacecraft to approach any of the serviced spacecraft must not exceed its allowable value, and the service spacecraft’s allowable energy consumption must not be exceeded. This paper addresses the problem of searching for emergency on-orbit servicing that would be allowable in terms of time and energy limitations and would meet technical and economical constraints. The aim of this work is to develop a mathematical constrained optimization model for phasing orbit parameter choice, whose use would allow one to minimize the maximum time of transport operations in emergency on-orbit servicing of a spacecraft group in the region of heliosynchronous orbits. The problem is solved by constrained minimax optimization. What is new is the formulation of a minimax (guaranteeing) criterion for choosing phasing orbit parameters that minimize the maximum time of emergency on-orbit servicing transport operations. In the minimax approach, the problem is formulated as the problem of searching for the best solution such that the result is certain to be attained for any allowable sets of indeterminate factors. The proposed mathematical model may be used in planning emergency on-orbit service operations to minimize the maximum duration of emergency on-orbit servicing transport operations due to a special choice of the service spacecraft phasing and parking orbit parameters.

Effect of the Altitudes and Eccentricity of the Initial Orbit on Satellite Transition Efficiency

This research dealt with choosing the best satellite parking orbit and then the transition of the satellite from the low Earth orbit to the geosynchronous orbit (GEO). The aim of this research is to achieve this transition with the highest possible efficiency (lowest possible energy, time, and fuel consumption with highest accuracy) in the case of two different inclination orbits. This requires choosing a suitable primary parking orbit. All of the methods discussed in previous studies are based on two orbits at the same plane, mostly applying the circular orbit as an initial orbit. This transition required the use of the advanced technique of the Hohmann transfer method for the elliptical orbits, as we did in an earlier research, namely the transition from the perigee of the initial orbit to the final orbit and then conducting the rotation of the orbit plane to match the plane for the desired final orbit. The effect of the perigee altitude of the initial orbit on the transition efficiency calculated for the values ​​between 300 to 3000 km. It was found that increasing the altitude reduces the energy and fuel needed for transportation, but the time required for transportation increases, into account that the increased height of the initial or parking orbit also implies the requirement of higher energy to reach it. The effects of eccentricity (e) values of the initial orbit between 0.01 to 0.2 on the transition efficiency were calculated. It was found that the increase in (e) reduces the energy and fuel, but does not affect the time, required for transportation.

On the choice of a parking orbit for a service spacecraft

At present, the requirements for increasing spacecraft active life and operational reliability and reducing spacecraft operation costs become more and more stringent. Because of this, on-orbit servicing becomes more and more attractive. One of the most promising ways to increase the efficiency of transport operations in space is to carry out on-orbit servicing using reusable spacecraft with low-thrust solar electrojet engines. The aim of this paper is to develop a mathematical model for the choice of an optimal low near-Earth parking orbit for a reusable service spacecraft. The case of noncoplanar near-circular orbits of spacecraft and a shuttle scenario of their servicing is considered. The solution of the problem of choosing an optimal parking orbit for a reusable service spacecraft involves repeated solutions of the problem of determining the delta-velocity of the service spacecraft’s orbital transfers between its parking orbit and the orbits of the serviced spacecraft. In this connection, using the averaging method, a mathematical model is developed for the analytical determination of orbital transfer program controls and trajectories and assessing orbital transfer energy expenditures. With its use, a mathematical model is developed for the choice of a service spacecraft’s optimal parking orbit. The objective function is the total delta-velocity of the service spacecraft’s orbital transfers from its parking orbit to the orbits of the serviced spacecraft and vice versa with the inclusion of the orbital transfer frequency. The optimizable parameters are the service spacecraft parking orbit parameters. The use of the proposed models is illustrated by an example of service spacecraft parking orbit optimization. What is new is the mathematical models developed. The results obtained may be used in the preliminary planning of on-orbit servicing operations.

Determination and evaluation of the orbital transition methods between two elliptical earth orbits

To transfer a satellite or a spacecraft from a low parking orbit to a geosynchronous orbit, one of the many transition methods is used. All these methods need to identify some orbital elements of the initial and final orbits as perigee and apogee distances. These methods compete to achieve the transition with minimal consumption of energy, transfer time and mass ratio consumed ), as well as highest accuracy of transition. The ten methods of transition used in this project required designing programs to perform the calculations and comparisons among them. The results showed that the evaluation must depend on the initial conditions of the initial orbit and the satellite mechanical exception as well as the target orbit. The most efficient methods of transition in terms of energy required were, sequentially, methods 10, 1, 8, 9, and 2, whereas the least efficient in terms of energy consumption, fuel and transition time were, sequentially, methods 5,6, and 7. Method 3 was the most efficient when the orbit needed to change the inclination with the transition. The first phase of multi-stage transition is the most energy consuming.

The effects of parking orbit elements on designing of on-orbit servicing missions

Nowadays on-orbit servicing operations such as satellite refuelling, debris removal and visual inspection are considered as the most important issues in the space missions. Mission planning has a key role on the designation of such missions and it is strongly dependent on the required fuel. In this study, a new approach is proposed for the designing of the on-orbit operations with considering the parking orbit elements and location of the servicing satellites. The proposed method improves the previous mission planning process of the multiple servicing satellites in the terms of the reduction in the mission fuel consumption. Furthermore, a special rendezvous maneuver is considered for meeting the servicing satellites and the targets. Also, the transfer orbits are obtained through Lambert targeting. The optimisation of the problem is carried out by particle swarm optimisation algorithm and Taguchi technique is employed for the robust design of the control parameters of the optimisation algorithm. The results reveal that the proposed approach is an efficient way in the reduction of the fuel consumption in the on-orbit servicing missions rather than the conventional methods.

Electron density profiles probed by radio occultation of FORMOSAT-7/COSMIC-2 at 520 and 800 km altitude

The FORMOSAT-7/COSMIC-2 (F7/C2) will ultimately place 12 satellites in orbit with two launches with 24–28.5° inclination and 520–550 km altitude in 2016 and with 72° inclination and 720–750 km altitude in 2018. It would be very useful for the community to construct the global three-dimensional electron density structure by simultaneously combining the two launch observations for studying ionospheric structure and dynamics. However, to properly construct the global electron density structure, it is essential to know and evaluate differences between the ionospheric electron densities probed by the two launches. To mimic the F7/C2 observations, we examine the electron density probed at the two satellite altitudes 500 and 800 km by means of FORMOSAT-3/COSMIC (F3/C) observations at the parking orbit 500 km altitude and mission orbit 800 km altitude, as well as a corresponding observing system simulation experiment (OSSE). Observation and OSSE results show that the sounding geometries by satellite orbiting at 500 and 800 km altitudes can cause the overall differences in the electron density, the F2 peak electron density, and the F2 peak height of about 18–24, 12–28 %, and 7–19 km, respectively. Results confirm that the discrepancies mainly result from the sounding geometry and the grid (contour) bias of the electron density.