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Low Cost Orbital Positioning for Small Satellites1,2

Mauro De Sanctis*, Marina Ruggieri*, Pietro Salvini**

(*) Dpt. of Electrical Engineering, (**) Dpt. of Mechanical Engineering University of Roma “Tor Vergata”

Via del politecnico 1, 00133 Roma, Italy mauro.de.sanctis@uniroma2.it, ruggieri@uniroma2.it, salvini@uniroma2.it

1 0-7803-8155-6/04/$17.00© 2004 IEEE 2 IEEEAC paper #1119

Abstract—This paper deals with the study of low-cost orbital positioning for the overall class of small satellites with orbital constraints. The paper proposes an integrated approach for satellite subsystems design in order to provide a greater number of possibilities for low cost launch. Low cost launches can be generally achieved with piggyback or shared launch approaches. In both cases, the small satellite has to correct its orbit from the release to the final one. The correction of the orbit can be performed by using the multiple burns technique. The paper addresses the above issue and provides computation of the propellant mass needed for the orbital transfer. TABLE OF CONTENTS

1. INTRODUCTION.........................................1 2. COST COMPONENTS .................................2 3. TYPES OF LAUNCH ...................................2 4. SPACECRAFT DESIGN ...............................3 5. ORBITAL POSITIONING .............................3 6. MASS COMPUTATION ...............................4 7. CONCLUSION............................................4

1. INTRODUCTION In the development of satellite missions, launch has a considerable impact on the overall cost. In addition, the recent shortage in public and private funding devoted to satellites and related applications brings to the need for an innovative exploitation of the available budget. In the above frame, an optimized approach to satellite launch could dramatically reduce the overall mission cost, after a case-by-case trade-off among platform complexity, mission time-schedule and reliability. This is particularly advisable in the case of small satellite missions [1], conceived for various applications, such as: communications (e.g. store and forward), earth observation (remote sensing), scientific space experiments, technology evaluation. A classification of small satellites is shown in Table 1.

Due to the constraints of low power, small antennas and radiation sensitivity, most small satellites are positioned into low earth orbit (LEO). Furthermore, small satellites located at LEO can make use of cheap GPS (Global Positioning System) receiver in order to determine their position.

Table 1: Small satellite classification. Type of Satellite Mass Diameter Height pico satellites < 1 kg ~ 0.1 m ~ 0.1 m nano satellites < 10 kg ~ 0.2 m ~ 0.2 m micro satellites < 100 kg ~ 0.5 m ~ 0.5 m mini satellites < 500 kg ~ 1 m ~ 1 m

The launch of a small satellite is cheaper than the launch of a large one because of the generally lower orbits and the larger number of launch possibilities, but this is not true in terms of cost per unit of mass. In order to lower the launch cost per unit of mass, small satellites are launched as auxiliary payloads making use of the surplus launch capability of large launch vehicles. To this respect, the type of satellite and mission in terms of size, mass, and orbit of the spacecraft, drives to the choice of the best suited and cheaper launcher. Launch cost depends on the launch type, orbit and reliability. The most cost effective launches are shared and piggyback launches. In a shared or in a piggyback launch, the small satellite is not released into his final orbit, and hence, in case of orbital constraints of the mission, the spacecraft has to correct the orbit toward the final one. The orbital correction is performed by using the multiple burns technique that exploits the thrusters on board of the satellite. To this respect, a computation of the propellant mass required for the orbital transfer is needed in order to allow the launch as secondary or piggyback satellite. The paper is organized as follows. In Section 2 the cost components for satellite mission deployment are introduced. Section 3 highlights the launch possibilities for small satellites. The conventional and proposed spacecraft design is investigated in Section 4, while Section 5 describes the orbital positioning technique used for the orbital transfer.

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Section 6 provides numerical results for the mass required for the orbital transfer. Finally conclusions are drawn in Section 7. 2. COST COMPONENTS The deployment cost of a small satellite mission includes the costs related to design, development, management, test, launch, operational procedures and ground support. A key issue in small satellite mission design is the development of cost models and their integration with the spacecraft design [2], particularly for non-commercial missions. An accurate cost model has to take into account at least the following components: platform, communication payload and launch. The platform includes the following subsystems: - attitude control (spin or three-axis), - propulsion subsystem for orbit control, - thermal control, - electric power supply (solar cells and batteries), - Telemetry, Tracking and Command (TTC) and On-

Board Data Handling (OBDH). The propulsion subsystem, composed by thrusters and propellant tank, is used for the spacecraft injection into the final orbit and for drift control. If necessary, the propulsion subsystem can be properly designed for the orbit correction from the orbit release to the final orbit. The communications payload consists of antennas and repeater (transparent, regenerative); the choice of the payload is based on the type of mission and orbital constraints. The larger portion of the overall mission budget consists of launch cost that can reach about 50% of the overall budget. Duration of the mission, development time, reliability of the system, reliability of the launcher and launch delay are project variables that can strongly improve the mission cost. 3. TYPES OF LAUNCH

There are three main types of low cost launch for small satellites: dedicated launch, shared launch and auxiliary payload launch. In a dedicated launch a small satellite can make use of small launchers cheaper than large launchers. In a shared launch, two or more satellites can be launched on the same expendable vehicle; in this case one or both satellites are not positioned in their final orbit. On the other hand, launch of large satellites does not exploit the full capability of a launcher vehicle, and, hence, residual capability can be exploited by one or more small satellites as auxiliary payloads (piggyback launch). When launched as auxiliary payload, the secondary satellite is left stranded into the primary satellite orbit. Generally the primary satellite orbit is useless for the secondary payload.

In both cases of shared and auxiliary payload launches, the small satellite with orbital constraints has to correct its orbit from the release to the final orbit. If these orbits have not intersection point, the final orbit can be reached with at least two orbital corrections. While the opportunity of launch as secondary payload is frequent for launches destined to the Geo-synchronous Transfer Orbit - GTO (both for the number of satellites destined to Geostationary Earth Orbit – GEO, and for the larger size of the launcher), the opportunity for piggyback launch into LEO is more rare. Taking into account that the most part of the small satellites missions make use of LEO orbits, the orbit transfer from a GTO orbit to a LEO orbit is very expensive in terms of energy (i.e. mass of propellant). The only way to make this orbit transfer feasible is by using the aerobraking technique [3]. Furthermore a satellite positioned into the GTO crosses the Van Hallen belt and, hence, the electronic components on board the spacecraft have to be implemented properly. In this frame, only launches into LEO will be addressed. Launcher performance is evaluated in terms of: cost, reliability, type of launch and orbit, availability and payload requirements in terms of size and mass. There are several launcher on the market and choosing the most suited for the mission is a complex issue. Furthermore the launcher market is dynamic and in continuous evolution. 4. SPACECRAFT DESIGN Conventionally, the design methodology of a satellite is based on a subsystem-by-subsystem approach; after requirements definition, each subsystem is separately designed and iteratively checked. The planning structure is shown in Figure 1.

Figure 1: Design methodology at subsystem level.

On the other hand the exploitation of commercial satellite platforms could be a restriction in the development of cost efficient missions.

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A novel mission design methodology for the exploitation of launch as secondary payload has to integrate the payload design, the choice of the thruster, the platform design and the choice of the launcher. This planning structure is shown in Figure 2.

Figure 2: Integrated mission design methodology for piggyback launch.

Platform design, choice of the launch vehicle and payload design are required to interact for the overall cost optimization. In fact, the integration of the subsystems design allows the minimization of the spacecraft mass, increasing the launch possibilities for the spacecraft, and hence reducing the launch cost. In order to reach the final orbit from the orbit of release the spacecraft makes use of the thrusters for orbit control, exploiting the multiple burns maneuver. The multiple burns maneuver is based on a non-impulsive velocity increments that can make use of several types of thrusters: bi/mono-propellant, ion thrusters, plasma thrusters. Furthermore, the multiple burns maneuver allows to correct non-accurate burns. Taking into account the exploitation of the multiple burns technique, a second aspect that has been investigated is the computation of propellant required for the orbital correction in the case of a not dedicated release in orbit. In fact, in a shared launch or in a piggybacked launch the satellite has to take into account mass and size constraints imposed by the launcher. The propellant mass increases size and mass of the spacecraft propulsion subsystem, hence, the computation of the needed propellant is a key-issue for the choice of launch possibilities. At the end of the design process, a set of useful orbits where the satellite can be stranded is provided. The larger the satellite, the lower the delay time for a suited launch. In order to develop a mission design methodology for the exploitation of shared launches, a further integration in the design has to be conceived.

Figure 3 shows the interaction between two different mission designs; each mission provides a set of useful orbits of release. After the useful orbits definition, a negotiation process is required in order to provide the choice of the shared orbit of release.

Figure 3: Integrated mission design methodology for shared launch.

5. ORBITAL POSITIONING The trajectory of a satellite in the space is completely defined by the following orbital parameters [4]: semi-major axis (a), eccentricity (e), inclination (i), right ascension of the ascending node - RAAN (Ω), argument of perigee (ω). While the argument of perigee only defines the orientation of the orbit in its plane, the other parameters describe the shape of the orbit and its orientation with respect to the earth. The correction of the semi-major axis and the correction of the eccentricity will be analyzed, while the correction of the inclination is very expensive in terms of energy consumption and will not be addressed. On the other hand, RAAN variation is energy efficient. The correction of the orbit will be performed with the exploitation of three thrusters in the direction of the axis x, y, z. The multiple burns is used in case of small thrusters, and it is not more efficient than the Hohmann orbit transfer. The advantage of the exploitation of multiple rocket firing is in the possibility of correction in case of orbit transfer error. Figure 4 shows the tracks of the orbits exploited for the orbital correction. The multiple burn technique here exploited is aimed at finding out the best sequence of single burns, each one causing a change in orbit, to achieve the requested shift from original to target orbit. When radical changes of orbit are considered, the least fuel-consuming solution is not

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trivial, and non-linear optimization is needed. Each individual burn composing the sequence is characterized by the location within the actual orbit, the direction of thrust in space and the time duration. Use of different types of thrusters produces different solution paths. The solution is reached by minimization, in the sense of mean squares, of a functional that accounts of the difference existing from the new orbit achieved after a burn and the target one. The non-linearity of the solution is highlighted when changing the weights used for the individual terms setting the object functional; therefore, more than one optimization process is needed to single out the best suited strategy.

Figure 4: Tracks of the orbits in the orbital correction process.

6. MASS COMPUTATION Mass computation (and size computation if necessary) is required in order to integrate the spacecraft with the launch vehicle. The total mass of the spacecraft is split up in the following:

where mplat is the mass of the platform, mprop is the mass of propellant and mpayl is the mass of the payload. The total mass of the spacecraft is generally defined as wet mass, while the mass of the spacecraft without propellant is the dry mass. The mass of propellant has to take into account the propellant required for the attitude control and the propellant required for orbital transfer. The propellant mass required for each rocket firing in the orbital correction process is computed with the following equation:

where mi is the initial mass, ∆v is the velocity variation, g is the gravity acceleration and I is the specific impulse that characterizes the type of thruster. In terms of propellant consumption, efficient thrusters are characterized by high values of the specific impulse (e.g. ion thrusters). The Artemis recovery is an example of efficient exploitation of ion thrusters [5]. The total mass of the spacecraft has to be at least equal to the total mass allowed by the launcher for the spacecraft. At the end of the design process, a classification of launch possibilities with respect to orbit, mass and overall cost has to be proposed. Figures 5, 6, 7 show the variation of the perigee altitude zp and the eccentricity e allowed with a propellant mass consumption of respectively 8%, 10% and 12% of the total mass. The computation has been addressed for a circular orbit of release located at an altitude of 1200 km. With respect to a dual spacecraft design for shared launches, a characterization of launch possibilities has been investigated; the first mission concerns the launch of a mini-satellite in LEO circular orbit located at an altitude of 1200 km, while the second mission concerns the launch of a micro-satellite in LEO circular orbit at an altitude of 500 km. Figure 8 shows a set of shared orbits of release where both micro and mini-satellite can be stranded allowing a propellant consumption, for orbital correction, of at most 10% of the wet mass. 7. CONCLUSION In the paper a novel concept for small satellite mission design and launch is proposed. The design methodology is based on the integration among platform design, payload development, choice of the thruster and choice of the launcher. The proposed approach would bring to a feasible deployment of low cost missions, integrating effectively launch schedules and budgets of other missions. REFERENCES [1] Small Satellite Missions, background paper #9, Third United Nations Conference on the Exploration and Peaceful Uses of Outer Space (UNISPACE-III), Vienna, Austria, 19-30 July 1999. [2] T. Mosher, M. Barrera, N. Lao, Integration of Small Satellite Cost and Design Models for Improved Conceptual Design-to-Cost, Eight Annual International Symposium of the International Council on Systems Engineering, Vancouver, Canada, July 26-30-1998. [3] P. Gloyer, T. Robinson, A. Mignogna, Y. Ahmad, Aerobraking to Lower Apogee in Earth Orbit with the Small Payload ORbit Transfer (SPORT™) Microsatellite Vehicle ,

)1(paylpropplattot mmmm ++=

)2()1( / gIvic emm ∆−−=

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The 14th Annual AIAA/Utah State University Conference on Small Satellites, 1998. [4] G. Maral, M. Bousquet, Satellite Communications Systems: Systems, Techniques and Technology, 4th Edition, John Wiley & Sons, 2002. [5] M. Ruggieri, G. Galati, The Space Systems Technical Panel, IEEE Aerospace and Electronic Systems Magazine, vol. 17, no. 9, pp. 3-11, Sept. 2002.

BIOGRAPHY

Mauro De Sanctis received the “Laurea” degree in Telecom-munications Engineering from the University of Roma “Tor Vergata” in 2002. He is currently a Ph.D. student of the Department of Electrical Engineering in the same University. He worked extensively on the development of a network simulator for LEO satellite networks. His main areas of interest are internetworking and resource management in satellite system. Marina Ruggieri graduated cum laude in Electronics Engineering in 1984 at the University of Roma La Sapienza. She was with FACE-ITT and at GTC-ITT (Roanoke, VA) (1985-1986). She was Research and Teaching Assistant at the University of Roma Tor Vergata (1986-1991), Associate Professor at the University of L'Aquila (1991-1994) and Roma Tor Vergata (1994-2000). Since November 2000 she is Full Professor in Telecommunications at the University of Roma Tor Vergata. She has participated to International Committees for Professor Chair, Ph.D and Master degrees (Lund-Sweden, Delft-The Netherlands, Toulouse-France, Trondheim-Norway, Aalborg-Denmark). In 1999 she has been appointed member of the Board of Governors of the IEEE AES Society (2000-2002) and re-elected for the period 2003-2005. Her research mainly concerns space communications systems (in particular satellites) as well as mobile and multimedia networks. She is the Principal Investigator of the ASI satellite communications mission DAVID and of a MIUR two-year national research program on CDMA integrated mobile systems. She is involved in the organisation of international Conferences/Workshops. She is Editor of the IEEE Transactions on AES for “Space

Systems”. She is member of the Editorial Board of WPC Journal (Kluwer). She was awarded the 1990 Piero Fanti International Prize and she had a nomination for the 1996 Harry M. Mimmo and 2002 Cristoforo Colombo Awards. She is an IEEE Member (S'84-M'85-SM'94) and Chair of the IEEE AES Space Systems Panel. Pietro Salvini received the “Laurea” degree in Mechanical Engineering from the University of Roma “La Sapienza in 1987. He is currently a Full Professor on Machine Design in the Department of Mechanical Engineering in the University of Rome “Tor Vergata”. His main area of interest regards structural analysis of mechanical systems, design optimization, analysis and identification of dynamical systems. He is member of several associations in the field of Mechanics such as ASME, SAE, AIAS and CIFI.

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Figure 5: Allowed perigee altitude and eccentricity variations with 8% of wet mass consumption (I=300 s).

Figure 6: Allowed perigee altitude and eccentricity variations with 10% of wet mass consumption (I=300 s).

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Figure 7: Allowed perigee altitude and eccentricity variations with 12% of wet mass consumption (I=300 s).

Figure 8: Allowed shared orbits with 10% of wet mass consumption for a mini-satellite located at 1200 km and a micro-satellite located at 500 km (I=300 s).