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University of Liege

Faculty of Applied SciencesCivil Electromechanical Aerospace Engineering

Mission Design for the CubeSatOUFTI-1

Supervisor: Professor Pierre Rochus

Author: Stefania Galli

Academic Year 2007-2008

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Space is probably the main symbol of technological progress in the modern

society.

Many daily activities imply the interaction with this environment that only fewjudge able to supply so many resources. Actually, despite to its guise of moder-

nity, the space conquest began many years ago when the planets motion was

studied more in details and the Keplers laws were formulated at the beginning

of XVII century. The climb to the peak was accelerated by one of the most ge-

nial personality of the history of physics, Isaac Newton. Forced to interrupt its

university studies because of an epidemic disease in England, he moved to the

countryside where he began studying the motion of celestial bodies. Quickly he

modeled the celestial mechanics as no one had never done before and he identi-

fied the gravitational force and the expressions of all the possible trajectories that

a body can follow in space. In al l his studies, he used only one hypothesis that

he was not able to justify: the gravitational potential of a point is equal to that

of a sphere having the same mass and uniformly distributed density. Because

of that, he left behind for many years one of the most important results of the

history of physics.

All around the world only few people are able to design space missions. The

few lucky who can, every time they do it, use as starting point the results of an

university student lived 400 years ago.

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Abstract

OUFTI-1 is the first satellite of the University of Liege, Belgium, and the firstnanosatellite ever made in Belgium. It is developed within the framework of along-term program called LEODIUM Project, whose goal is to provide hands-on experience to aerospace students in cooperation with the space industriesof the region of Liege. It is the first satellite ever equipped with a recentlydeveloped amateur radio digital-communication technology: the D-STAR pro-tocol. This system represents both the satellites communication system andits payload. The mission target is in fact, on the one hand, to give a spacerepeater to the amateur radio community and, on the other hand, to test this

new technology into space in order to use it on the future nanosatellites foreseenby the LEODIUM Project, satellites that will have different payloads. It will behopefully launched with the new European launcher Vega and placed in ellipticorbit around the earth.

Keywords: OUFTI-1, CubeSat, LEODIUM, D-STAR, amateur radio.

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CONTENTS

1 Introduction 13

2 The LEODIUM Project 15

3 The Flight Opportunity 17

4 The CubeSat OUFTI-1 194.1 The CubeSat concept . . . . . . . . . . . . . . . . . . . . . . . . 20

4.1.1 Amateur Radio and D-STAR system . . . . . . . . . . . 22

5 Mission Analysis 255.1 The Vega Launcher . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.1.1 Typical Mission Profile . . . . . . . . . . . . . . . . . . . 27

5.1.2 Performances . . . . . . . . . . . . . . . . . . . . . . . . 285.1.3 Launch Campaign . . . . . . . . . . . . . . . . . . . . . 285.1.4 The Vega Maiden Flight . . . . . . . . . . . . . . . . . . 32

5.2 The orbit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335.2.1 Orbital mechanics . . . . . . . . . . . . . . . . . . . . . . 335.2.2 The orbit of OUFTI-1 . . . . . . . . . . . . . . . . . . . 37

5.3 Orbit perturbations . . . . . . . . . . . . . . . . . . . . . . . . . 405.3.1 The earths oblateness . . . . . . . . . . . . . . . . . . . 405.3.2 The atmospheric drag . . . . . . . . . . . . . . . . . . . 415.3.3 The solar radiation pressure . . . . . . . . . . . . . . . . 43

5.3.4 Orbital parameters variation . . . . . . . . . . . . . . . . 445.4 The launch window . . . . . . . . . . . . . . . . . . . . . . . . . 505.5 Earth coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . 505.6 Communication time . . . . . . . . . . . . . . . . . . . . . . . . 525.7 The radiation environment . . . . . . . . . . . . . . . . . . . . . 54

6 Structure and deployment 576.1 Pumpkin structure . . . . . . . . . . . . . . . . . . . . . . . . . 586.2 ISIS structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.3 Deployment System . . . . . . . . . . . . . . . . . . . . . . . . . 61

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LIST OF FIGURES

4.1 A typical 1-unit CubeSat structure . . . . . . . . . . . . . . . . 21

5.1 Vega launcher . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.2 Vega typical mission profile: altitude . . . . . . . . . . . . . . . 275.3 Vega typical mission profile: relative speed . . . . . . . . . . . . 275.4 Vega performances: payload mass . . . . . . . . . . . . . . . . . 285.5 Vega: spacecraft preparation and checkout phase . . . . . . . . 295.6 Vega: spacecraft hazardous operations phase . . . . . . . . . . . 305.7 Vega: combined operations phase . . . . . . . . . . . . . . . . . 315.8 Orbital Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 345.9 Eccentric and mean anomalies. . . . . . . . . . . . . . . . . . . 365.10 OUFTI-1 orbit representation for 12 hours orbit(STK) . . . . . 375.11 OUFTI-1: orbits tridimentional view. . . . . . . . . . . . . . . 38

5.12 OUFTI-1 orbit: true, eccentric and mean anomaly . . . . . . . . 395.13 Earth oblateness and not uniform mass effect . . . . . . . . . . 415.14 Aerodynamic drag acceleration for the first day mission. . . . . 425.15 Solar pressure acceleration for the first day mission . . . . . . . 445.16 Orbit variation over a year. . . . . . . . . . . . . . . . . . . . . 455.17 Semi-major axis variation over a year. . . . . . . . . . . . . . . . 455.18 Eccentricity variation over a year. . . . . . . . . . . . . . . . . . 465.19 Perigee and apogee altitude variation over a year. . . . . . . . . 465.20 Inclination variation over a year. . . . . . . . . . . . . . . . . . . 475.21 Right ascension of ascending node variation over a year . . . . . 47

5.22 Argument of perigee variation over a year . . . . . . . . . . . . 485.23 Evolution altitude until the end of life for the elliptic orbit . . . 485.24 Evolution of altitude until the end of life for the circular orbit . 495.25 Field of view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515.26 Worst case for communication . . . . . . . . . . . . . . . . . . . 535.27 Best case for communication . . . . . . . . . . . . . . . . . . . . 535.28 Radiation dose for the OUFTI-1 elliptical orbit . . . . . . . . . 555.29 Radiation dose for the OUFTI-1 circular orbit . . . . . . . . . . 55

6.1 CubeSat-Kit structure skeletonized and solid-walls . . . . . . . . 58

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6.2 ISIS structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.3 P-POD: deployment system for three CubeSats . . . . . . . . . 62

7.1 Example of OUFTI-1 configuration . . . . . . . . . . . . . . . . 647.2 Gravity gradient couple in case of non updated configuration . . 687.3 Aerodynamic couple in case of non updated configuration . . . . 697.4 Gravity gradient couple in case of updated configuration . . . . 707.5 Gravity gradient couple in case of updated configuration . . . . 70

8.1 Reference sistems . . . . . . . . . . . . . . . . . . . . . . . . . . 748.2 Sun rays direction on the ecliptic plane . . . . . . . . . . . . . . 758.3 Sun rays direction projected on the orbit plane. . . . . . . . . . 768.4 Eclipse duration as a function of earth anomaly . . . . . . . . . 77

8.5 Total power produced: simulation over one year orbit. . . . . . . 808.6 Integrated power: simulation over one year orbit . . . . . . . . . 808.7 Total power and integrated power for the orbital parameters after

one year mission . . . . . . . . . . . . . . . . . . . . . . . . . . . 818.8 Total power and integrated power for the circular orbit with =

0 and = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 828.9 Total power and integrated power for = 90 and = 0 . . . . 838.10 Total power and integrated power for = 0 and = 90 . . . . 838.11 Total power and integrated power for = 90 and = 90 . . . 83

9.1 Nodes model for thermal analysis . . . . . . . . . . . . . . . . . 89

9.2 Equilibrium for radiative heat exchange . . . . . . . . . . . . . . 909.3 Radiative equivalent resistance . . . . . . . . . . . . . . . . . . . 919.4 Typical Thermal Excel layout: operating case whit black coating 94

10.1 Communication system block diagram . . . . . . . . . . . . . . 9810.2 Detailed link budget for the satellite at the apogee, 5 elevation 10210.3 Downlink link budget . . . . . . . . . . . . . . . . . . . . . . . . 103

11.1 Qualification level test for sinus vibrations . . . . . . . . . . . . 10811.2 Qualification level for random vibrations . . . . . . . . . . . . . 10911.3 Shock Response Spectrum . . . . . . . . . . . . . . . . . . . . . 109

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LIST OF TABLES

5.1 Comparison between the two possible orbits . . . . . . . . . . . 39

6.1 CubeSat Kit mass . . . . . . . . . . . . . . . . . . . . . . . . . . 59

6.2 ISIS structure mass . . . . . . . . . . . . . . . . . . . . . . . . . 60

8.1 Solar cells mechanical properties . . . . . . . . . . . . . . . . . . 788.2 Solar cells electrical and thermal properties . . . . . . . . . . . . 788.3 Elliptic orbit with orbital parameters after one year . . . . . . . 818.4 Operating modes . . . . . . . . . . . . . . . . . . . . . . . . . . 84

9.1 Surface thermal properties . . . . . . . . . . . . . . . . . . . . . 879.2 Equilibrium temperatures . . . . . . . . . . . . . . . . . . . . . 879.3 Structure properties . . . . . . . . . . . . . . . . . . . . . . . . . 929.4 Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

10.1 Communication system parameters . . . . . . . . . . . . . . . . 10110.2 Link budget at 1200 Km altitude, 5 elevation . . . . . . . . . . 101

11.1 Thermal vacuum qualification test for the PFM. . . . . . . . . . 11011.2 Thermal cycling qualification test . . . . . . . . . . . . . . . . . 110

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CHAPTER

1

INTRODUCTION

This work represents the feasibility study for the CubeSat OUFTI-1, the firststep of the LEODIUM Pro ject of the University of Liege, Belgium.The goals of the project are soon introduced, as well as an explanation of theOUFTI-1 mission, including the concepts of CubeSat and amateur radio. Thena description of all the satellite subsystems is treated, with the attention concen-

trated on the mission analysis. For each subsystem an analysis of the operationalconditions is carried out and the foreseen solutions are presented.We start with the mission analysis as it is the subsystem that mainly influencesall the others. We pass then to the structure and deployment system, that arecommercial off-the-shelf elements, and to the attitude control system, which isthe most controversial subsystem for the OUFTI-1 satellite project. Then astudy on the power produced in orbit is carried out to determine if we haveenough power to supply our satellite. Afterward the thermal system is intro-duced and the solutions to control the satellite temperature are presented. Thelast subsystem is the communication system which is especially important asit also represents the CubeSat payload: with a link budget we find out if thesatellite has enough power to communicate with the earth.At the end, the tests philosophy is explained and a choice of possible payloadsfor the future missions of LEODIUM Project is introduced.

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CHAPTER

2

THE LEODIUM PROJECT

The LEODIUM Project is a project involving the University of Liege and LiegeEspace, a consortium of space industries and research centers in the Liege regionwith the goal of increase the cooperation between the members and to promotethe space activity.LEODIUM is the Latin name of Liege and stands for Lancement En Orbite

de Demonstations Innovantes dune Universite Multidisciplinaire(Launch intoOrbit of Innovative Demonstrations of a Multidisciplinary University). Theproject started in 2005 when Mr. Pierre Rochus, president of Liege Espace andDeputy General Manager for Space Instrumentation of the Liege Space Center,was charged with the training of students to the design of miniaturized satellites.Some possible scenarios to involve students in the design of a space mission wereforeseen and each one had its advantages and drawbacks:

Design of a CubeSat or of a Nanosatellite: quick and relatively simple butwith a scientific payload not really efficient due to the low mass and poweravailable.

Design of a Microsatellite: very interesting on the scientific point of viewbut requiring much more time and economical resources.

Participation to the design of a space instrument among a professionalteam: interesting mission but less possibility to actively participate.

The project started with the participation in the Student Space Exploration andTechnology Initiative (SSETI) of the European Space Agency: the Universityof Liege took part in the European Student Earth Orbiter (ESEO) designing

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3

THE FLIGHT OPPORTUNITY

The Education Office of the European Space Agency (ESA), in cooperationwith the Directorate of Legal Affairs and External Relations and the Vega Pro-gramme Office in the Directorate of Launchers, issued a first AnnouncementOpportunity on 9 October 2007 offering a free launch on the Vega maiden flightfor six CubeSats. In the meantime, the Vega Maiden Flight CubeSat Workshop

was held at the European Space Research and Technology Center (ESTEC): theUniversity of Liege participated presenting the LEODIUM Project [RD1]. On15 February 2008, the ESA published a call for proposal for CubeSat on-boardof Vega [RD2] and on 17 mars 2008 the proposal was submitted to the ESA[RD3].Up to know, we are still waiting for an hopefully positive answer.

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CHAPTER 4

4.1 The CubeSat concept

During the last years, a complex process is taking place in the space industry: onthe one hand, there is a growing tendency for satellite to become larger, on theother hand, many miniaturized satellites are designed. In fact, from the hugespacecraft of Hubble Space Telescope launched in 1990 which weighed morethan 11 tons, there is an actual trend to reduce at most the size of the satellite:this reduces not only the costs connected to the launch but also those directlyimplied in the design and construction of the spacecraft. The miniaturizedsatellite can be classified according to their wet mass (including fuel) :

Minisatellite: wet mass between 100 Kg and 500 Kg. They are usuallysimple but they use the same technology as the bigger satellites and they

are often equipped with rockets for propulsion and attitude control.

Microsatellite: wet mass between 10 Kg and 100 Kg. The miniaturizationprocess begins to be important but sometimes they still use some kind ofpropulsion.

Nanosatellite: wet mass between 1 Kg and 10 Kg. Every component hasto be reduced in terms of mass and volume and no kind of propulsion isusually foreseen. They can be launched piggyback, using excess capabil-ity on larger launch vehicle.

Picosatellite: wet mass between 0.1 Kg et 1 Kg. The miniaturizationprocess is maximum and many new technologies have to be used in orderto accomplish the requirements. They are launched piggyback with somepeculiar deployment system.

These miniaturized satellites go toward many technical challenges, especiallyconcerning the attitude control and the electronic equipment, including thecommunication system: they need indeed to use more up-to-date technology,which often needs to be carefully tested and modified in order to be space hard-ened and resistant to the outer space environment.

The CubeSat design is an example of a Picosatellite with dimensions of10x10x10 cm and typically using commercial off-the-shelf electronic compo-nents. The concept was originally developed by the California Polytechnic StateUniversity and by the Stanford University, with Professor Robert Twiggs, andafterward it widely circulates among the academic world . At the moment, over60 University, high schools and industries are involved in the development ofCubeSats. Some of them are designing double and triple CubeSats: they can fitin the traditional deployment system but they can have more mass and volume.As a matter of fact, a CubeSat represents the best way to give some experience

Galli Stefania 20 University of Liege

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CHAPTER 4. THE CUBESAT OUFTI-1

Figure 4.1: A typical 1-unit CubeSat structure

to students during their education: it can fit into the universitys budget and itcan be designed, tested and launched in two year, allowing student to partici-pate to all the missions phases.Until some years ago, the most complex achievement for a CubeSat was to ob-tain a launch as the providers were often distrustful of a small satellite designedby students which was launched inside the same fairing as a much more ex-pensive mission and which risked to damage the main satellite. More recently,thanks to the great success of CubeSat project among the universities all aroundthe world, some safe interfaces for CubeSats have been developed and the launch

providers are definitely favorable to use the free space to set into orbit this kindof Picosatellite. In fact, all the main launchers dispose now of a special interfacefor the piggyback launches. In order to fit into the deployment system and toguarantee the preservation not only of the main satellite but also of the otherCubeSat, the structure has to fulfills many requirements as explained in [AD4].The key requirement for a CubeSat are here summarized:

its dimensions must be 10x10x10 cm it may not exceed 1 Kg mass

its center of mass must be within 2 cm of its geometric center the CubeSat must not present any danger to neighboring CubeSats, to the

launch vehicle or to the primary payload: all parts must remain attachedduring launch, ejection and operation and no pyrotechnics are allowed

whenever possible, the use of NASA or ESA approved material is recom-mended: this allow a reduction of out-gassing and contamination.

rails have to be anodized to prevent cold-welding and provide electricalisolation between the CubeSat and the deployment system. They also


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have to be smooth and their edges rounded

the use of Aluminium 7075 or 6061-T6 is suggested for the main structure.If others materials are used, the thermal expansion must be similar to thatof the deployment system material (Aluminium 7075-T73) and approved.This prevents the CubeSat to conk out because of an excessive thermaldilatation.

no electronic device may be active during launch. Rechargeable batterieshave to be discharged or the CubeSat must be fully deactivated

at least one deployment switch is required

antennas can be deployed only 15 minutes after ejection into orbit whilebooms and solar panels after 30 minutes it has to undergo qualification and acceptance testing according to the

specifications of the launcher: at least random vibration testing at a levelhigher than the published launch vehicle envelope and thermal vacuumtesting. Each CubeSat has to survive qualification testing for the specificlauncher. Acceptance testing will also be performed after the integrationinto the deployment system.

4.1.1 Amateur Radio and D-STAR systemBefore proceeding with the description of OUFTI-1, a brief introduction of thesatellites payload, represented by its communications system, is necessary.D-STAR, which stands for Digital Smart Technology for Amateur Radio, isan open ham radio protocol recently developed by the Japan Amateur RadioLeague (JARL). Its main features are the simultaneous transmission of voiceand data, the complete routing capacity (including roaming), the cross-bandcapability and the possibility of passing through the internet.It works over three possible frequencies and data rates:

144 MHz ( 2m, VHF ), 4.8 Kbit/s

440 MHz ( 70 cm, UHF ), 4.8 Kbit/s 1.2 GHz ( 23 cm, SHF ), 4.8 Kbit/s or 128 Kbit/s

Presently, in Europe only the first two frequencies are available.The D-STAR technology is in fact really developed in the United States, wheremany repeaters are operational, but its quickly extending in Europe: the firstrepeater in Belgium is at the University of Liege and it has been installed withinthe OUFTI-1 project.


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CHAPTER 4. THE CUBESAT OUFTI-1

The idea of using a satellite for amateur radio communication is not new: thefirst ham radio satellite OSCAR-1 has been launched in 1961 and OSCAR-7,

launched in 1974, is still operational. Many satellites for radio amateurs arein low earth orbit and guarantee the communications all around the world:even on the International Space Station (ISS) there is a amateur radio stationand a new one has been recently added on the Columbus module. The reasonis simple: in normal atmospheric conditions the zone of visibility of a radiorepeater is around 50 Km, while the footprint of a satellite is much wider (orderof thousands Km): a satellite allows in this way the communication between twousers far away from each other and, even more important, it offers a repeaterto those who are to far away from any ground repeaters to have a traditionalair link.

As a drawback, both the two users have to be in the satellite footprint and thetime for communicate could be short.During the last months, OUFTI-1 has been presented to the amateur radiocommunity and to other CubeSats developers [RD4] and it has been greetedenthusiastically.


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CHAPTER

5

MISSION ANALYSIS

The mission analysis is the process of quantifying the system parameters andthe resulting performance: its main goal is to analyse whether the mission meetsthe requirements or not.The first step is therefore to define the mission requirements. In this case, due tothe absence of a scientific payload, the only real requirement is to guarantee to

the amateur radio operators a sufficient communication time with a convenientquality. Being the amateur radio operators common all around the world, wechose as main criteria a passing time over Belgium as longer as possible: thisfavor the Belgian amateur radio operators, which seems logical as the CubeSatis Belgian, but guarantees also a sufficient passing time of the spacecraft in viewof the ground station in Liege. Concerning the lifetime, the goal is to ensureenough operating time to successfully test the D-STAR system but, also in thiscase, we are not able to quantify it.The reason of this lack of mission requirements is simple: on the one hand,the ESA offers free launch on board the Vega launcher but it imposes the orbit

and, on the other hand, a CubeSat needs to meet some requirements in termsof mass, size, shape and pyrotechnics.We cannot therefore neither choose an orbit that guarantees a longer lifetimeand a sufficient passing time over Belgium, nor add any kind of propulsion, noradopt any peculiar shape of the structure. The only thing that we can do, isto use the available mass and size as good as possible, in order to screen thesensible equipments from the radiation, and to choose omnidirectional antennasto communicate as long as possible with the small amount of power producedin orbit.

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CHAPTER 5

5.1 The Vega Launcher

Vega, Vettore Europeo di Generazione Avanzata, is the new European smalllauncher. It has been designed as a single body launcher with three solidpropulsion stages and an additional liquid propulsion restartable upper mod-ule, AVUM, used for attitude and orbit control and for satellite release. Unlikemost small launchers, Vega will be able to place multiple payloads into orbit.Its development started in 1998 and the first flight was initially expected in2007 from the Guyana Space Center, CSG, but different reasons causes somedelays and, up to know, it is scheduled for the December 2008.It is funded by Belgium, France, Italy, Spain, Sweden, Switzerland and TheNetherlands.

Vega is 30 m high, has a maximum diameter of 3 m and weights 137 tons atlift-off. As shown in fig.5.1, it has three sections: the Lower Composite, theUpper Composite known as AVUM and the Payload Composite.

Figure 5.1: Vega launcher


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CHAPTER 5. MISSION ANALYSIS

5.1.1 Typical Mission Profile

A typical mission profile consists of three phases: Phase I: Ascent of the first three stages of the launch vehicle into the low

elliptic trajectory (sub-orbital profile)

Phase II: Payload and upper stage transfer to the initial parking orbitby first AVUM burn, orbital passive flight and orbital manoeuvres of theAVUM stage for payload delivery to final orbit

Phase III: AVUM deorbitation or orbit disposal manoeuvres.

Figure 5.2: Vega typical mission profile: altitude as a function of time after liftoff.

Figure 5.3: Vega typical mission profile: relative speed as a function of timeafter lift off.


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CHAPTER 5

Typically, the AVUM burns three times: the first to place the satellite andhimself into an elliptical orbit with the apogee at the target altitude, the second

to raise the perigee to the required value or for orbit circularization and thethird for deorbiting himself. Jettisoning of the payload fairing can take place atdifferent times, depending on the aero-thermal flux requirements on the payload,but normally it happens between 200 and 260 seconds from lift-off.

5.1.2 Performances

Vega is designed to launch a wide range of missions and payload configuration:in particular, it can place in to orbit masses ranging from 300 to 2500 Kg intoa variety of orbit, from equatorial, to sun synchronous and polar. Its perfor-

mances are shown in figure 5.4.

Figure 5.4: Vega performances: payload mass as a function of orbit inclinationand altitude required.

Vega can also operate the launch of multiple payloads.

5.1.3 Launch Campaign

The spacecraft launch campaign formally begins with the delivery in CSG of thespacecraft and its associated Ground Support Equipments (GSE), and concludeswith GSE shipment after launch. It cannot exceed 30 days: 27 days beforelaunch and 3 days after it.A typical launch campaign can be divided in three parts:

1. Spacecraft autonomous preparationIt includes all the operations conducted from the spacecraft arrival to theCSG up to the readiness for integration with the launch vehicle.


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It can be divided in two parts: the spacecraft preparation and checkout in-cluding the assembly and functional test, the verification of the interface

with the launch vehicle and the battery charging (fig. 5.5) and the space-craft hazardous operations including the filling of satellites tanks withfuels (fig. 5.6).

Figure 5.5: Vega: spacecraft preparation and checkout phase


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Figure 5.6: Vega: spacecraft hazardous operations phase

2. Combined operationsIt includes the spacecraft integration on the adapter and installation insidethe fairing, the verification procedures and the transfer to the launch pad.


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Figure 5.7: Vega: combined operations phase

3. Launch countdownIt covers the last launch preparation sequence up to the lift-off.


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CHAPTER 5

5.1.4 The Vega Maiden Flight

The Vega maiden flight is targeted officially targeted for December 2008: theprimary scientific payload is the LAser RElativity Satellite (LARES). Its anitalian satellite, designed by the Italian Space Agency (ASI) in cooperation withthe University of Rome testing a prediction following from the Einsteins theoryof General Relativity, the so-called frame-dragging or Lense-Thirring effect.Its basically a solid sphere maid of Tungsten with a diameter of 376 mm anda mass of 400 Kg. The surface is covered by 92 Corner Cube Reflectors (CCR)which, hit by laser beams sent from earth, will reflect them allowing an accurateorbit determination. Correcting for a number of effects, most importantly thedeviation of the earth gravitational field from an ideal sphere, yields the frame-dragging effect. To achieve its scientific objectives, LARES needs to be injected

into a circular orbit at 1200 Km altitude with an inclination of 71.Furthermore, an adaptation of the Upper Composite test dummy used duringmechanical test campaign will be the main passenger on the Vega maiden flight:it will measure the actual launch loads experienced by a typical payload in orderto correlate them with the numerical models used during the launchers designphase.Besides, an educational payload of six CubeSat, placed into two PicosatelliteOrbital Deployers (POD), will be accommodated into the fairing. They willbe released in a 1200x350 Km elliptical orbit thanks to the AVUM multi-burnfacility. A manoeuvre into a circular orbit at 350 Km altitude is also under

study. Both these two orbit guarantees a lifetime much less than 25 years,compliant with the international requirement related to space debris.


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- The squares of the orbital period of planets are directly proportional tothe cube of the semi-major axes of their orbit.

The same laws can be applied to the motion of a satellite around a planet.In orbital mechanics, the spacecraft and the central body are considered aspoints with mass but without dimensions. As to describe the position and thespeed of a point in a tridimensional space we need six parameters, to completelycharacterize the motion of the satellite over an orbit we need the six so-calledorbital elements: the semi-major axis a, the eccentricity e, the true anomaly or , the inclination i, the longitude or right ascension of ascending node or RAAN and the argument of perigee . As shown in fig.5.8, the firsttwo describe the orbit shape and the last three the position of the orbit plane

respect to the earth. The true anomaly, sometimes substituted by the time sinceperigee passage, introduces the position of the satellite on the orbit starting fromthe perigee: ita the only parameter that varies along the orbit as long as wemaintain the hypothesis of ideal motion.

Figure 5.8: Orbital Parameters

The motion is in fact considered to be ideal and determined only by the

gravity force between the masses and the fictitious centrifugal force, withoutany perturbation as the aerodynamic drag and the presence of others bodies.Starting from the Newtons laws and from the gravitational laws, we can de-fines the orbital elements and some other parameters that can be useful for thecontinuation.

We place ourself on the orbit plane and we call rp and ra the radius respec-tively of perigee and apogee and the earth gravitational constant. We definethen the following parameters that remain constant:


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the semi-major axis:

a=rp+ ra

2 (5.1)

the eccentricity:

e=ra rpra+ rp

(5.2)

the angular momentum and its magnitude:

h= r v h= |h| =rvcos() (5.3)wherer is the radius, v the speed and the flight angle.

the orbit parameter which represents the radius of the circular orbit havingthe same angular momentum:

p= a

1 e2 = h2

=rc (5.4)

the speed on the circular orbit having the same angular momentum:vc=

h (5.5)

the energy

E= 2a

=v2

2

r (5.6)

wherev and r are the magnitude of speed and the radius.

the period

T = 2

a3

(5.7)

Introducing the true anomaly we can identify the radius on each orbitpoint:

r= p

1 + ecos() (5.8)


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Hence, the perigee and apogee radius can be expressed as:

rp=r (= 0) = p1 + e

=a (1 e) (5.9)

rp = r (= ) = p

1 e =a (1 + e) (5.10)

We would also like to find a connection between the time and the true anom-aly in order to know the necessary time to go from a point to another: if this isextremely simple for a circular orbit where the speed is constant, for an ellipticorbit its a bit more complicate.

To solve this, Kepler introduced the quantity M, called mean anomaly, whichrepresents the fraction of an orbit period which has elapsed since perigee, ex-pressed as an angle:

MM0 = n (t t0) (5.11)where n, called mean motion, is the average angular velocity.But this method gives only an average position and velocity. To have a moreprecise value, we need to define the eccentric anomaly E. Shown in fig.5.9,its the angle between the direction of perigee and the current position of thesatellite projected onto the ellipses circumscribing circle perpendicularly to the

major axis, measured at the center of the ellipse.

Figure 5.9: Eccentric and mean anomalies.

It can be connected to the true anomaly with the relation:

tan

2

=

1 + e

1 etan

E

2

(5.12)

Once the eccentric anomaly is know, the time comes from the following timelaw:


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Figure 5.11: OUFTI-1: orbits tridimentional view. Optimum case: the sub-satellite point at apogee is at the same latitude as Liege.

Given a perigee of 350 Km and an apogee of 1200 Km altitude, we calculatedall the above mentioned parameters:

semi-major axis: a= 7153.14Km eccentricity: e= 0.0594

angular momentum: h= 5.33

104 Km

2

s

orbit parameter: p= 7127.7Km energy: E= 27.8Km2

s2

period: T= 6020.8s= 100.35min perigee speed: vp = 7.922Kms apogee speed: va = 7.034Kms

mean motion: n= 14.35 rev

day


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5.3 Orbit perturbations

The Keplerian orbit, considering only the earth gravitational force and thesatellite fictitious centrifugal force, provides an excellent reference but, for amore accurate study, we need to take into account some minor effects thatmake deviate the nominal orbit.We classify these variations of orbital elements in three main categories:

the secular variations: they are a linear variation of the element. Theireffect cumulates in time and therefore they are the cause of changing shapeand orientation of the orbit.

the long-period variations: they are those with a period greater than theorbital period.

theshort-period variations: they have a period less than the orbital period.They can usually be neglected.

In the sequel, three main effects will be considered: the earths oblateness, theatmospheric drag and the solar radiation pressure.

5.3.1 The earths oblateness

The gravitational potential in the Keplerian theory corresponds to that of an

uniform sphere or, equivalently, to that of a punctual mass:

V = r

(5.14)

Unluckily, the earth isnt a perfect sphere and its mass isnt uniformly dis-tributed: therefore some secondary effects are produced. To take them intoaccount, a more accurate model is necessary. We introduce, besides the radialcoordinate r representing the distance from the center of the earth, the lati-tude and the longitude . The complete expression of the earth gavitationalpotential becomes:

V(r,,) =

r

1

n=2

Re

r

n

JnPnsin () +n

m=1

Re

r

n

(Cnmcos (m)Smnsin (m))Pnmsin ()

The coefficientCnm etSnmare constant while Pnmsin () are the associatedLegendre functions.The gravitational potential can be so expressed as a sum of infinite terms thatcan be classified into three groups (fig.5.13):

ifm = 0 the potential depends only on the latitude. This effect, calledzonal harmonics, takes into account the earth oblateness. Often we callsCm0 = Jm.


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if m = n the potential depends only on longitude. This effect, calledsectorial harmonics, is used to consider the difference in density between

the oceans and the continents. They are also called Cmm= Jmm

ifm =n and m = 0 the potential depends both on latitude and longitude.This effect, called tesseral harmonics, is used to take into account greatmass concentration (Ex. the Himalaya).

Figure 5.13: Earth oblateness and not uniform mass effect: zonal harmonics(left), sectorial harmonics (middle) and tesseral harmonics (right)

The most important effect is theJ2: all the others are usually neglected withthe exception of the J22effect that needs to be considered for geostationary orbit.

In OUFTI-1 case, the only harmonic considered is J2: its principal effectsare the secular motions of the ascending node and of the perigee.The motion of the ascending node and therefore the variation of its right ascen-sion occurs because of the added attraction of earths equatorial bulge, whichintroduces a force components toward the equator. The resultant accelerationcauses the satellite to reach the equator before the crossing point for a sphericalearth. The secular nodal variation of can be numerically evaluated with theformula:

=9.9639(1 e2)2

Rea

35

cos(i) deg

day (5.15)

The secular motion of perigee occurs because the force is no longer propor-

tional to the inverse square radius and the orbit is consequently no longer aclosed ellipse. It can be expressed as:

=9.9639(1 e2)2

Rea

35

2 5

2sin2 (i)

deg

day (5.16)

5.3.2 The atmospheric drag

For low earth orbit, the effect of the residual atmosphere is often the mainperturbation. Drag acts in the opposite direction of the velocity vector and


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removes energy from the orbit. As a consequence, the semi-major axis is reducedand the orbit leans towards becoming circular. In case of elliptic orbit, the drag

acts mainly at the perigee but its effect is a reduction in altitude of the apogee.It generates therefore a force and the acceleration tangent to the orbit trajectory:

D= 12

v2ScD

m

m

s2 (5.17)

where is the atmosphere density, v the speed with respect to the at-mosphere, S the satellite cross-sectional area, cD the drag coefficient and mthe mass. The term m

cDA is called ballistic coefficientand is often considered

constant for a satellite. For small satellites this coefficient is small and there-

fore the acceleration is bigger: the situation is therefor particularly critical fornanosatellites.Drag cause a variation of the semi-major axis and of the eccentricity. It hasalso an effect on the argument of perigee but unimportant with respect to theeffect of the earth oblateness.For our simulation we consider the cross-sectional area as the surface of a cubeface and cD = 2.2.The atmosphere density varies depending on the solar activity which has a cycleof 11 years: as the solar minimum is happened in 2006, we used a mean densityvalue.

Figure 5.14: Aerodynamic drag acceleration for the first day mission.


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5.3.3 The solar radiation pressure

Solar radiation pressure generates a force in all the direction and varies as afunction of sun, earth and satellite position. It makes vary periodically all theorbital elements and its especially intense for small satellites at high altitude:it needs to be considered for the OUFTI-1 orbit.The following formulas are an approximation of the solar pressure accelerationeffect averaging the eclipses and the sunlight.The perturbing acceleration of an earth satellite can be computed by means ofthe following equation:

asum= 0.97 107g (1 + R) SW

(5.18)

where R [1, 1] is the optical reflection constant (-1 if transparent body, 0 ifblackbody, 1 if mirror),g the gravitation acceleration at sea level, Sthe effectivesatellite projected area and Wthe total weight.We used R=0.6 to take into account the solar cells and the thermal coating:this value is probably elevated but, not having precise details on the surfaces,we preferred to overestimate the perturbing force.Anyway, the solar perturbing force is much smaller than the atmospheric drag.

The direction ofasunis perpendicular to the effective area and its normalizedcomponents along the satellite orbit radius vector, perpendicular to it in theorbit plane and along the orbit normal are:

Fr,sun = cos2

i

2

cos

2

2

cos ( )

sin2i

2

sin

2

2

cos ( + )

12sin (i) sin () [cos ( ) cos ( )]

sin2i

2

cos

2

2

cos ( + )

cos2i

2 sin2

2 cos ( ) m

s2

F,sun= cos2

i

2

cos

2

2

sin ( )

sin2i

2

sin

2

2

sin ( + )

12sin (i) sin () [sin ( ) sin ( )]

sin2i

2

cos

2

2

sin ( + )

cos2i

2

sin

2

2

sin ( ) m

s2

(5.19)


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F,sun= sin (i) cos2

2

sin ( ) sin (i) sin2

2

sin (+ )

cos (i) sin () sin ()

m

s2

where:

d= M JD 150195.5epsilon= 23.44

M= 358.48 + 0.98560027d

= 279.70 + 0.9856473d+ 1.92sin(M)

MJD is the Modified Julian Date: Julian Date - 2400000.5.As shown in figure 5.15 this acceleration is much less intense than the one caused

by the aerodynamic drag.

Figure 5.15: Solar pressure acceleration for the first day mission

5.3.4 Orbital parameters variationThe acceleration obtained above for the solar pressure and the atmosphere dragcan be used the quantify the variation of orbital elements:

a= 2a2

vft

e= 2v(e+ cos ()) ft ravsin () fn

i= rh

cos () f

e= 2sin()v

ft+

2e+ ra

sin ()

1v

fn ecos (i)sin (i) = r

hsin () f

(5.20)


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where = . ft, fn, f are the acceleration respectively tangent andnormal to the orbit in the orbital plane and normal to the orbital plane.

This acceleration are the integrated in order to have the parameters variation.The effect of earths oblateness on and is calculated and directly added.The results for the OUFTI-1 orbit over one year obtained with Matlab and withSTK are here presented:

Figure 5.16: Orbit variation over a year.

Figure 5.17: Semi-major axis variation over a year.


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Figure 5.18: Eccentricity variation over a year.

Figure 5.19: Perigee and apogee altitude variation over a year.


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Figure 5.20: Inclination variation over a year.

Figure 5.21: Right ascension of ascending node variation over a year


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Figure 5.22: Argument of perigee variation over a year

The Matlab results fit almost perfectly to those of STK: the small differenceprobably comes from the fact that the density model of STK is more accuratethan the one developed for the Matlab routine.As the apogee altitude strongly decreases, we would like to know when OUFTI-1will definitely enter the atmosphere ending its life. In order to study the end of

life, we have used the software STK: it estimate a lifetime of 4.2 years or 22915orbits. The evolution of the altitude of perigee and apogee are represented infigure 5.23

Figure 5.23: Evolution of perigee and apogee altitude until the end of life forthe elliptic orbit


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A four year lifetime is probably much more than operating lifetime of ourD-STAR payload. In fact, as explained in paragraph 5.7, the radiation envi-

ronment in the foreseen orbit is pretty hard and we still do not know neitherthe total radiation dose that can be tolerated nor the frequency of Single EventPhenomena (SEP) in that orbit for a given electronic part.Concerning the circular orbit at 350 Km altitude, the lifetime with the sameconditions (cD = 2.2 and cross-sectional area equivalent to a faces surface) wehave a lifetime of 54 days (867 orbits) and the evolution of the perigee andapogee altitude is represented in figure 5.24

Figure 5.24: Evolution of perigee and apogee altitude until the end of life forthe circular orbit


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5.4 The launch window

The launch window represents the time gap useful to place the satellite in apredetermined orbit from a specific launch site. As the orbital plane is fixed inthe inertial space, the exact launch instant is the time when the launch site onthe surface of the earth rotates through the orbital plane.The launch is possible only if the latitude of the launch site is smaller than theorbit inclination or equal to it: here comes the importance of having a spaceportas near as possible to the equatorial line.The time to launch depends on the right ascension of ascending node and onthe inclination required.In the OUFTI-1 case, as it will be secondary payload on the launcher, we cannotchoose any of these parameters and therefore we cannot determine the launchwindows.

5.5 Earth coverage

Earth coverage refers to the surface that a spacecraft instrument or antenna cansee at one instant or over an extended period. The leading parameters are thecovered area and the rate at which new land comes into view as the spacecraftmoves. We can so identify four key parameters:

Footprint Areaalso called instantaneous Field Of View area(FOV): areathat an instrument can see at any instant

Instantaneous Access Area(IAA): all the area that an instrument couldpotentially see at any instant if it were scanned through its normal rangeof orientations

Area Coverage Rate (ACR): the rate at which the instrument is sensingor accessing new land

Area Access Rate(AAR): the rate at which new land is coming into thespacecrafts access area

For an omnidirectional antenna, the footprint corresponds to the access area,as well the coverage rate to the access rate: for OUFTI-1 we need therefore tocalculate only two parameters.We consider a minimal elevation of the spacecraft over the horizon of = 5 andwe proceed to the determination of the field of view and of the area coveragerate. The notations are indicated in figure 5.25

The first step is to find out the angle : for a directional antenna or anoptical payload it represents the beam width and is therefore imposed. In caseof omnidirectional antenna, the directivity diagram has an angle with a loss of


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Figure 5.25: Field of view (out of scale)

3dB in gain much bigger than the earth angular radius: we can therefore assumethat all the earth is in the access zone of the antenna. In this case dependsfrom the fact that a point on the earths surface can see the satellite only if itis higher than 5 over the horizon.

2

=asinResin (90 + )Re+ h

= 56.9 (1200Km)70.8 (350Km)

(5.21)

Once is known, can be calculated:

= 180 2 (90 + ) =

28.1 (1200Km)

14.2 (350Km)(5.22)

An approximated formula permits to calculate the footprint length, in thiscase we have the footprint radius:

LFOV2

= 111.319543 =

3128Km (1200Km)

1580Km (3500Km)(5.23)

We would also like to know the footprint area, the area of the spherical cap:

F OV area= 2R2e(1 sin (90 )) =

3.0 107Km2 (1200Km)7.8 106Km2 (350Km) (5.24)


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5.7 The radiation environment

The trajectory of charged particles of solar wind, electrons and protons, is mod-ified by the interaction with the earth magnetic field: they remain trapped intothe so-called radiations belts, or Van-Allen belts. They are two belts where theradiation environment is therefore extremely hard and the spacecrafts passingthrough them needs to be protected. We can in fact identify two different belts:

the inner belt extending approximately between 1,000 and 15,000 Km. Itcontains high concentrations of energetic protons with energies exceeding100 MeV and electrons in the range of hundreds of kiloelectronvolts

the outer belt extending till 50,000 Km. It contains mainly energeticelectrons.

The belts altitude strongly depends also from the solar activity.Anyway OUFTI-1 will have the apogee inside the inner belt and therefore somecares have to be taken. Trapped particles in the radiation bells, as well as solarflare protons and galactic cosmic rays, can cause in fact the so-called SingleEvent Phenomena(SEP) within microelectronic devices. There are three dif-ferent types of SEP: the Single-Event Upset, SEU, the Single-Event Latchup,LEL, and the Single-Event Burnout, SEB. If the first case neither damages thepart nor interferes with its subsequent operation, the second one causes the part

to hang up and to no longer operate until the power to the device is turned offand than back on. The most critical situation is the Single-Event Burnout: inthis case in fact the devices fails permanently.In order to prevent these events, we need to blind somehow the sensible partsbut to do that we need to know the total radiation dose, which represent thesum of the protons, electrons and bremsstrahlung dose produced by the inter-action of electrons with the shielding material.The estimation of the total dose has been done with the software SPENVIS,SPace ENVironment Information System, a software developed by the BelgianInstitute for Space Astronomy and funded by the European Space Agency.

In figure 5.28 the radiation dose as a function of equivalent aluminium shieldingthickness is represented. The unit for the radiation dose is the rad which isthe amount that deposits 100 ergs (6.25 107MeV) per gram of target material.These values have been calculated for the total mission duration with the hy-pothesis of solar maximum: they are therefore higher that the real values. Theanalysis has been done for a finite slab with silicon as target material.

As expected, the radiation dose of protons and electrons is especially intensebut, already with 2 mm of shielding aluminium, it can be greatly reduced.Once the value of total radiation dose that can be tolerated by the electronicsdevices on board and the frequency of Single Event Phenomena (SEP) will be


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Figure 5.28: Radiation dose for the OUFTI-1 elliptical orbit

known, a suitable shielding protection will be added.

The same analysis has been done for the circular orbit at 350 Km altitude.The results are represented in figure 5.29: as in this case the satellite is far awayfrom the radiations bells, the dose is much smaller.

Figure 5.29: Radiation dose for the OUFTI-1 circular orbit


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6

STRUCTURE AND DEPLOYMENT

A CubeSat is a 10 cm cube with a mass up to 1 Kg: the structures shape iscompulsory and its mass has to be reduced at most. Furthermore, the OUFTI-1schedule is really challenging as the foreseen development time varies betweentwo and two and an half year. For these reasons, we chose to buy an off the shelfstructure. If on the one hand developing our own structure would have helped

in reaching the educational goal which characterized the project, on the otherhand it would have required a great amount of time and resources not availableat the moment and the result would have probably been less successful.As mentioned in paragraph 4.1, being a CubeSat impose some precise char-acteristics ( for more details see [AD4]). Furthermore, the European SpaceAgency add in its Call for proposal [RD2] a precise requirements: two separa-tion switches are compulsory on Vega.There are actually on the market two CubeSat structure developers: Pumpkinand ISIS. Both the two structures have their advantages and drawbacks thatwill be exposed in the following paragraph. After an accurate analysis we chose

the structure of Pumpkin as it better fits our requirements not only in terms ofstructure performances but also in terms of provided services.Concerning the antennas deployment system, they have to be folded duringlaunch and deployed once in orbit. To this end, they will be wrapped aroundcontact points and maintained in this configuration using the deployment mech-anism.

57

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6.1 Pumpkin structure

The structure developed by Pumpkin.Inc (San Francisco,CA,USA) is the mainpart of the so-called CubeSat-Kit. They offer in fact a wide range of productsfor CubeSat from hardware to software. At the moment, two of this structuresare flying on the CubeSats Libertad-1 (University Sergio Arboleda, Bogota,Colombia) and Delfi-C3 (TU Delft, The Netherlands). Concerning the last one,its a 3-Unit structure.The base configuration is composed by:

- Flight Model

- FM340 Flight Module

- Salvo Software and libraries

Furthermore a development board to test the CubeSat, a rechargeable elec-trical power system and an attitude determination and control system based onreactions wheels, torque coil dampers and magnetometers are available.

Two kind of structure are actually available: skeletonized or solid-walls(fig.6.1).

Figure 6.1: CubeSat-Kit structure skeletonized and solid-walls

The standard one is the skeletonized as it minimize the mass (see table 6.1).The materials employed are two aluminium alloys: 5052-H32 for the chassis, thecover plate and the base plate and 6061-T64 for all the machined components(i.e. feet, spacers). The surfaces in contact with the launcher are hard anodyzedto prevent galling and the other surfaces are gold alodyned to guarantee theconductivity.


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All the systems have an operating temperature between -40C and +85C.The mass balance is reported in the following table:

Table 6.1: CubeSat Kit mass

Skeletonized Mass [g] Solid-Walls Mass [g]Cover plate assembly 37 49Base plate assembly 50 62

Main structure 71 132Chassis screws (x4) 2 2

Total structure 166 251Flight module 50 50

Total 216 301

The skeletonized structure results much lighter than the solid-walls one.Even if the mass balance wont be the most critical problem for OUFTI-1 be-cause there wont be any added payload and we are not planning to use anyattitude control, we chose the skeletonized structure. In fact, one of the goals ofthe LEODIUM project is the development of a space platform that can be useby the future CubeSats for scientific experiments: we have to make it as lighteras possible in order to have a greater mass available for payloads and attitudecontrol in the next missions, even if it wouldnt be necessary for OUFTI-1.The main advantages of this structure is that we are sure of its reliability astwo CubeSats are already flying with it: this is the key feature that make uschoose the CubeSat-Kit. The D-STAR system into space already represents infact a challenging technology demonstration, even if we havent any evidencethat it wont correctly works: adding a possible structure failure to the alreadyexisting risks seemed us too much.Certainly some budget considerations have been done too, but they have neverbeen the driving requirements.

6.2 ISIS structureSince one and an half year, ISIS, Innovative Solution In Space (Delft, AL, TheNetherlands), has developed a CubeSat structure based on the experience gainedwith the project of Delfi-C3. They also have some other products for CubeSatsand more in general for miniaturized satellites, as antennas and ground stationand they provide a launch service.The structure is entirely made of an aluminium alloy 6061-T6 with the side-frames black hard anodised and the ribs and shear-panels black alodyned.


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Figure 6.2: ISIS structure

In table 6.2 the mass balance is reported: the primary structure is composedby the chassis and the side frames, the secondary one by all the internal stacksand spacers.

Table 6.2: ISIS structure mass

Mass [g]Primary structure 171

Secondary structure 35Total 206

The mass is much higher than in the previous case: 206 g versus 166 g. Themain reason is that the ISIS structure is completely solid-walls. If we considerthe solid-walls structure of Pumpkin we see that the ISIS one is lighter: thisprobably comes from having used everywhere the same material with a betterratio between density and mechanical properties.Anyway, in our case this structure is not advantageous respect to the skele-tonized one of CubeSat-Kit.As said in the previous paragraph, the fact that the the ISIS structure has neverbe sent into orbit make us decide to buy the Pumpkin structure.


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6.3 Deployment System

The deployment system is designed to provide a standard secondary payloadinterface between the CubeSats and the launch vehicle. Its key features are, onthe one hand, to protect the launch vehicle and its main passenger from anymechanical, electrical or electromagnetic interference from the CubeSats in theevent of a catastrophic picosatellite failure and, on the other hand, to releasethe CubeSats with a minimum spin and without any collision.The fact that the structure for a CubeSat is fixed allows the development of stan-dard deployment systems, usually called Picosatellite Orbital Deployer (POD).Currently there are four different deployment system:

P-POD: Poly-Picosatellite Orbital Deployer. Developed by the Stanford

University (Stanford, CA, USA) and the California Polytechnic Institute(San Luis Obispo, CA, USA), it holds three single CubeSats stacked ontop on each other

T-POD: Tokyo-Picosatellite Orbital Deployer. Developed by the Techni-cal University of Tokyo (Japan), it holds a single CubeSat

X-POD: eXperimental-Push Out Deployer. Developed by the Space FlightLaboratory (SFL) of the University of Toronto Institute of AeroSpace(UTIAS) (Canada), ita custom, independent separation system for threeCubeSats and can be tailored for satellites of different size

SPL: Single-picosatellite Launcher. Developed by Astrofein (Berlin, Ger-many) ita a custom deployment system for a single CubeSat

As explained in [RD2], the deployment system for the Vega maiden flight issupplied by the Educational Office of the European Space Agency. Among thepossible choices, they selected the two standard flight-proven POD of the Cali-fornia State University (P-POD) and of Toronto University (X-POD). Each oneof them can carry three CubeSats fastened with an electrically activated spring-loaded mechanism. After a signal is sent from the launch vehicle to release the

mechanism, the spring-loaded door is open and the CubeSats are pushed out bythe main spring along guidance rails, ejecting them into orbit with a separationspeed of few m/s. The door open anywhere between 90 and 260, measuredfrom its closed position, depending on how the POD is mounted. The two fore-seen POD have the only main difference that the X-POD has an independentrelease mechanism for the spring deployer and feedback to indicate that thedeployment has taken place.

The POD is a rectangular box made of high-strength Aluminium 7075-T73.Its also coated Teflon-impregnated anodization to prevent cold-welding and


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Figure 6.3: P-POD: deployment system for three CubeSats

to provide a smooth guiding surface for the CubeSats during deployment. Adeployment sensor send telemetry data to the launcher: the switch is wired asa normally closed circuit and, when the door is open, the circuit opens. Thisguarantees that the door remains close until the CubeSats are deployed.Currently negotiations are going on between the Educational Office and thePOD suppliers: the final choice hast been communicated yet but this doesnt

change anything in the CubeSat development as both meet the same standard.


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7

ATTITUDE CONTROL SYSTEM

The Attitude Control System (ACS) stabilizes the spacecraft and orients it indesired directions despite to the external disturbing forces acting on it. Ac-tually, its part of a more complex system: the Attitude Determination andControl System (ADCS) but, in the case of OUFTI-1, speaking about attitudedetermination is inappropriate as it wont be on board.

An ADCS needs in fact sensors and actuator with the consequent mass andpower needed: this is often incompatible with a CubeSat.The incompatibility with OUFTI-1 doesnt come much from the mass require-ment as we expect to fulfill it but from the power. As explained in chapter 10,the power produced in orbit is low because of the limited solar arrays surfaceand just enough to guarantee a good communication when the satellite is atthe apogee. Furthermore, we intend to provide OUFTI-1 with omni-directionalantennas: in this context, it does not need a priori to point in a specific di-rection and may gently tumble about all three axes. Therefore we opt for twopossible solutions: not having any kind of ACS or have a totally passive ACS

with the goal of slowing down its rotation rate due to disturbing torques and ofguaranteeing an acceptable equilibrium position.

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7.1 Inertia properties

Before proceeding with the estimation of the disturbing torques acting on thesatellite, we need to know its inertia properties. As the position of the elementsinside the structure is still unknown, we will use a totally simplified model. Asshown in figure 7.1 there are four antennas: they are approximately Llong = 50cm and lshort = 17.5 cm long as they are 1/4 of the wavelength. Made ofaluminium and with a diameter of 2 mm, they have respectively a mass ofmlong = 4.15 g and mshort = 1.44 g. The mass of the cubic central body istherefore mcube = 0.994 Kg. The longest antennas are directed as the y-axisand the shortest as the z-axis.

Figure 7.1: Example of OUFTI-1 configuration

We study the CubeSat as a cube with uniform density, whose gravity centeris situated in the geometrical center, to which we add a mass Mon the corner[0.05 0.05 0.05] m respect to the geometrical center of the cube in order to keepinto account all the non-symmetrical components. We calculate it in order todisplaces the gravity center 2 cm away from the geometric center of the cube:this is the maximum allowed by the CubeSat specifications.

M=0.02mcube

0.05 = 0.3976 Kg (7.1)

The mass of the uniform cube is then munif= 0.5964 Kg.

We calculate then the inertia moments of all the parts and we place theminto the gravity center of the satellite thanks to the Huygens-Steiner theoremof parallel axis:

IP =IGC+ md2 (7.2)


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where IGC and IP are respectively the inertia moment respect to an axispassing through the gravity center and the one respect to an axis parallel to the

previous one and passing through the point P; d id the distance between thetwo axis.

So the moments of inertia of the cube of uniform density respect to thegravity center of the satellite are:

Ix,cube=Iy,cube =Iz,cube =munifl

2

6 + munif

0.032 + 0.032

= 1.47 103 Kgm2(7.3)

Then, the moment of inertia of the mass Mrespect to the gravity center

are:

Ix,M=Iy,M=Iz,M=M

0.032 + 0.032

= 7.16 104 Kgm2 (7.4)

If we call 3 the longitudinal axis of each antenna, its moments of inertiarespect to its extremities are:

Ilong =I1,long =I2,long =mlongl

2long

3 = 3.32 104 Kgm2

Ishort=I1,short = I2,short = mshortl2short

3 = 1.39 105 Kgm2

I3,long=I3,short=0(7.5)

With the y-axis directed as the longer antennas and the z-axis as the shorter,we can now have the antennas moments of inertia respect to gravity center:

Ix,ant =Ilong+ mlong

0.022 + 0.033

+ Ilong+ mlong

0.022 + 0.073

+

+Ishort+ mshort

0.022 + 0.033

+ Ishort+ mshort

0.022 + 0.073

=

=7.28

104 Kgm2

Iy,ant =mlong

0.022 + 0.023

+ mlong

0.022 + 0.023

+

+Ishort+ mshort

0.022 + 0.033

+ Ishort+ mshort

0.022 + 0.073

=

=4.38 105 Kgm2Iz,ant =Ilong+ mlong

0.022 + 0.033

+ Ilong+ mlong

0.022 + 0.073

+

+mshort

0.022 + 0.023

+ mshort

0.022 + 0.023

=

=6.93 104 Kgm2

(7.6)

Hence, the total moment of inertia are:


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where Cs is the solar constant, c the speed of light, R the reflectivityfactor, rsk the vector from the center of mass to the kth surface element

Ak,nk the outward surface normal and S the unit vector from satellite tosun.We pose R= 0.6, in a simplified scalar expression and we have:

TSP,max=Cs

c A (1 + R) cos(i) (cSP cGC) = 2.06 109 Nm (7.11)

where i = 0 is incidence angle of sun and cSP cGC =

0.022 + 0.022

the distance between the center of mass and the center of solar pressure,projected on the surface.Its usually cyclic when the satellite turns around the earth or arounditself (constant only for sun-oriented vehicles) and depends mainly fromthe surface properties and from the spacecraft geometry.

Aerodynamic drag: generated by the aerodynamic drag acting on the facein a point non coinciding with the gravity center.

TA =1

2v2cD

rsk

nTk V

VAk (7.12)

wherecD is the drag coefficient, rsk the vector from the center of mass tothe kth surface element Ak, nk the outward surface normal, V the unitvector of velocity and V the module of the velocity vector.With cD = 2 and at the perigee we have:

TA =1

2v2AcD(cA cGC) = 1.84 107 N m (7.13)

wherecA the center of aerodynamic force.

Variable for inertially oriented vehicle, it depends from the altitude andon the geometry.

Magnetic field: generated by the coupling between the earth magneticfield and the satellite residual dipole.

TM=D B (7.14)

where B is the earth magnetic field and D the residual dipole. For themoment we are not able to estimate it.


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This rough estimation is extremely useful to have an idea of the maximumintensity of each perturbing couple but, as their directions are unknown, we

cannot add them to have the rotation rate of the satellite.We made therefore a simulation for one day of the disturbing couples and wecalculate the cumulated angular momentum. A priori, a longer simulation couldbe possible but the absence of attitude control causes the satellite to turn abouttheir axis and a really small time step is needed the have reliable results: thecomputing time becomes quick huge and difficult to handle.

If we accept the hypothesis that the satellite is not turning, we have theresults shown in figures 7.2 and 7.3.

Figure 7.2: Gravity gradient couple for one orbit in case of non updated config-uration


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Figure 7.3: Aerodynamic couple for one orbit in case of non updated configu-ration


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Otherwise, an orbit simulation with the updated satellite attitude has beenrun: the results are shown in figures 7.4 and 7.5.

Figure 7.4: Gravity gradient couple for one orbit in case of updated configura-tion

Figure 7.5: Gravity gradient couple for one orbit in case of updated configura-tion


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We can see that the couples trend in the updated case is almost the samethan in the non-updated.

7.3 Attitude control hardware

The main question in the OUFTI-1 project is if we really need an attitudecontrol system. In fact, the use of omnidirectional antennas doesnt require aspecific orientation of the satellite respect to the earth. In theory, there wouldbe only one position to be avoided: the ideal antennas gain diagram shows infact that the only case that prevents the communication is when the antenna ispointing directly to the ground station. In the real world, as the presence of theCubeSat structure between the antennas avoids the perfect dipole, the gain is

non-null even along the antennas direction. Anyway it will be really small andprobably not enough to guarantee the communication. In this case we wouldlike to avoid these undesired positions.Another problem connected to the attitude control system is that the rota-tion rate of the satellite shouldnt be too high. In fact, an high rotation ratecombined with the satellite speed on the orbit, could generate an huge speedrespect to the ground station with the consequent doppler effect. Event if it canbe corrected on earth, we cannot accept a too high value to guarantee a goodcorrection. Zero angular velocity is also undesired because of the risk of havingthe antennas pointing towards the earth and because of thermal behavior with

a side continuously in sunlight.Excluded all the active ACS devices as inertia and momentum wheels becausethey require a power that is not available and because basically we do not needto control the satellite but only to avoid some angular positions, we have twopossible choices: leave out any attitude control system or choose a passive sys-tem. The KISS philosophy would push us towards the first one but the need ofa good communications level makes us think it out.A possible ACS would be a Passive Magnetic Attitude Control System (PMACS).It has been used before on other CubeSats as Delfi-C3 and in XI-IV, respec-tively at the University of Delft (The Netherlands) and at the University of

Tokio (Japan).Generally, it consists of a strong permanent magnet and hysteresis material onone or two axes to damp rotation. The only rotation left is therefore the oneabout the longitudinal axis of the magnet and the hysteresis material dampthe rotations about the others. As the magnet would align itself with the earthmagnetic field (almost always parallel to the earth surface on the OUFTI-1 orbitas the inclination is low), we could in this case place the magnet on a directionthat prevents the antennas to be pointed towards the earth.Otherwise, we could use only hysteresis material on all the three axes: in thiscase, they wouldnt try to align themself to a precise direction but they would


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only slow down the rotation rate.The two possibilities are under study and only more detailed analysis would

allow the choice between them.


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CHAPTER

8

POWER SYSTEM

The electrical power system provides, stores, distributes and controls spacecraftelectrical power.In this chapter, we will take care only of the power source: the hardware forpower control and distribution wont be part of this work.The power source on an earth orbiting satellite is usually the sun power: through

solar arrays we can in fact collect the sun rays and transform their energy intoelectrical power. As the performances of solar cells are subjected to degradationalong the mission, we speak about Beginning Of Life (BOL) and End of Life(EOL). As the radiation environment over the foreseen orbit is hard, the solarcells will be affected by an important degradation of their efficiency: all theanalysis will be carry out with the EOL parameters.Usually the first step is to identify the power needed in order to adapt the solararrays surface to the requirements. In the case of a CubeSat, the problem isdifferent as the surface if fixed: even if deployable orientable solar arrays areavailable, the constraints of mass and volume often hold the design back from

these heavy and risky elements. Furthermore, OUFTI-1 need power only forthe communication system and for the on-board computer. We will thereforeproceed in the identification of the available power and then we will size theD-STAR system in order to work with it.Two scenarios are still open, depending on the final design of the communicationsystem: the payload can be on all the time or it can be switch off when its notused, for instance over the oceans. If the former option is the safer as the systemis never turn off and there isnt any risk of problems in turning it on, the latterwould allow an important power saving. As we follow the KISS principle asfar as its possible, we would prefer to leave the payload active all the time in

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order to prevent any failure due to the switching it on and off, but we need toguarantee enough power. Furthermore, turning on and off the payload implies

that commands have to be generated by the on-board computer or sent fromthe ground station.All the following analysis is made for the elliptic orbit in the hypothesis of = 0and = 0. However at the end of this chapter a parametric study for the powerproduced in orbit will be carry out making vary this two parameters: the resultsare basically the same but shifted in time and the most critical situation withthe minimum power always happen. Furthermore, the orbital parameters aresupposed to remains constant.

8.1 Eclipses durationThe first step to have an idea of the available power is to know the time ofeclipse: to have it, we need to know the direction of the sun rays on the orbitplane.As shown in figure 8.1, three planes play a role in this calculation with theirreference system: the ecliptic plane, the equator plane and the orbit plane.

Figure 8.1: Reference sistems

As shown in figure 8.1, the sun rays arrive to earth on the ecliptic plane onthe direction:

NS= {cos (e) sin {e} 0} (8.1)

As above mentioned, the goal of this part is to express this direction intothe orbit reference. We can transform a vector from the ecliptic plane into theequatorial plane thanks to a rotation about the xecl =xeq with the the rotationmatrix R1


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Figure 8.2: Sun rays direction on the ecliptic plane

xeqyeqzeq

=

1 0 00 cos (ieq) sin (ieq)

0 sin (ieq) cos (ieq)

xeclyeclzecl

= R1

xeclyeclzecl

(8.2)One we have our vector expressed in the equatorial plane, we pass into a

first intermediate reference by turning of the right ascension of ascending node about the zeq =z

axis with the rotation matrix R2:

x

y

z

=

cos () sin () 0sin () cos () 0

0 0 1

xeqyeqzeq

= R2

xeqyeqzeq

(8.3)

Then we can consider the orbit inclination i for a rotation about thex =x

axis thanks to the rotation matrix R3 and passing into a second intermediatereference:

x

y

z =

1 0 0

0 cos (i) sin (i)0 sin (i) cos (i) x

y

z = R3

x

y

z (8.4)

This second reference system is on the orbit plane but the abscissas axisisnt oriented to the perigee. We consider therefore the argument of perigee byrotating about the z =zorb with the matrixR4:

xorbyorbzorb

=

cos () sin () 0sin () cos () 0

0 0 1

x

y

z

= R4

x

y

z

(8.5)


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CHAPTER 8

We have now the vector Ns expressed into the orbit reference:

xorbyorb

zorb

= R4R3R2R1

xeclyecl

zecl

(8.6)

As the satellite is moving on the orbit plane, what we are interested in tocalculate the eclipses time is actually the projection ofNs on the orbit plane.As indicated in figure 8.1, we calculate the angle that the projection ofNsgenerates with the xorb:

Ns=atanNs,yNs,x (8.7)

Figure 8.3: Sun rays direction projected on the orbit plane.

So far, we know the eclipses central angle = 180 +and therefore weknow the corresponding orbit radius.As the distance between earth and sun is much bigger than the earths radius,we can make the hypothesis that the lines determining the entrance and the exitfrom eclipses are tangent to the earth surface, as shown in figure 8.1. Hence,

we have:

out= 90 acos

Rerout

in= 90 acos

Rerin

(8.8)

We can also exploit the relationship between radius and anomaly and wehave:


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cos 90 out = ReP 1 + ecos +outcos

90 in

=

ReP

1 + ecos

in

(8.9)We solve this two equations and we have out and in. Then we transform

them into the corresponding eccentric anomalies in order to calculate the eclipsesduration.

A simulation over an year orbit shows the eclipse duration shown in figure8.4: it means that, given the position of earth respect to sun, roughly corre-sponding to the day of the year, all the orbit taking place on that day have the

indicated eclipses duration.

Figure 8.4: Eclipse duration as a function of earth anomaly

8.2 Configuration and solar cells

In order to quantify the available power, we also need to know the satelliteconfiguration and, more specifically, the solar panels orientation.The first thing to point out, is that, as we are not planning any attitude control,we need solar panels on each face: in fact, we cant risk to have a face withoutsolar cells watching the sun causing a fall in the power production.


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Here we add an important hypothesis: the satellite turns on its orbit remain-ing inertially fixed. Considering that, as mentioned in the previous chapter, we

are trying to avoid the attitude control, this is a big approximation as its almostimpossible that its not tumbling about its axis. Aware of this limitation, wealso recognize that we are performing a feasibility study and that all the resultsobtained are only indicative and will be useful to have an idea of the producedpower.Another possibility is to study the so-called barbecuemode: as the satellite isspinning around its axis and as all the faces are covered by solar cells, we couldidentify an equivalent surface to use for the calculation.

We define each solar panel though its normal vector, its area and its effi-

ciency. The area is the effective surface of solar cells and the efficiency is theEOL efficiency. This latter is defined as the maximum percent of incident powerconverted into electrical power:

=Pmax

CsS (8.10)

Where Cs is the solar constant and S the cells surface.

In particular, for this simulation we used a triple junction Gallium-Arsenidecell type having the properties reported in tables 8.1 and 8.2. We place twocells on each face.

Table 8.1: Solar cells mechanical properties

Area[cm2] 30.18Weight[mg/cm2] 86Thickness[m] 15020

Table 8.2: Solar cells electrical and thermal properties

BOL 1E14 5E14 1E15 % 26.8 0.953 0.913 0.886

Max Power Voltage Vmax [mV] 2275 0.0953 0.920 0.908Max Power Current Imax [mA/cm

2] 7.922 1 0.993 0.976dVmax/dT [mV /

C] -6.4 -6.8 -6.8 -7.0dImax/dT [A/cm

2/C] 4.2 6.7 7.6 8.4absorbivity at 28C 0 0.91 1 1 1

The values indicated in the last three columns are the coefficient to apply forthe fluence of electrons having 1 Mev energy indicated on top of the column in


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Eectrons/cm2. For our mission the fluence over the lifetime, estimated throughthe software Spenvis, is of 8.55

1011: we can use the values of the third column

even if they are too pessimistic.They give a value for the efficiency of 25.5 %: we will use 25% to be sure of notoversetimating the power.

8.3 Power produced

We have now all the elements to calculate the power produced: the directionof sun rays, the eclipse duration and the solar arrays orientation. The programdeveloped calculates the eclipses anomalies of entrance and exit. Looping on

the satellite anomaly, it determine whether its in sunlight or not: if yes, itcalculate the scalar product between the sun rays direction and the normal toeach face in order to have the incidence angle of sun:

cos (i) = Ns Ni i= 1 : 6 (8.11)where i indicates the face.Ifcos (i)< 0, it means that the face is not watching the sun as its turned in theopposite direction: it doesnt contribute to the power production. Otherwisewe have the power produced by the i-th face:

Pi=CsAiicos (i) (8.12)

As logical, the maximum power of a face is generated when the sun raysare perpendicular to it. This doesnt mean that the total maximum power isproduced when one solar array is perpendicular the sun: in fact, in order tohave the total maximum power we need to add the contributions of all thefaces. Indeed, the Delfi-C3 team performed a study to optimize the orientationof solar cells: it came out that the best configuration is when a corner is directedto the sun.

Once we have the power generated by each face, we sum the contribution andwe have the total power.

8.3.1 Elliptic orbit with starting orbital elements

For the OUFTI-1 elliptical orbit in case of = 0, = 0 and for a simulationstarting at the vernal equinox we have the result represented in figure 8.5.

Each vertical line represents one orbit on the moment of the year indicatedby the earth anomaly in abscissa. In blue are represented the eclipses and inthe dark red the maximum power.


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Figure 8.5: Total power produced: simulation over one year orbit.

Anyway, we are more interested in the power that we can effectively use at eachtime: we calculated therefore the integrated power shown in figure 8.6. To haveit, we integrate the power over each orbit to have the total energy availableand then we divided it by the orbit duration. In this way, we know exactly thepower that we can guarantee continuously to our payload. All the losses on the

electrical power system and in the ba

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