Smart Dust Relative Motion in a Heliocentric Mission Scenario

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Department of Civil and Industrial

Engineering

Master of Science in Space Engineering

Smart Dust Relative Motion in a

Heliocentric Mission Scenario

Candidate:

Antonio Figliuolo

Advisors:

Prof. Alessandro A. Quarta

Prof. Giovanni Mengali

Engr. Marco Bassetto

Engr. Lorenzo Niccolai

Academic year 2016/2017

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“Remember who you are. Wherever you go, with whoever you go with, you should never forget your roots and where it is you come from.” Walt Disney

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Abstract

A deep bibliographic research on current femtosatellites layouts has led to a spacecraft design suitable for solar sailing purposes. A Smart Dust equipped with an ElectroChromic System (ECS) concept has been proposed as can-didate satellite for heliocentric mission scenarios. In this context, the aim of the current work consists of demonstrating that an ECS-based femtosatel-lite, after having moved away from the deployer, is able to approach again the chief for sending the collected data. A Smart Dust has a characteristic side length and a small weight that allows the generation of a propulsive thrust by exploiting the solar radiation pressure. The electrochromic coat-ing applied on the Smart Dust surface exposed to the sunlight is used to vary the sail attitude following a proper control law. No relevant works on the Smart Dust attitude control proposed in this work are currently available in specific literature, so the collected results could constitute the basis for an innovative way to exploit the opportunities offered by an ECS-based fem-tosatellite. A mathematical model has been developed and implemented on MATLAB R _{software, in order to determine the relative motion of a Smart} Dust with respect to a chief satellite covering a heliocentric circular orbit both in a linearised and a non-linearised form. The preliminary analysis of the mission scenario treated in this work has highlighted that the analyt-ical results of the linearised model are often not precise. However, if the non-linear model is used, an accurate determination of the relative motion in which the Smart Dust reapproaches the chief spacecraft can be obtained.

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Aknowledgements

Desidero ringraziare il Prof. Alessandro A. Quarta e il Prof. Giovanni Men-gali, per avermi concesso l’opportunità di indagare un campo dell’ Ingeg-neria Spaziale estremamente affascinante, e per avermi guidato nell’ elabo-razione della presente tesi con grande professionalità e cortesia.

Un ringraziamento particolare va all’ Ing. Marco Bassetto e all’ Ing. Lorenzo Niccolai, per aver dimostrato estrema disponibilità nei miei confronti, for-nendo preziosi consigli nel corso del lavoro di ricerca ed elaborazione dei risultati.

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List of Figures

1.1 Reaction forces on a perfectly reflecting solar sail, taken from

Ref. [1] . . . 5

1.2 Solar sail cone angle and clock angle . . . 8

1.3 Optimal sail cone angle as a function of a required cone angle, adapted from Ref. [1] . . . 9

1.4 Optimisation of the sail cone angle, taken from Ref. [1] . . . 10

1.5 Solar sail force components, taken from Ref. [1] . . . 10

1.6 Definition of spherical coordinates . . . 11

2.1 Small satellites cost saving advantage: unit satellite cost when mass-produced, taken from Ref. [18] . . . 18

2.2 Very small satellite complexity VS cost, taken from Ref. [19] 18 2.3 SWIFT swarm mimicking the shape of ISS, taken from Ref. [21] 20 2.4 SWIFT prototypes, taken from Ref. [21] . . . 21

2.5 PUCP-SAT-1 and Pocket-PUCP, taken from Ref. [22] . . . . 22

2.6 PCBSat, taken from Ref. [19] . . . 24

2.7 WikiSat prototypes, taken from Ref. [23] . . . 25

2.8 Notional Barnhart’s SpaceChip representation, taken from Ref. [8] . . . 27

2.9 Manchester’s Sprite, taken from Ref. [9] . . . 29

2.10 Manchester’s Sprites mounted on ISS, taken from Ref. [9] . . 30

2.11 KickSat spacecraft deployer, taken from Ref. [9] . . . 32

2.12 Manchester’s Sprites in KickSat, taken from Ref. [9] . . . 32

3.1 Atchison’s Sprite bus layout, taken from Ref. [6] . . . 34

3.2 SD’s Faceted surface, taken from Ref. [6] . . . 42

3.3 SRP induced torque as a function of α for SD’s faceted sur-face, taken from Ref. [6] . . . 43

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3.4 Attitude time-history for SD’s faceted surface, taken from Ref. [6] . . . 44 3.5 Etching and coating process to produce facets on a SD, taken

from Ref. [6] . . . 45 3.6 SEM image of the end of a sample SD’s faceted surface trench,

taken from Ref. [6] . . . 45 3.7 SEM image of a coated sample SD’s faceted surface trench,

taken from Ref. [6] . . . 46 3.8 Chipsat configuration with electrochromic panels at each

cor-ner, taken from Ref. [30] . . . 47 3.9 Sun-pointing corner-cube SD architecture, taken from Ref. [6] 47 3.10 SpaceChip plate with two coated sides, taken from Ref. [29] 49 3.11 SpaceChip with grated-plate, taken from Ref. [29] . . . 50 3.12 SpaceChip with grated-plate: restoring torque; taken from

Ref. [29] . . . 51 3.13 Atchison’s design VS typical solar sail designs, taken from

Ref. [6] . . . 53 3.14 Geocentric scenario No.2: orbit evolution of six spacecraft

using electrochromic control strategy; taken from Ref. [7] . . 55 3.15 Heliocentric scenario No.1: constant ChipSat’s anomaly

for-mation and along-track separation; taken from Ref. [6] . . . 56 3.16 Heliocentric scenario No.2: planar reference frame; taken

from Ref. [34] . . . 58 3.17 Heliocentric scenario No.2: periodic β-control; taken from

Ref. [34] . . . 59 3.18 Heliocentric scenario No.3: reference frame and state

vari-ables; taken from Ref. [35] . . . 60 3.19 Heliocentric scenario No.3: SD1 state variables; taken from

Ref. [35] . . . 62 3.20 Heliocentric scenario No.3: SD1 Relative trajectory; taken

from Ref. [35] . . . 62 4.1 Relative motion problem: reference frames and geometry;

taken from Ref. [36] . . . 64 5.1 Variation of SD1-chief relative distance over one year for

dif-ferent α0; dashed line (linear model), solid line (exact model) 78 5.2 SD1-chief relative distance over one year for α0 = α0opt . . . 79

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5.3 Inefficacy of other α strategies: time variation of SD1-chief relative distance over one year; dashed line (linear model), solid line (exact model) . . . 80 5.4 Variation of SD2-chief relative distance over one year for

dif-ferent α0; dashed line (linear model), solid line (exact model) 82 5.5 SD2-chief relative distance over one year for α0 = α0opt . . . 83 5.6 Variation of SD3-chief relative distance over one year for

dif-ferent α0; dashed line (linear model), solid line (exact model) 84 5.7 SD3-chief relative distance over one year for α0 = α0opt . . . 85 5.8 SD-chief relative distance over one year for SDs with optimum

pitch angle; dashed line (linear model), solid line (exact model) 85 5.9 Variation of SD-chief relative distance over one year

consider-ing equal α0 for creasing β; dashed line (linear model), solid line (exact model) . . . 86 5.10 Exact model VS linear model for SDs with optimum α0:

|~r0_|

ex − |~r0|lin for t ∈ (0, TC) . . . 88 5.11 Exact model VS linear model for SDs with optimum α0:

|~r0_|

ex − |~r0|lin for t ∈ (0, 0.2 TC) . . . 88 5.12 Time variation of the SDs’ semimajor axis over one year

as-suming α0 = α0opt; dashed line (linear model), solid line (ex-act model) . . . 90 5.13 Time variation of the SDs’ eccentricity over one year

assum-ing α0 = α0opt; dashed line (linear model), solid line (exact model) . . . 92 5.14 Time variation of the SDs’ argument of the perihelium over

one year assuming α0 = α0opt; dashed line (linear model), solid line (exact model) . . . 94 5.15 Time variation of the SDs’ true anomaly over one year

assum-ing α0 = α0opt; dashed line (linear model), solid line (exact model) . . . 95 5.16 Time variation of the SDs’ angular momentum over one year

assuming α0 = α0opt; dashed line (linear model), solid line (exact model) . . . 96 5.17 Variation of the SD angular momentum over one year

con-sidering equal α0 for creasing β; dashed line (linear model), solid line (exact model) . . . 97

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5.18 Variation of the SD semimajor axis over one year considering equal α0 for creasing β; dashed line (linear model), solid line (exact model) . . . 98 5.19 Variation of the SD eccentricity over one year considering

equal α0 for creasing β; dashed line (linear model), solid line (exact model) . . . 98 5.20 Variation of the SD argument of the perihelium over one year

considering equal α0 for creasing β; dashed line (SD1-SD2’s linear model), solid line (SD1-SD2-SD3’s exact model), red dashed line (SD3’s linear model) . . . 99 5.21 Variation of the SD true anomaly over one year

consider-ing equal α0 for creasing β; dashed line (SD1-SD2’s linear model), solid line (SD1-SD2-SD3’s exact model), red dashed line (SD3’s linear model) . . . 99 5.22 Variation of SD1 state variables over one year assuming α0 = α0opt; dashed line (linear model), solid line (exact model) . . . 100 5.23 Variation of SD2 state variables over one year assuming α0 = α0opt; dashed line (linear model), solid line (exact model) . . . 101 5.24 Variation of SD3 state variables over one year assuming α0 = α0opt; dashed line (linear model), solid line (exact model) . . . 101 5.25 Variation of SDs relative velocity modulus over one year

as-suming α0 = α0opt; dashed line (linear model), solid line (exact model) . . . 102 5.26 SDs relative trajectory in the cartesian reference frame T (C; x, y)

over one year assuming α0 = α0opt; dashed line (linear model), solid line (exact model) . . . 103 5.27 SDs relative trajectory in the polar reference frame T (C; |~r0_{|, ξ)}

over one year assuming α0 = α0opt; dashed line (linear model), solid line (exact model) . . . 104 5.28 SDs relative trajectory in the rotating polar reference frame

T (C0; ρ, θ) over one year assuming α0 = α0opt; dashed line (linear model), solid line (exact model) . . . 106 5.29 SDs absolute trajectory in the polar reference frame T (O; rc+

ρ, τ +θ) over one year assuming α0 = α0opt; dashed line (linear model), solid line (exact model) . . . 107 6.1 Futuristic scenario involving a swarm of SDs deployed from

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List of Tables

2.1 Small satellites classification . . . 13

2.2 Femtosatellites classification . . . 14

2.3 SWIFT characteristics, data from Ref. [21] . . . 22

2.4 Pocket-PUCP characteristics, data from Ref. [22] . . . 23

2.5 PCBSat current system configuration, data from Ref. [19] . . 25

2.6 WikiSat characteristics, data from Ref. [23] . . . 26

2.7 Barnhart’s SpaceChip outcomes, data from Ref. [8] . . . 28

2.8 Barnhart’s Spacechip solar sailing performances . . . 28

2.9 Manchester’s Sprite solar sailing performances, data from Ref. [9] . . . 29

3.1 Atchison’s Sprite power budget, data from Ref. [6] . . . 37

3.2 SD1 solar sailing performance parameters . . . 38

3.3 Corner-Cube SpaceChip solar sailing performances . . . 48

3.4 Femtosatellites comparison . . . 52

3.5 Candidates Smart-Dusts Characteristics, data from Ref. [26] 52 3.6 Representative SDs characteristics, data from Ref. [34] . . . 58

5.1 Candidates SDs solar sailing performance parameters . . . . 76

5.2 r0_max and |r0|t=TC for SDs with optimum α0; data referred to the exact model . . . 81

5.3 SD-chief relative distance at t = TC for SDs with equal α0 . 87 5.4 |~r0_| ex − |~r0|lin at t = TC . . . 87

5.5 Values assumed by SDs’ semimajor axis at t = TC/2 and at t = TC . . . 91

5.6 Values assumed by SDs’ angular momentum at t = TC/2 and at t = TC . . . 93

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Chapter

1

Solar sailing

1.1 Introduction

Solar sailing serves as an alternative method of providing propulsion to a spacecraft. It uses sunlight instead of conventional on-board consumables such as propellant. According to Ref. [1], this propulsion concept transcends the reliance on a finite reaction mass and then it can provide a continuous acceleration limited only by the lifetime of the sail material in the space environment. The sail is slowly but continuously accelerated thanks to the momentum gained by exploiting the continuously available solar radiation pressure (SRP). Then, theoretically, it has unlimited ∆V capability, en-abling a wide-range of potential high-energy and/or long-duration mission scenarios. In particular, we will see that solar sails are capable of exotic non-Keplerian low thrust orbits that are impossible for any other type of spacecraft.

Sunlight is comprised of quantum packets of energy called photons. The momentum carried by individual photons is extremely small. Then, we require the sail to have a large surface, while maintaining a mass as low as possible, to provide a suitably large momentum transfer. Thus, the efficacy of SRP as a mean of propellantless propulsion is strictly related to the solar sail scale. This factor has implications not only for performances but also in hardware design, implementation and testing.

The original solar sail concept involves very large membranes, so the range of magnitudes involved usually make structural analysis complex, with fabrication demanding and very demanding ground testing nearly im-possible. Despite 30 years of attempts, eminent scientists as G. Greschik, declared during the 2000s that these dimensional challenges were primarily

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responsible for the as yet unsuccessful solar sail tests, motivating the devel-opment of sails that minimise these scaling challenges [2]. C. R. McInnes went beyond the concept of a classical high-performance solar sail (esti-mated 31400 m2 for 41 kg) as early as the year 1999, when he introduced the concept of a microsolar sail with estimated 16 m2 _{for 0.24 kg in Ref. [1].} Actually even, a small sail a few meters diameter called solar kite was pro-posed in Ref. [3] back in 1997. NASA started to make substantial progress in the development of small solar sail propulsion systems in the early to mid-2000s. It proposed a 3-unit CubeSat measuring 30 × 10 × 10 cm, with a mass of 4 kg. Such a small satellite, called NanoSail-D, flew on-board the ill-fated Falcon Rocket launched in 2008. It never achieved orbit due to the failure of that rocket [4].

However, the miniaturization process has led to the design of really small spacecraft classified as femtosatellite only over the last ten years. These particular satellites have characteristic dimensions on the order of the centimetre and a mass below 100 grams. Recent efforts in the field of small satellites have progressively led to particular chip-scaled femtosatel-lites commonly known as Satelfemtosatel-lites-on-a-Chip (also known as ChipSats or SpaceChips). On the other hand, recent studies on the orbital dynamics of dust particles and further technological advancement in miniaturization technologies, as well as in ElectroChromic Systems (ECS), have led to the concept of "Smart-Dust" (or simply SD). SDs are self-contained spacecraft whose length scale enables promising mission scenarios, based on propellant-less propulsion. This work investigates the SD relative motion with respect to a mother-ship acting as its deployer in a heliocentric mission scenario. This is currently a promising topic in the solar sailing field. In particu-lar, such a mission scenario can be obtained by modulating the Smart-Dust attitude through ECS devices.

1.2 Foundation of solar radiation pressure

Solar radiation pressure (SRP) acts when solar photons impinge on a surface exposed to the sunlight, imparting a momentum exchange upon the Sun-exposed solar sail surface. C. R. McInnes in Ref. [1] derives the expression of the pressure force exerted on a solar sail due to the solar radiation flux and the resulting acceleration of the solar sail. From Planck’s law, multiplying the frequency ν of a photon by Planck’s constant (h = 6.6262 × 10−34Js),

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yields the energy E of a photon:

E = hν (1.1)

In addition to this quantum view, the mass-energy equivalence of Einstein’s special relativity allows the total energy E of a moving body to be written as:

E2 = m2₀c4+ p2c2 (1.2)

where c = 2.998 × 108 _{m/s is the speed of the light, m}

0 is the rest mass of the body, and p is its momentum. Since a photon has a zero resting mass, its energy can be written as:

E = pc (1.3)

Therefore, using the photon energy defined by Eqs. (1.1)–(1.3), the amount of momentum p transferred by a single photon with frequency ν is given by:

p = hν

c (1.4)

In order to determine the amount of momentum exerted upon the sail by numerous photons, the energy flux W on the sail has to be considered. The energy flux W is the amount of energy transferred on a unit area A per unit time t. It may also be written as a function of the distance from the Sun r, the distance between the Sun and Earth r⊕, the energy flux measured at the Earth from the Sun W⊕, and the solar luminosity LS:

W = ∆E A∆t = W⊕ r_⊕ r 2 (1.5) where: W⊕ = LS 4πR2⊕ (1.6) The energy ∆E transported across a surface of area A normal to the incident radiation in a time interval ∆t is given by:

∆E = W A∆t (1.7)

From Eq. (1.3), this energy ∆E transports a momentum ∆p is:

∆p = ∆E

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The solar pressure P due to the solar radiation flux is defined as the mo-mentum transported per unit time per unit area:

P = 1

A ∆p

∆t (1.9)

Therefore, combining the last three equations, we obtain:

P = W c = W⊕ c r_⊕ r 2 (1.10) Note that, for a perfectly reflecting surface, the observed solar pressure exerted on the solar sail is twice the value of P provided by Eq. (1.10). This effect is due to the momentum transferred to the surface by incident photons and the reaction provided by reflected photons.

At a distance of 1 au from the sun, taking into account that LS = 3.828 × 1026 J/s, the mean value of W⊕ is 1368 J/sm2. Because of the slightly elliptical orbit of the Earth around the Sun, this energy flux varies by approximately 3.5% during the year. Using the mean value of W⊕ in Eq. (1.10), the solar radiation pressure P at 1 au, named P⊕ is taken to be 4.56 × 10−6 N/m2_{. Consequently, the solar radiation pressure effectively} exerted on a Sun-facing perfectly reflecting solar sail is 9.12 × 10−6 N/m2_.

1.3 Force on an ideal solar sail

The acceleration experienced by a solar sail is a function of its attitude. A solar sail can be considered ideal if it is flat and if it has 100% specular reflection. According to Ref. [1], considering an ideal solar sail of area A with a unit vector ˆn normal to the surface, the force exerted on the surface due to photons incident from the ˆui direction is given by:

~

fi = P A(ˆui· ˆn)ˆui (1.11)

where A(ûi · ˆn) is the projected sail area in the ûi direction, as shown in Fig. 1.1. Similarly, the reflected photons exert a force of equal magnitude on the solar sail, but in the specular reflected direction -ûr, viz:

~

fr= −P A(ˆui· ˆn)ˆur (1.12)

Using the vector identity ûi − ûr = ( ûi· ˆn)ûr, the total force ~f exerted on a solar sail of mass m, according to the second Newton’s law, is therefore given by:

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Figure 1.1: Reaction forces on a perfectly reflecting solar sail, taken from Ref. [1]

~

f = 2P A(ˆui· ˆn)2ˆn = m~a (1.13)

where ~a is the solar sail acceleration. Using Eq. (1.10) this total force may be written as: ~ f = 2AW⊕ c r_⊕ r 2 (ˆui· ˆn)2 nˆ (1.14)

On the other hand, using Eq. (1.14), the solar sail acceleration may be expressed as: ~a = 2W⊕ σc r_⊕ r 2 cos2α ˆn (1.15) where:

• α is defined as the pitch angle (the angle between the sail normal and the incident radiation, as shown in Fig. 1.1);

• σ is the sail loading m/A (the total spacecraft mass per unit area). Now that the solar sail performance is parametrised by σ, different solar sail designs can be compared defining a standard performance metric. In analogy with Ref. [1], the solar sail characteristic acceleration a0 is chosen as common metric. It is defined as the maximum acceleration that a Sun-pointing (α = 0) solar sail can generate at a heliocentric distance of 1 au:

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a0 = 2P⊕η

σ (1.16)

where η is an overall efficiency factor due to reduced reflectivity because of non-perfect optical properties of the sail material and its billowing. Its typical values is around 0.9, although a conservative value of 0.85 is generally assumed. Note that in this formulation, expressing P⊕ in N/m2 and σ in g/m2_{, a}

0 is given in terms of mm/s2.

The versor ˆui is defined by the radial versor ˆr (from the Sun to the solar sail) when considering a solar sail in heliocentric orbit. Accordingly, the solar sail acceleration may also be written in terms of the solar gravitational acceleration as: ~a = βµ r2 (ˆr · ˆn) 2 ˆ n (1.17) where:

• µ= 1.327×1011km3/s2 is the Sun standard gravitational parameter; • β is the lightness number of the solar sail, that is, the ratio between the modulus of the propulsive acceleration and the modulus of the local gravitational acceleration.

Since both the SRP and the solar gravitational accelerations vary as the inverse square distance from the Sun, β results independent of the Sun-sail distance. Then, the solar sail lightness number may be written as:

β = a0 mµ/r2 = 2P⊕ηr 2 ⊕ µσ (1.18)

with 2P⊕ = 9.12 × 10−6 N/m2. Since σ resides in the denominator of Eq. (1.16), a larger a0 is obtained through a larger β. The lightness number is dependent on the design of the solar sail. Thus, as the spacecraft mass to solar sail area ratio increases, both a0 and β decrease, affecting the overall performance of the solar sail.

Assuming η = 0.85, the lightness number could be written also as:

β = σ

∗

σ (1.19)

where the critical sail loading parameter σ∗ = Ls/2πµ is found to be 1.53 g/m2_.

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Note that the acceleration ~a computed through Eq. (1.13) is related to a perfectly specularly reflecting solar sail, so if the sail is assumed to be opaque, the contributions of the diffusely reflected and absorbed photons must be taken into account. According to Ref. [5], in this case it is neces-sary to introduce a model based on three efficiency coefficients instead of a single efficiency η henceforth taken to be 0.85. According to this model, the acceleration due to SRP is given by:

~a = P cos α σ 2ηsrcos α + 2 3ηdr ˆ n + (ηdrηab)ˆui (1.20) with: ηsr+ ηdr+ ηab = 1 (1.21)

where ηsr, ηdr and ηab are dimensionless constants that account for how the incoming light is respectively specularly reflected, diffusely reflected, or absorbed.

1.4 Solar sail heliocentric orbital dynamics

Traditionally, solar sailing is applied to heliocentric mission scenarios. The thrust of an ideal sail is given by a force vector aligned along the sail normal direction ˆn. The vectorial equation of motion of such a solar sail spacecraft moving in a heliocentric orbit is:

¨ ~r +µ r2r = βˆ µ r2 (ˆr · ˆn) 2_ˆ_n _(1.22)

where ~r is the position vector of the spacecraft with respect to the Sun, at time t.

This vector equation of motion may be resolved into any suitable coor-dinate system, but firstly the orientation of the solar sail force vector has to be defined.

1.4.1 Orientation of ideal solar sail force vector

The sail normal versor ˆn defines the orientation of the ideal solar sail thrust vector. This versor can be expressed in terms of a cone angle α and a clock angle δ, as shown in Fig. 1.2. The sail cone angle is the angle between ˆn and the Sun-line, while the sail clock angle is the angle between the projection of the sail normal onto a plane normal to the Sun-line and a fixed reference

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Figure 1.2: Solar sail cone angle and clock angle

direction. Note that the cone angle is equivalent to the sail pitch angle used in the previous Section for a planar case. Using these definitions and resolving along the radial, orbit normal and transverse directions it is found that [1]:

ˆ

n = cos α ˆr + sin α cos δ ˆp + sin α sin δ ˆp × ˆr (1.23) where ˆp is the versor normal to the orbit plane.

In order to maximise the component of the SRP force in a given direction ˆ

q, the following optimization process can be considered. Expressing ˆq as:

ˆ

q = cos ˜α ˆr + sin ˜α cos ˜δ ˆp + sin ˜α sin ˜δ ˆp × ˆr (1.24) where ˜α and ˜δ are the cone and the clock angles of the required force direc-tion, the force magnitude fq in this direction is therefore given by:

fq= 2P A(ˆr · ˆn)2(ˆn · ˆq) (1.25) Substituting Eqs. (1.24)-(1.23) in Eq. (1.25), fq may be written in terms of cone and clock angles:

fq = 2P A cos2α [cos α cos ˜α + sin α sin ˜α cos(δ − ˜δ)] (1.26) It is clear that fq is maximised if δ = ˜δ, while, setting its derivative with respect to α equal to zero, the optimal sail cone angle α∗ which maximises the component of SRP force in direction ˆq is found to be:

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tan α∗ = −3 + √

9 + 8 tan2_α_˜

4 tan ˜α (1.27)

The variation of α∗ with the required ˜α is shown in Fig. 1.3. The required

Figure 1.3: Optimal sail cone angle as a function of a required cone angle, adapted from Ref. [1]

˜

α must be less than 90◦, since the force vector of the solar sail has always a positive radial component. It can also be seen that the optimal sail cone angle is limited to approximately 35◦ as the required cone angle reaches 90◦. This is due to the reduction in total force magnitude as the sail cone angle increases, see Fig. 1.4. The latter result is visible in Fig. 1.5 too, where the solar sail force components as a function of the cone angle are depicted. This graph clearly shows that whereas the radial force component monoton-ically decreases with increasing cone angle, the transverse component has a turning point with a single maximum. Given all the previous assumptions, we will consider only pitch angles not exceeding 35◦ in the analysis carried on in this thesis.

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Figure 1.4: Optimisation of the sail cone angle, taken from Ref. [1]

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1.4.2 Polar equations of motion

The vector equation of motion expressed by Eq. (1.22) can be transformed into scalar components in the spherical coordinate system shown in Fig. 1.6. The plane ϕ = 0◦is defined as the ecliptic with ϕ = 90◦directed to the North

Figure 1.6: Definition of spherical coordinates

ecliptic pole. The direction θ = 0◦ is defined as the first point of Aries _](an astronomical reference direction in the ecliptic plane). According to Ref. [1], resolving Eq. (1.22) into radial ˆr, transverse ˆθ and normal ˆϕ components and using Eq. (1.23), it is found that:

¨ r − r ˙ϕ2− r ˙θ2cos2ϕ = −µ r2 + β µ r2 cos 3 α (1.28a) 1 rcos ϕ d dt(r 2_{θ) − 2r ˙}_˙ _{θ ˙}_{ϕ sin ϕ = β}µ r2 cos 2_{α sin α sin δ} (1.28b) 1 r d dt(r 2_{ϕ) + r ˙}_˙ _θ2_{sin ϕ cos ϕ = β}µ r2 cos 2_{α sin α cos δ} _(1.28c)

Notable simplifications are introduced when considering the solar sail equations of motion in a planar case (i. e., in the ecliptic plane (ϕ = 0), with a clock angle δ of 90◦). Under this assumption, the sail attitude results to be defined solely by the cone angle α. Then, the sail cone angle will be referred to as the sail pitch angle in this work because of the planar motion

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considered. According to this assumption, Eq. (1.28) reduces to: ¨ r − r ˙θ2 = −µ r2 + β µ r2 cos 3_α _(1.29a) r ¨θ + 2 ˙r ˙θ = βµ r2 cos 2_{α sin α} _(1.29b)

Eq. (1.29) represents the planar equations of motion of a solar sail in heliocentric orbit.

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Chapter

2

Femtosatellites

Since the dawn of the space age in 1957, more demanding mission require-ments have driven up satellite mass from Sputnik’s 84 kg to over 6000 kg for some systems today. Consequently, cost, complexity, program timeta-bles, and management overhead have grown considerably. In the last two decades, a fast-growing "small satellite" industry has reversed this trend. It has enabled capable and cost-effective space missions, basing on sensibly reduced requirements and leveraging modern commercial technology. At the beginning, the concept of a "small-satellite" was dismissed as academic, not capable of providing real value. However, nowadays it is a matter of fact that small satellites have opened the doors to space access for universities, new businesses, and countries providing real value and interesting mission profiles.

When discussing small satellites, the international community has gen-erally agreed on the mass classifications shown in Table 2.1. Dimensional

Classification Mass (kg) Microsatellite 10 - 100

Nanosatellite 1 - 10 Picosatellite 0.1 - 1 Femtosatellite < 0.1

Table 2.1: Small satellites classification

challenges have recently led the solar sailing space industry to look at fem-tosatellites. As highlighted in Chapter 1, solar sail performance may be parametrised by the Sun-exposed area-to-mass ratio A/m. Through this pa-rameter, we can easily compute the satellite characteristic acceleration (a0) and its lightness number (β). The sub-100-grams satellites class includes

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spacecraft with significantly different values of characteristic acceleration. Starting from a0 on the order of 10−4 mm/s2, design advancements have led to a0on the order of 10−1mm/s2 [6]. Consequently, a subclasses subdivision is required because of such profoundly different thrust performances.

2.1 Femtosatellites subclasses

Femtosatellites architectures reported in this thesis are grouped in two sub-classes, as shown in Table 2.2.

Femtosatellites

< 0.245 A/m femtosatellites > 0.245 A/m femtosatellites (SpaceChips)

SWIFT Barnhart’s SpaceChip Manchester’s Sprite Pocket-PUCP Atchison’s Sprite

Corner-Cube SpaceChip PCBSat Coated-Sides SpaceChip Grated-Plate SpaceChip WikiSat SpaceChip with facets

SpaceChip with ElectroChromic System (ECS)

Table 2.2: Femtosatellites classification

This subdivision is based on the area-to-mass ratio A/m. According to Ref. [7] spacecraft with a area-to-mass ratios between 0.4 and 17.3 m2_/kg are classified as SpaceChips (or, alternatively, Satellites-on-a-Chip, or Chip-Sats). This lower limit refers to the Barnhart’s SpaceChip proposed in Ref. [8]. However, a recent interesting example of chip-scale device pro-posed by Z. Manchester in Ref. [9] is included in this subclass. Therefore its A/m lower limit has been extended to 0.245. The upper limit is referred to the ChipSat concept proposed in Ref. [6], but obviously technological advancements are going to lead to higher values.

The first femtosatellites subclass proposes spacecraft equipped with a certain number of components, providing multiple functionalities. On the contrary, SpaceChips have really essential components and they show an higher A/m with respect to the first subclass, enabling the use of photonic propulsion. When the orbital dynamics of SpaceChips significantly influ-ence the motion due to SRP and its Sun-exposed surface is covered with electrochromic materials, they are also termed as "engineered Smart-Dust devices", or simply Smart Dusts (SDs).

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This subdivision can be related to the characteristic sizes through a length-scaling process: the area-to-mass ratio increases with decreasing length scale because the mass scales as the length-scale cubed, whereas the area scales as the length-scale squared. The effect of length scaling for three different geometries (sphere, cube, and thin square plate) on environ-mental perturbations due to gravity, particle collisions, SRP, and magnetic fields has been analysed in Ref. [10]. It has been demonstrated that be-cause of length scaling, in some satellites (i.e., a ChipSats) some forces (i.e., the one coming from the SRP) that may be neglected for larger spacecraft, will dominate the acceleration of a small spacecraft. By harnessing these so-called perturbing forces to achieve useful thrust, novel methods for con-trolling attitude and orbit parameters are revealing.

Note that in analogy with Refs. [6] and [8], SpaceChip’s A/m values reported in this thesis are obtained considering the spacecraft’s "die mass" (that is, according to Ref. [8], the mass of the volume of the substrate on which the satellite subsystems are fabricated). Then, the resultant lightness numbers are overestimated.

2.2 An emerging technology

Femtosatellites are not a novel idea: first femtosatellites were lunched in May 1963 as part of the West Ford Experiment [11]. Actually, it was only a package containing 4.8 × 108 _{copper dipoles, each one having 17.8 µm of} diameter and 1.78 cm of length, placed into a nearly circular, nearly polar orbit at a mean altitude of 3650 km to allow passive global radio commu-nications. Arguably, these were not real satellites, but they set the stage for massively future distributed satellite concepts. The next appearance of a femtosatellite concept can be found in Ref. [12], where a rudimentary concept of a Satellite-on-a-Chip was proposed thirty years later. Several femtosatellite concepts have been proposed since then, following the minia-turization downward trend "Smaller, Lighter, Cheaper" of the electronics consumer in general.

Such tiny satellites are only recently feasible due to the miniaturization of commercial off-the-shelf (COTS) electrical components such as processors, solar cells, batteries, GPS receivers, cameras, and other micro-electromechanical systems (MEMS) components. Even with these advance-ments, M. Peck in Ref. [13] notes that miniaturization inevitably means

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limitation in terms of less power, fewer instruments, reduced ability to store and broadcast data. For example, a tiny surface area for solar cells means very limited power available to broadcast a radio signal. Moreover, the an-tenna clearly will be restricted in size. Regarding the propulsion system, there are several potential solutions for the femtosat platform, starting from exploiting the SRP force for producing thrust as proposed in this thesis. Al-ternatively, a passive, propellantless method relying on Lorentz force actu-ation has been proposed in Ref. [14]. Furthermore, technologies proven for CubeSats, such as MEMS thrusters may ultimately shrink to sub-100-grams masses in a not far future.

Despite these challenges, several groups are advancing the femtosatellites state of the art. For example, as Ref. [15] recalls, a competition called N-Prize (where "N" stands for Nanosatellite or Negligible Resources) was launched by a Cambridge biologist in 2008 and 60 teams were listed as competitors. The N-Prize was a contest to put a femtosatellite with a mass between 9.99 and 19.99 grams into orbit, spending less than £999.99 on the launch, and making it complete at least 9 orbits. It was established "to encourage creativity, originality and inventiveness in the face of severe odds and impossible financial restrictions".

Between 2007 and 2009 two different approaches in very-small-satellites design were proposed [8, 16]. The first one was a monolithic approach based on commercial complementary metal-on-silicon (CMOS) technology, which is the most common integrated-circuit (IC) fabrication technology. This approach led to the thumbnail-sized IC here named as Barnhart’s ChipSat putting the entire functionality on a chip-scale satellite. The second one was developed in parallel to the first one and it led to the spacecraft here named as PCBSat (Satellite-on-a-Printed-Circuit-Board). Unlike the first approach, it was a "bottoms-up" one: all the components of the electronic apparatus were mounted on and a finite set of payload and subsystem com-ponents, constrained by commercial off-the-shelf (COTS) parts availability, were integrated to determine the overall system capability, which in turn determined its range of applications.

2.2.1 Why femtosatellites?

There are mainly four reasons to consider femtosatellites for space missions: 1. a chip-scale design costs significantly less to put into orbit with re-spect to a kg-scale-design, and also has economic benefits when mass

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produced: if a mother-spacecraft deploys many femtosatellites after reaching orbit, the launch cost could be shared among several groups; 2. deploying a constellation of hundreds of tiny satellites provides inher-ent risk mitigation via redundancy: should even a large percinher-entage of the tiny satellites in a constellation fail to provide measurement data, the mission could still succeed;

3. this constellation can achieve interesting tasks that simply cannot be accomplished by one single large satellite orbiting alone: a cloud of femtosatellites could be coordinated to provide simultaneous measure-ments of space phenomena over a large 3D volume, while the mother-satellite orbits for further research objectives, aside from serving as ChipSat deployer;

4. the possibility to demonstrate useful propellantless mission.

In 2011 an entirely new approach for modelling and accounting for un-certainty in space missions was published in Ref. [17]. This work assigned the mission objective to a cloud of ChipSats, rather than a single satellite. A mission planning statistical approach was proposed, where the number of ChipSats deployed yielded to a particular confidence level of success. A set of equations governing the time-evolution of a cloud of ChipSats in terms of probability distributions was presented, discussing several methods for solv-ing them and concludsolv-ing that simply because there are many of them, the designer is dealing with a large sample size, and then statistical inferences can be made with greater confidence.

The cost saving advantage coming from the possibility to produce more economically multiple femtosatellites has been summarised in Ref. [18] through the trend curves shown in Fig. 2.1. The blue curve represents a minimum-capability 1U CubeSat while the other three curves represent different ap-proaches for femtosatellite manufacturing. These data points were derived from 2013 vendor component costs. It is important to clarify that SpaceChip results obtained through this data are based on theoretical space weather sensor design for a literal Satellite-on-a-Chip concept, but cost data are re-ferred only to the satellite die. In contrast, the other three approaches are based on actual existing component and sensor technologies, packaged in three different ways: traditional CubeSat, MCM-based (multi-chip module) packaging, PCB-based (printed circuit board) packaging. This preliminary

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Figure 2.1: Small satellites cost saving advantage: unit satellite cost when mass-produced, taken from Ref. [18]

cost model indicates that PCB-based manufacturing methods may be more cost-effective than MCM-based (multi-chip module) packaging. In any case, the per-unit cost decreases for every small satellite designs, if mass produc-tion is possible.

A cost and complexity comparison for competing small satellites tech-nologies is challenging at this stage of research due to the differing maturity of each technology. Fig. 2.2 shows a comparison between the relative com-plexity and the cost of "very-small satellites" [19]. In this picture relative

Figure 2.2: Very small satellite complexity VS cost, taken from Ref. [19] complexity is roughly estimated, based on the combined perception of the manufacturing technology maturity and the flexibility to adapt the design for various mission scenarios. Note that here "Satellite-on-a-Chip" does not included Atchison’s ChipSat and Smart-Dust concepts.

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Application opportunities

According to Ref. [19], femtosatellites are especially suited for distributed satellite systems, which can fall into two categories: cluster and constella-tion. The first type describes a local cluster, where the satellites positions are actively controlled to remain close to a common target. For example, formation flying would fall under this category. The second type describes multiple satellites sparsely distributed to achieve various mission objectives. In this thesis we will proceed considering a single SpaceChip, leaving to fu-ture works the opportunity to extend our results to a swarm of SpaceChips. Femtosatellites provide interesting opportunities both geocentric mis-sions and heliocentric ones. For example, they could detect and map iono-spheric plasma depletions. Alternatively, they could monitor terrestrial gamma ray flashes that sometimes occur during a lighting strike, as in-vestigated in Refs. [18, 19]. The mother-spacecraft could be a CubeSat containing a swarm of femtosatellites, deployed to collect imagery over a specified location on Earth. Each individual image would have a low reso-lution, but the collective imagery could be processed into a super-resolution composite photograph, as highlighted in Ref. [20]. Detailed mapping of the LEO drag environment could also be possible: femtosatellites could in-flate spherical balloons, becoming high drag spacecraft, broadcasting their GPS-derived locations, as proposed in Ref. [18]. Another near-Earth ap-plication could be the measurement of the deceleration due to atmospheric drag through ChipSats equipped with ultra-sensitive accelerometers, as il-lustrated in Ref. [19]. Moreover, in Ref. [17] an exotic scenario is suggested, in which a satellite could deploy a large number of ChipSats in a cloud formation aiming to impact a near-Earth object such that, statistically, at least one of them survives the impact and transmits sensor data from the surface of the asteroid.

Femtosatellites could also serve the needs of their mother spacecraft in interesting ways. For example, hundreds of femtosatellites could orbit their mother-ship to serve as one large sparse-aperture antenna. They could serve as satellite inspectors by assessing issues like: improper antenna de-ployment, micro-meteoroid damage, surface damage due to impact with materials from the upper stage, and decreased solar cell output due to sur-face contamination, as reported in Ref. [18].

Apart from near-Earth opportunities, femtosatellites provide interesting applications in heliocentric scenarios too. Next chapters focus on this topic.

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2.3 Less-than-0.245 A/m femtosatellite designs

SWIFT

The Silicon Wafer Integrated Femtosatellite (SWIFT) is an approximately 100-gram satellite made from 3D silicon wafer fabrication and integration techniques [21]. The design concept includes 6-DOF control, enabling a synergistic behaviour and interaction between the spacecraft. The goal of the designers was to launch in LEO a swarm of these femtosatellites capable of maintaining a specified 3D shape, such as the illustration in Fig. 2.3.

Po-Figure 2.3: SWIFT swarm mimicking the shape of ISS, taken from Ref. [21] tential missions that would benefit from such a constellation include: sparse aperture interferometers, distributed sensors for space weather monitoring and communication relays.

SWIFT acts as a transceiver and it has low mass and low power electron-ics for long distance communication. It is integrated at the chip-level, such that discrete components are evaluated and selected either within a package or separate packages. As depicted in Ref. [21], two prototypes based on two different propulsion system were designed. Table 2.3 collects SWIFT’s de-sign characteristics. The lightness number of SWIFT results prohibitive for solar sailing purposes. However, the dynamics of this satellite and its con-trol were deeply investigated. To sum up, it represents a promising study on guidance, control, and navigation methods for swarms of femtosatellites

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(a) Prototype with digital micro-thruster system; 1.6 W total power, 95.5 g total mass

(b) Prototype with miniaturized warm gas hydrazine system; 1.7 W total power, 104.7 g total mass

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Mass Size A/m a0 β Power Attitude

(g) (cm) (m2_/kg) _(mm/s2₎ _control

∼100 4 × 4 × 4.25 1.6 × 10−2 1.3 × 10−4 2.2 × 10−5 Batteries 3-axis Solar cells

Table 2.3: SWIFT characteristics, data from Ref. [21]

equipped with modest sensing and control capabilities. Pocket-PUCP

The first two satellites completely constructed in Peru happen to be a 1U CubeSat call PUCP-SAT-1, which carried and deployed an even smaller femtosatellite, Pocket-PUCP [22]. An artistic illustration of the satellite pair in orbit taken from Ref. [22], as well as a close-up photo of the real femtosatellite, are shown in Fig. 2.5. The satellite pair has made history as

Figure 2.5: PUCP-SAT-1 and Pocket-PUCP, taken from Ref. [22] the first CubeSat to effectively launch a femtosatellite. Nowadays, Pocket-PUCP remains the only femtosatellite to successfully operate in orbit after deployment from a mother-satellite.

Pocket-PUCP acts as a transceiver with 10 mW transmission power. It is equipped with one high efficiency (28%) GaInP/GaAs/Ge solar cell, a Li-polymer battery, radio, and three conduction sensors to monitor the temperatures of internal electric components. Its characteristics are sum-marised in Table 2.4.

It was launched on November 21, 2013. Thirteen days later, the PUCP team received the telemetry signal from PUCP-SAT-1, which indicated that the CubeSat was healthy and its batteries were recharging successfully. Two

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Mass Size A/m a0 β Power Attitude

97 8.4 × 4.9 × 1.6 4.2 × 10−2 3.5 × 10−4 5.9 × 10−5 Batteries 3-axis Solar cells

Table 2.4: Pocket-PUCP characteristics, data from Ref. [22]

days after that, on December 6, Pocket-PUCP was released from PUCP-SAT-1 at an orbital altitude of 630 km. Due to limited available power, Pocket-PUCP is able to transmit a very weak signal power of 10 mW in Morse code. From a link budget analysis, it was expected that the fem-tosatellite signal would be difficult to track, but this was further complicated by two challenges. First, the 8 meters ground dish was not yet fully con-structed, thus only Yagi antennas were available. Second, after its deploy-ment from the CubeSat, Pocket-PUCP’s position was not exactly known. Eventually, after a few months, a weak signal was detected with the help of a radio receiver.

PCBSat

After two revisions, a PCBSat for distributed satellite system providing real time, simultaneous, multi-pointing sensing was proposed in 2009 [8, 19]. Figure 2.6 represents the PCBSat final system configuration.

The design is confined to a single PC104 form factor configuration. It has been programmed that next phases of the project would give a complete space system engineering approach, addressing the structure and the space environment issues. The final system configuration summarised in Table 2.5 is compatible with existing Poly Picosat Orbital Deployer (P-POD) space-craft separation mechanism, in which 15 PCBSats could be jettisoned from each P-POD. Table 2.5 demonstrates that a PCBSat has not sufficiently good solar sailing performances for our purposes. Despite this, the commu-nity has usually envisioned one or more than one of those femtosatellites for Earth orbit missions, using solar energy as the power source and requiring a larger satellite to serve as an intermediary telemetry relay. Therefore, a swarm of PCBSats could be used to take simultaneous measurements of phenomena over a large 3D volume aimed at detecting and mapping of "plasma bubbles" (more known as ionospheric plasma depletions), or at detailed mapping LEO drag environment.

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(a) Front side

(b) Back side

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System mass 70g

Dimensions 9 × 9.5 × 1 cm (PC104) A/m 0.12 m2_/kg

a0 10−3mm/s2

β 1.7 × 10−4

Cost $300 per prototype Payload 640 x 480 CMOS Imager Electrical power subsystem 3.3V regulated system bus

689mW silicon solar array 645 mAh Li-ion battery

Peak power tracking Battery charge regulation

6-channel telemetry Communications system 2.4 GHz, 60mW RF Attitude and orbit control systems GPS receiver

Front and back digital sun sensors Single-axis magnetotorquer

Thermal Solar cell and battery temperature telemetry Propulsion None planned

Table 2.5: PCBSat current system configuration, data from Ref. [19]

WikiSat

The WikiSat research group is one of the teams competing for N-Prize and their ongoing research effort is to design a femtosatellite called WikiSat [23]. From left to right in Fig. 2.7 are shown WikiSat version 1, 2, 3, 4 and ver-sion 4 without the battery. Components chosen are COTS, with the goal of

Figure 2.7: WikiSat prototypes, taken from Ref. [23]

achieving accuracy and reliability at a low cost.The subsystem requirements are met while staying within the 19.99 grams mass constraint levied by the N-prize. The power system relies on a coin cell battery, but this is iden-tified as undesirable because of the limited power available. Other chosen key components include: fiberglass as the structural base, optic sensors and Inertial Measurement Unit for attitude and position determination, surface

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mount Low-noise Amplifier and high gain antenna for transmission, magne-torquer for attitude control, and 1.3 Mpx HD camera for imagery. WikiSat acts as a transceiver and the prototype has not been tested in orbit yet, even if many simulations and validation tests were performed in labs.

Table 2.6 recalls WikiSat’s relevant characteristics. WikiSat’s

area-to-Mass Size A/m a₀ β Power Attitude

∼20 14 × 3 × 0.7 0.21 1.7 × 10−3 _{2.9 × 10}−4 _Batteries _3-axis Table 2.6: WikiSat characteristics, data from Ref. [23]

mass ratio is really close to the Barnhart’s SpaceChip one.

2.4 SpaceChips: towards Smart-Dust devices

A SpaceChip houses all of the functionality of a satellite on a monolithic thumbnail-sized integrated circuit (IC): discrete components are not at-tached separately and design approach relies on commercial complementary metal-on-silicon (CMOS) technologies. This design has evolved from Barn-hart’s ChipSat and Manchester’s Sprite into Smart Dust designs based on the Atchison’s ChipSat.

2.4.1 Barnhart’s SpaceChip

Barnhart’s team research proposed a SpaceChip design in 2007. The ref-erence mission envisaged a fleet of SpaceChips, deployed from a host small satellite in LEO, that would naturally drift apart, collecting scientific data, and transmitting this information back to the host satellite for relay to Earth [8]. The maximum range achieved between SpaceChip and host was 5 m in testing, which was well below the mission requirement of 1 km.

CMOS processes available when this satellite was designed allowed to es-timate an IC area of 20 × 20 mm. Assuming a silicon density of 2330 kg/m3 and wafer thickness of 0.75 mm, the die mass would be approximately 1 g. Successive silicon fabrication advancement have fixed more advantageous manufacturing dimensions limits allowing less die mass, as we will see in the Atchison’s Sprite design. The design of this SpaceChip provided for two identical die sandwiched together with the active sides facing outward. This solves the issue of maintaining the active side of the wafer towards the

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Sun: one side at a time is active due to solar illumination. It was estimated a final mass of approximately 10 g for a thickness of 3 mm. A notional representation of Barnhart’s SpaceChip is illustrated in Fig. 2.8.

Figure 2.8: Notional Barnhart’s SpaceChip representation, taken from Ref. [8]

The Satellite-on-a-Chip approach greatly limited payload options: con-sidering the reference mission, no sensors on a chip scale were possible at this time to detect plasma-bubble phenomenon, so, for demonstration pur-poses, a visible CMOS imager was considered as payload for the feasibility study. Table 2.7 summarises Barnhart’s SpaceChip system requirements and testing outcomes.

According to Ref. [8], the main advantage (i. e., the cost) of the Satellite-on-a-Chip approach was satisfied in the prototype proposed by Barnhart. A potential cost of under $1000 per satellite node in volume quantities was estimated. Deploying 1000 SpaceChips would cost $1 million plus launch costs of $50,000 for the 10-kg mass, assuming a midrange launch cost of $5000/kg.

D. J. Barnhart in Ref. [8] affirmed: «Although SpaceChip cannot cur-rently support the reference mission, it is still potentially suitable for simple missions, but any mission architecture will require a co-orbiting relay satel-lite. As Satellite-on-a-Chip technology improves, perhaps SpaceChip will be able to support a wider range of interesting missions». As Table 2.8 high-lights, its β (computed considering the die mass of approximately 1 gram [7]) is too low to enable solar sailing, even being greater than femtosatel-lites described in Section 2.3. However, Barnhart’s words predicted what happened some years later: J. Atchison’s team designed a lighter, more

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System Requirements Outcomes Top level SpaceChip shall be implemented on commercial CMOS tech SiGe-Bi CMOS

0.35µm thickness Payload The payload shall detect space weather phenomenons Limited options

A simple demonstration payload shall be considered CMOS Imager Orbit SpaceChip shall operate in an orbit to support the mission ∼500km altitude

low inclination Config and Configuration shall be a monolithic Satellite-on-a-Chip Deviations required

structure Size shall not exceed typical CMOS process reticle limit 20 x 20 mm max

Mass shall be less than 10 g ∼10g package

The design shall incorporate a launch-vehicle interface TBD Power Power source shall be solar energy via integrated solar cells ∼1mW budget

Secondary power storage shall be investigated No monolithic options

Data Shall be based on a low-power Design-hardened

handling reduced-instruction-set microcontroller asynchronous Nonvolatile memory technologies shall be investigated microcontroller Design shall withstand natural radiation environment

Telecom 2.4-GHz unlicensed ISM band shall be used 1µW RF, 1km range External antenna required AOCS Attitude determination shall not be required Passive ADCS

Orbit-determination options shall be investigated No orbit determination possible Propulsion Propulsion shall not be required No monolithic option

Thermal Passive control shall be used Thermal substrate

Table 2.7: Barnhart’s SpaceChip outcomes, data from Ref. [8]

A/m a0 β

(m2_/kg) _(mm/s2₎

0.4 3.3 × 10−3 5.5 × 10−4

Table 2.8: Barnhart’s Spacechip solar sailing performances

compact, SpaceChip reaching lightness numbers of the order of 10−2 thanks to miniaturisation process advancements.

2.4.2 Manchester’s Sprite

Figure 2.9 shows a ChipSat prototype nicknamed "Sprite". The idea was initially proposed by Z. Manchester, an american graduate student at Cor-nell University. It was designed and developed at CorCor-nell University, rising much of the funding through the crowd-funding website Kickstarter. In 2010, J. Atchison (one of the major contributors to SDs advancements), highlighted how this ChipSat efficiently contained the essential components to transmit a signal: "Seven tiny solar cells, a micro-processor with a built-in radio, an antenna, an amplifier, and switchbuilt-ing circuitry to turn on the microprocessor whenever there is enough stored energy to create a single radio-frequency emission, a digital beep". The main goal of this ChipSat was ultimately satisfied: it effectively brings down the huge cost of

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space-Figure 2.9: Manchester’s Sprite, taken from Ref. [9]

flight, demonstrating how anyone, from a university student to a professional scientist, could explore what has been the exclusive realm of governments and large companies.

Table 2.9 shows Manchester’s Sprite solar sailing performances. Note that the lightness number of the Manchester’s Sprite is not as high as re-quired for solar sailing purposes. However, this femtosatellite plays a key

A/m a0 β

(m2_/kg) _(mm/s2₎

0.245 2.0 × 10−3 3.4 × 10−4

Table 2.9: Manchester’s Sprite solar sailing performances, data from Ref. [9]

role in this thesis for the following motivations:

• apart from the Pocket-PUCP, this is the only femtosatellite that was inserted in a real space mission;

• Manchester’s Sprites’ mother-sat can be considered as a suitable de-ployer of secondary payloads for mission scenarios involving ChipSats like SDs considered in this thesis;

• the deploying ∆V of the Manchester’s Sprites’ can be assumed as SD deploying relative velocity from the mother-satellite;

• this SpaceChip was developed in the same University where J. A. Atchison and M. A. Peck designed a satellite also nicknamed "Sprite" and here named as "Atchison’s ChipSat" (see Chapter 3).

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Mission profiles

Manchester’s SpaceChip has been part of two important missions.

First, in 2011, three Sprite prototypes were included in MISSE-8 (Ma-terials International Space Station Experiment), an external test-bed for studying how materials are effected by the space environment. The Chip-Sats were not deployed into orbit, but they were mounted on the external pallet for two years and 51 days and then returned to be studied. Fig-ure 2.10 shows the three Sprite units on MISSE-8 and where the experi-ment was mounted on the outside of ISS. From left to right, we can see the

Figure 2.10: Manchester’s Sprites mounted on ISS, taken from Ref. [9] three Sprite test articles (circled in yellow), the MISSE8 mounted outside of ISS, and the deployment of MISSE-8 (circled in red) relative to the ISS structure. One of the objectives was to establish if the transmitted radio pulses could be detected on the ground, but this was never achieved. The other goal was testing the electrical components in a space environment. The group at Cornell determined that two of the three returned units could still function and transmit a strong radio signal.

In April 2014, 104 Sprites were launched inside of a larger 3U Cube-Sat called KickCube-Sat, as part of the Educational Launch of Nanosatellites program. The goal of the mission was to track their signals and thereby demonstrate that direct communication between femtosatellites in LEO and Earth ground stations is possible. Also, they should proof that the COTS, non-radiation-hardened, electronic components could operate in the space environment. Unfortunately, after reaching LEO, the 3U mother-sat suf-fered a master clock reset (suspected to be due to a radiation event) and the software did not initiate the deployment of the Sprites prior to KickSat re-entering the atmosphere. The Cornell research group will try again: it is planning to launch a KickSat-2. In February 2015, NASA announced that KickSat-2 has been selected for launch as part of its CubeSat Launch Initiative.

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ChipSat structure

The Sprite uses modern, low-cost, low-power ICs to create a general purpose spacecraft bus for chip-scale sensors. It includes solar cells, a microcontroller clocked at 8 Mhz and radio system-on-chip, a 3-axis magnetometer, and a 3-axis MEMS gyro, as well as associated passive components, on a printed circuit board measuring 3.5 × 3.5 centimetres with a mass of 5 grams. Its core provides 4 kB of RAM and 32 kB of flash memory. Manchester’s SpaceChip acts only as a transceiver, with output powers up to 10 mW and data rates up to 500 kbps.

Sprite’s antenna has an isotropic gain pattern and it is can easily tuned. The antenna is made of nitinol, a nickel-titanium alloy commonly referred to as "shape-memory alloy" or "memory metal", which can be deformed to a tremendous degree and still return to its original shape. Nitinol was chosen so that the antenna could be coiled within the small footprint of the Sprite PCB and still return to its intended geometry upon deployment.

Solar cells deliver up to 60 mA of current at 2.2 Volts directly to the electronics with no energy storage or power conditioning. The maximum current consumption of the Sprite is approximately 35 mA, so there is con-siderable margin. Several lithium-ion and lithium-polymer batteries that fit the size, mass, and power constraints of the Sprite were investigated, but it was determined that none could survive the low temperatures encountered during eclipse. Therefore, the Sprites can operate only in sunlight and will be completely unpowered over the night-side of the Earth.

Sprites deployer

KickSat is a 3U CubeSat consisting of a 1U bus and a 2U Sprite deployer as Fig. 2.11 illustrates. The bus is built using primarily COTS components, and it provides power, communication, command and data handling, and attitude determination and control functions. The deployer contains 128 Sprites stacked in four columns in a 2-by-2 arrangement.

Each Sprite is housed in an individual slot and constrained by a carbon fibre rod that runs the length of the column, passing through a hole in the corner of every Sprite, as shown in Fig. 2.12. The nitinol wire antennas on the Sprites are coiled in such a way that they act as springs, pushing the Sprites out of their slots. All four carbon fibre rods are attached to a single plate at the end of the deployer that is actuated by a compressed spring and held in place by the locking mechanism shown in Fig. 2.12. The deployment

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Figure 2.11: KickSat spacecraft deployer, taken from Ref. [9]

(a) Sprite housing (b) Deployer locking mechanism

Figure 2.12: Manchester’s Sprites in KickSat, taken from Ref. [9]

is triggered by a nichrome burn wire which unlocks the mechanism, allowing the spring to pull the four rods out. Then, the antennas push them from the deployer housing with an estimated ∆V of 5-10 cm/s.

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Chapter

3

Smart-Dust devices

A Smart-Dust device is an innovative and fascinating femtosatellite concept that explores how small a functional spacecraft can be nowadays feasible. A SD is characterised by a side length of some centimetres and high values of the area-to-mass ratio. Its Sun-exposed surface is usually coated with elec-trochromic material. It can be thought as the evolution of the traditional Satellite-on-a-Chips concept treated in the previous Chapter. The solar ra-diation pressure produces a significant propulsive acceleration, sufficient for modifying its trajectory. As the optical properties of the electrochromic material change with the application of suitable voltage, the SD propul-sive acceleration may be modulated within some limits. This variation can regard the modulus of the acceleration vector, its direction or both of them. The "Sprite" bus design proposed by J. A. Atchison and M. A. Peck (see Ref. [6]), has been selected as SD design guideline. Its layout is depicted in Fig. 3.1. The intrinsic limit of this technology is, of course, in the extremely reduced payload mass that can be stowed on-board and in a substantial number of problem related to the miniaturization approach that currently have no solution.

In accordance with the specific literature, Atchison’s ChipSat is com-monly retained a SD, even if the electrochromic covering was not considered in its initial design.

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Figure 3.1: Atchison’s Sprite bus layout, taken from Ref. [6]

3.1 Atchison’s ChipSat

3.1.1 Ensemble characteristics

Structure

The structure of this spacecraft consists of a volume of semi-conductive substrate on which the other subsystems are fabricated. A gallium-arsenide substrate offers desirable radiation hardening and the opportunity to pro-duce high efficiency solar cells. However, the cost of integrating MEMS subsystems on such a substrate may discourage its use. Therefore, a more common silicon substrate has been used. At 2300 kg/m3, solid Silicon is significantly denser than 100 kg/m3_.

Like traditional structural subsystems, the substrate has to support and mechanically interface the other subsystems, facilitate ground handling, and withstand vibrations during transportation and launch. The SD design is less concerned with vibration control because the natural frequencies of such a structure are far higher than the likely attitude-control bandwidth of any launch vehicle and the SD itself. The design is based on the lightest structure on which components can be fabricated: the thinnest possible substrate for a required surface area. For polished silicon wafers, this limit is approximately 200 µm (thinner silicon is too brittle to machine). Silicon-on-Insulator (SOI) wafers are an alternative. Such wafers consist of an ultra-thin layer of silicon on top of a siliconoxide layer. This substrate offers

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structural rigidity and handling during fabrication, after which the silicon-oxide layer can be removed to leave the processed device on the ultra-thin silicon layer. Then, arbitrarily thin silicon can be produced, although the thickness in this thesishas a conservative minimum value of 25 µm.

J. A. Atchison estimated that sufficient functionality can be achieved in 1 cm2_{. It has been considered a flip-chip fabrication method, in order to} maximise the use of the surface area. In this process, two chips are manufac-tured such that their backsides can be mated and both chips face outward. This technique allows the MII spacecraft to incorporate devices whose fab-rication techniques are incompatible by producing them separately and in-tegrating them as a final step. The placement of solar cells on both sides of the chip ensures that power is always available, regardless of attitude.

The mass of a 1 cm2 silicon substrate is 5.75 mg. For conservatism, the mass budget includes 30% margin, yielding a total mass of 7.46 mg. This value has been used in this thesis. Even if the silicon fabrication process consists of additive and subtractive processes, which add or remove material from the substrate to form a device, the net contribution of these processes has been assumed to be negligible.

Propulsion

Traditional propellant mechanisms such as chemical or ion thrust systems cannot be easily scaled to the IC level. A novel exception is the so called "digital propulsion". A device that delivers discrete amounts of thrust using microscopic chambers and chemical propellant has been manufactured [25]. Though digital propulsion may prove relevant for research in the long run, the current research in ChipSats is motivated primarily by propellantless propulsion approaches (i.e., by harnessing SRP as demonstrated in this thesis).

Future work could probably include Lorentz force actuation as a means of propellantless propulsion for near-Earth missions by examining the ac-celeration and plasma-charging benefits associated with small length scales. This mean has been proposed for a 1 cm2_{× 500 µm SpaceChip concept in} Ref. [14], estimating a total mass of 0.15 grams. This concept would pas-sively orients itself along the line of action of the Lorentz force and then it could offer an alternative approach in the attitude control with respect to the SPR-based one proposed in this work.

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Communications

An obvious challenge for a Satellite-on-a-Chip is the communication subsys-tem. Since 2007, D. J. Barnhart in Ref. [8] considered the communication subsystem a key factor that limits SpaceChip applicability and even nowa-days this problem as not a clear solution.

Barnhart’s SpaceChip design resulted in a maximum communication range of only 5 meters between the SpaceChip and a host satellite in a geocentric mission scenario. For Atchison’s SpaceChip it has been demon-strated what are the results for a near-Earth orbiting mission at 500 km alti-tude in which is required data transmission directly with the Earth station. Nowadays, it is nearly impossible to design a telecommunication system al-lowing SpaceChip’s data transmission directly with Earth in a heliocentric SpaceChip mission scenario. Hence, a potential solution would be to exploit a mother-satellite orbiting in its vicinity, serving as the master relay to the ground station.

Atchison’s Sprite communications subsystem has been conceived as a continuously transmit-only beacon. Data consist of a single beep at a single frequency: a binary output based on the presence or absence of the carrier. The carrier frequency would likely be generated by a crystal oscillator. Such a oscillator circuit uses the mechanical resonance of a vibrating crystal of piezoelectric material (i. e., an electric charge accumulates in response to applied mechanical stress) to create an electrical signal with a precise frequency.

The frequency stability of a crystal oscillator depends on the temper-ature. This dependence can be characterised and used to infer data on temperature. The carrier signal would then be impedance matched to an antenna consisting of two very thin 17 cm stiff filaments radiating from the chip. The impedance matching can be achieved with micro-fabricated capacitors and inductors. Such resultant RLC oscillator circuit aimed to produce temperature-dependant RF beacon could receive energy from a storage capacitor triggered by a transistor.

Power

Solar cell power generation is the natural choice for power in our application. Silicon-based (first generation) solar cells have been selected„ which use a single-layer p-n junction diode to pass photovoltaic currents. With sets of individual cells strategically connected in parallel or series, an array can be

Smart Dust Relative Motion in a Heliocentric Mission Scenario

Department of Civil and Industrial

Engineering

Master of Science in Space Engineering

Smart Dust Relative Motion in a

Heliocentric Mission Scenario

Candidate:

Antonio Figliuolo

Advisors:

Prof. Alessandro A. Quarta

Prof. Giovanni Mengali

Engr. Marco Bassetto

Engr. Lorenzo Niccolai

Academic year 2016/2017

Aknowledgements

Contents

List of Figures

List of Tables

Chapter

1

Solar sailing

1.1

Introduction

1.2

Foundation of solar radiation pressure

1.3

Force on an ideal solar sail

1.4

Solar sail heliocentric orbital dynamics

1.4.1

Orientation of ideal solar sail force vector

1.4.2

Polar equations of motion

Chapter

2

Femtosatellites

2.1

Femtosatellites subclasses

2.2

An emerging technology

2.2.1

Why femtosatellites?

2.3

Less-than-0.245 A/m femtosatellite designs

2.4

SpaceChips: towards Smart-Dust devices

2.4.1

Barnhart’s SpaceChip

2.4.2

Manchester’s Sprite

Chapter

3

Smart-Dust devices

3.1

Atchison’s ChipSat

3.1.1

Ensemble characteristics