Feasibility Study of the Implementation of a Space Sunshade Near the First Lagrangian Point

DEGREE PROJECT IN MECHANICAL ENGINEERING, SECOND CYCLE, 30 CREDITS STOCKHOLM, SWEDEN 2020

Feasibility study of the implementation of a space sunshade near the first Lagrangian point

MARÍA GARCÍA DE HERREROS MICIANO

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES Feasibility study of the implementation of a space sunshade near the ﬁrst Lagrangian point

MARÍA GARCÍA DE HERREROS MICIANO

Master in Aerospace Engineering Date: July 15, 2020 Supervisor: Christer Fuglesang Examiner: Christer Fuglesang School of Engineering Sciences Swedish title: Möjlighetsstudie av solparasoll i rymden nära Lagrangepunt L1

III

Abstract

The lack of strong measures to avoid the possible fatal consequences of global warming is pushing researchers to look for other alternatives such as geoengineering. Within geoengineering, this study focuses on the space based solar radiation management methods. More precisely, the project evaluates the feasibility of implementing a space sun shade near the first Lagrangian point in the Sun-Earth system within a thirty year period time from now. The study is structured in three main blocks: spacecraft configuration, trajectory definition and launch. An analysis looking at the minimum cost system was carried out, starting with the definition of the mass and size of spacecraft. Furthermore, an optimization of the trajectory was developed in order to minimize the travel time to the vicinity of the Lagrangian point. The shades will be formed by swarms of 10 000 m2 solar sails that will cover an area of 6.3 × 1012 m2 with a total mass of around 5.7 × 1010 kg. The sails will be injected into a LEO and will start a trajectory to the vicinity of the first Lagrangian point that will take around 2.3 years. The total cost of the project is approximated to be 10 trillion dollars. The mission appears to be feasible from a technological point of view, with some development needed in the attitude control subsystem. The main challenge will be the launch of all the spacecraft. A space mission of this dimensions has never been attempted before so it will require a big advance from the launch vehicle industry. IV

Sammanfattning

Bristen på åtgärder för att undvika de konsekvenser som den globala uppvär- mingen leder till, har drivit forskare att leta efter alternativa lösningar, varav geoengineering är en av dem. Denna studie fokuserar på rymdbaserade strål- hanteringsmetoder, mer specifikt på hur huruvida implementationer av solpa- rasoller nära Lagrangepunkten L1 i sol-jord-systemet är möjlig eller ej. Studi- en är strukturerad i tre huvudsakliga block: rymdskeppskonfiguration, banade- finition och uppskjutning. Med målet att minimera kostnaderna, definierades rymdskeppets utforming, massa och storlek. Vidare så, optimerades vägen till närheten av L1 med avseende på att minimera tiden. Solparasollerna kommer vara placerade i svärmar med en area på 10 000 m2 vardera, totalt kommer solparasollerna att täcka en yta av 6.3 × 1012 m2 med en total massa på 5.7 × 1010 kg. Solparasollerna kommer skjutas upp till LEO och därefter star- ta sin resa till närheten av L1, vilket kommer ta cirka 2.3 år. Totala kostanden för projektet uppskattas till 10 billioner dollar. Efter genomförd studie visades projektet vara genomförbart sett från en teknisk synvinkel, men vidare studi- er behövs göras för att utveckla och fastställa styrsystemet. Huvudutmaningen kommer att vara uppskjutningen av rymdskeppen, då det kräver stora framsteg och utveckling inom rymdindustrin. Contents

1 Introduction 1 1.1 Current Climate Situation and Policies ...... 1 1.2 Geoengineering the Climate ...... 3 1.3 Literature Review on Space Sun Shades ...... 4 1.4 Present Work ...... 5

2 Methodology 7 2.1 Initial Assumptions ...... 7 2.2 Launch ...... 8 2.2.1 Launcher Selection and Assumptions ...... 8 2.2.2 Target orbit ...... 9 2.3 Trajectory ...... 11 2.3.1 Reference Frames ...... 11 2.3.2 Solar Sail Dynamics ...... 12 2.3.3 New Equilibrium Point ...... 15 2.3.4 Escape Trajectory Optimization ...... 15 2.3.5 Trajectory to Sub-L1 Optimization ...... 16 2.4 Spacecraft Conﬁguration ...... 18 2.4.1 Total Mass and Size Study ...... 19 2.4.2 Mass Budget ...... 20 2.4.3 Control ...... 21

3 Results 24 3.1 Spacecraft Conﬁguration ...... 24 3.1.1 Total Mass and Size ...... 24 3.1.2 Mass Budget ...... 28 3.1.3 Control ...... 29 3.2 Launch ...... 31 3.2.1 Launcher Selection ...... 31

V VI CONTENTS

3.2.2 Launch in Numbers ...... 32 3.2.3 Target Orbit Deﬁnition ...... 33 3.3 Final Trajectory ...... 33 3.3.1 Escape Trajectory ...... 34 3.3.2 Travel to Sub-L1 ...... 35

4 Cost Analysis 40 4.1 Launch Cost ...... 40 4.2 Spacecraft Cost ...... 41

5 Discussion 43 5.1 Spacecraft ...... 43 5.2 Launch ...... 46 5.2.1 Launch in Numbers ...... 46 5.2.2 Environmental Impact ...... 47 5.3 Trajectory Results ...... 49 5.4 Cost ...... 50

6 Conclusions 52 Chapter 1

Introduction

The emissions of greenhouse gases (GHG) have been changing the planet for decades but it was not until ﬁfteen years ago, with the Kyoto Protocol, that climate change started to get attention from governments. Since then, the importance of it has been growing. However, up to now actions against it have not been taken with the urgency that the problem requires in order to avoid possible fatal consequences [1] [2]. This is pushing researchers to look for alternatives away from the reduction of greenhouse gases emissions, which as time passes seems harder to achieve on time and requires the commitment of the whole world [3] [4].

1.1 Current Climate Situation and Policies

Since the pre-industrial age, the world’s climate has changed signiﬁcantly because of the emission of GHG, but there has been a great acceleration of these changes in the past ﬁfty years. The main contribution to the emissions is fossil carbon dioxide (CO2), which mainly comes form energy and industrial use. This explains the acceleration during the industrial era and specially in the last decades.

After 2010, GHG emissions have been growing at a rate of 1.5 per cent per year and the peak of these emissions does not seem like it is going to take place any time soon [2]. Every year that this peak is delayed translates into a larger rise of the global mean temperature by the end of the century. Diﬀerent scenarios are considered by the United Nations–sponsored Intergovernmental Panel on Climate Change concluding that in order to stabilize the mean global temperature around 2◦C above pre-industrial levels by 2100, this peak should

1 2 CHAPTER 1. INTRODUCTION

take place between 2020 and 2050 [5].

By 2017 temperature had already risen 1◦C [5] and as a consequence global warming effects are already observable on the planet, although these will be more intense in the following decades [6]. Some of the most important are the rise of sea level as a result of the melting ice, the increase of extreme weather events such as droughts, heavy rainfalls or heatwaves, the extinction of plant and animal species, the reduction of crop fields and the increase of wildfires [7]. All these phenomena translate in large costs for society (increase in mor- tality, consequences in human health) and economy (damage of infrastructure, agriculture, tourism and energy sectors).

The most recent international agreement regarding climate change was the Paris Agreement (2016), ratified by 187 countries as of 2019. Here, all signa- tories compromised to: “holding the increase in the global average temperature to well below 2◦C above pre-industrial levels and pursuing efforts to limit the temperature increase to 1.5◦C" [8]. Therefore, the upper limit that should not be trespassed is nowadays set to 2◦C. It must be kept in mind that the 0.5◦C difference between both limits means a significant increase in the intensity of the global warming effects mentioned above [5].

With the current climate policies and the ones expected to be implemented in the following years, by the end of the century temperature is predicted to rise between 2.6◦C and 3.7◦C, depending on the compliance with these policies [1]. Thus, it seems clear that stronger measures need to be taken to reduce GHG emissions in order to achieve the deﬁned goals. To meet the 1.5◦C limit, global CO2 emissions would need to reach zero by 2050 and keep decreasing afterwards. This means that emissions would need to start dropping immedi- ately at a faster rate than ever and once zero emissions were reached, carbon removal techniques would have to be implemented [9]. The chances of achiev- ing these objectives seem remote, specially keeping in mind that, in order to do so, an international response needs to be coordinated on a global level. Oth- erwise, despite all the climate policies that are being implemented in a lot of countries, the decrease of emissions in these will not be enough to oﬀset the increase in others [2]. CHAPTER 1. INTRODUCTION 3

1.2 Geoengineering the Climate

As it has been described before, historically the dominant approach to fight climate change has been the reduction of GHG emissions. While the achieve- ment of the necessary levels of emissions in time is each year further away from reaching the goal, other alternatives are being considered in addition to these reductions. One of the options is so-called geoengineering, which consists on deliberately modifying Earth’s environment in order to counteract climate change. As addressed in Geoengineering the climate. Science, governance and uncertainty [3], these measures are still highly controversial but they are alternatives that can provide help, mitigating both short-term and long-term global warming effects. Despite being an important alternative to be considered, it must be acknowledged that geoengineering methods should not be seen as a solution but as part of a larger set of measures to fight climate change.

Geoengineering techniques can be divided in two different groups: Carbon Dioxide Removal (CDR) and Solar Radiation Management (SRM). The first group aims to reduce the level of carbon dioxide in the atmosphere, while SRM techniques reduce the net incoming solar radiation received at the surface of the planet by deflecting it before reaching Earth or increasing the reflectivity of the planet surface or its atmosphere. Inside the second group, it is possible to find different techniques, such as the release of stratospheric aerosols, surface albedo enhancement or space based techniques. Although space based proposals are not seen as affordable given their large cost and necessary technology development, they have two important advantages compared to Earth based techniques: they do not require the modification of the Earth surface or atmosphere and they have a more uniform effect [3]. Furthermore, they would be the most cost effective if long term geoengineering is necessary [3].

The implementation of the space based proposals aims to reduce the solar radiation reaching Earth. Theoretical calculations [10] point out that, in order to be able to oﬀset the eﬀects caused by a doubling of the carbon dioxide content in the atmosphere (compared to pre-industrial levels) the solar radiation would need to be reduced 1.7% . This would be equivalent to reducing the average global temperature by approximately 2◦C [11]. 4 CHAPTER 1. INTRODUCTION

Table 1.1: Literature review. Authors Year Concept Total mass (tonnes) Mautner [12] 1991 Solar screen orbiting the Earth 108 − 109 Reﬂecting discs in L1 2.6 × 108 McInnes [17] 2002 Absorbing discs in L1 5.2 × 107 Particle rings orbiting the Earth 5 × 109 Pearson et al. [13] 2002 Spacecraft rings orbiting the Earth 2.3 × 1012 Angel [15] 2006 Cloud of spacecraft near L1 2.3 × 1012 Struck [14] 2007 Dust clouds at stable lunar Lagrange points 2.1 × 1011 Sánchez & McInnes [16] 2015 Discs in orbit near L1 1.4 × 107

1.3 Literature Review on Space Sun Shades

Among SRM geoengineering methods, space based techniques aim to avoid part of the solar radiation from reaching Earth’s atmosphere. The implementation of these techniques has been discussed numerous times in the literature, considering a wide range of alternatives that can be found in Table 1.1. The creation of reflective rings in orbits around Earth has been mentioned by different authors as Mautner [12] and Pearson et al. [13], but these techniques would create a large orbital debris hazard and they could affect how light is perceived from the surface of the planet [11]. Other options considered are related to the use of stable points in space to place these reflectors, both in the Moon-Earth system (Struck [14]) and the Sun-Earth system (Angel [15], Sánchez and McInnes [16], McInnes [17]). Out of these, the most effective method so far appears to be the use of the L1 point in the Earth-Sun system [11], since the use of the Earth-Moon system stable points would only allow to reduce solar radiation for a certain period of time each month. On the con- trary, the use of the first Lagrange point, which is located in the Sun-Earth line, would reduce solar radiation the whole time the reflector is in place.

The type of reﬂectors used to avoid sunlight from reaching Earth has also been discussed as well as where they should be manufactured. Struck [14], Pearson et al. [13] and Mautner [12] considered the use of clouds of dust particles that should be obtained from asteroids or the moon surface. Other and more recent authors consider diﬀerent kinds of spacecraft, with various levels of control over their movement. Angel [15] proposes the use of a large number of small and light vehicles placed in a random cloud with little control, mean- while Sánchez and McInnes [16] present two discs in a certain controlled orbit close to the L1 point. As pointed out by McInnes [17], the large discs proposed would need to be manufactured in space, while a smaller spacecrafts could be CHAPTER 1. INTRODUCTION 5

manufactured on Earth, as Angel [15] describes.

Comparing the mass to make these studies a reality, as it can be seen in Table 1.1, the lightest option proposed is the most recent one [16], but the mass of the system is not always a driver in this case. For those proposals built in space, the mass is not a constraining factor. Although a new constraining factor appears here, which is the necessary advance in technology to be able to mass produce in space, which so far is not even contemplated.

1.4 Present Work

The aim of this project is to study the feasibility of the realization of space based geoengineering ideas in the near future. Considering the studies described in section 1.3, among all these methods, the alternative which is ap- parently more eﬀective is the deployment of large discs in the vicinity of the ﬁrst Lagrange point.

One of the problems faced by the most common space based techniques proposed is that, even though a uniform reduction of the solar radiation would decrease the global mean temperature, the effects at a regional level would change depending on the latitude [3]. More precisely, as studied in [16], there would be a cooling of latitudes close to the equator and a warming of the poles. This is the reason why the most recent study regarding this type of geoengineering option [16] studies the optimal configuration of the shades in order to minimize the differences. The final result of the paper written by Sánchez and McInnes [16] leads to the deployment of two discs orbiting around the sub-L1 point (new point resulting of the equilibrium of gravitational forces and solar radiation pressure). From now on, it will be assumed that this is the configuration of the shades to be deployed. The area and exact orbit of the discs are to be defined further in the project once the features of the spacecraft are described.

Since the goal is to ﬁnd the best mean to accomplish the deployment of the shades in the following decades, the approach is focused on their trajectory to the vicinity of the ﬁrst Lagrange point, the features of the spacecraft used regarding control and layout, and the launch of these spacecraft into orbit. The technologies contemplated in the project already exist or are being developed inside the space sector, with technology readiness levels between four and nine. As any other space mission, and specially given the dimensions 6 CHAPTER 1. INTRODUCTION

of this project that can be anticipated going back to the literature study, the leading driver during the study is the cost of the mission, which in space usually translates into mass. On a second level it is also considered the time of the mission. The reason for the lesser importance given to the time is that the period in which the shades should be put into place is not speciﬁcally deﬁned.

The ﬁnal goal of the shade is to avoid surpassing the 2◦C global mean temperature rise in order to avoid severe consequences [6]. Therefore, the time limit for the project must be deﬁned based on this goal. In the worst case scenario studied in [1], which corresponds with a world where emissions keep rising till 2100, the 2◦C limit would be surpassed by 2050. Looking at these results, it was decided to set this as the time limit when the shades should be in position and operating by this year.

The first step in the study of the trajectories is the definition of the propulsion system used in the spacecraft to travel to the Lagrange point. It is assumed that in the near future the production of large structures in space would not be possible, therefore the discs would be manufactured on Earth. As a consequence, the spacecraft size needs to be modified so it can be launched from the Earth’s surface into space. Later on, once the discs are in place, the control strategy that they will follow will be described. Next, the general layout of the spacecraft will be addressed, focusing on the materials, the mass budget, the size and the control techniques used, as well as the control strategy. To close the thesis, a discussion and a conclusion will be carried out. Here the results of the project will be commented, as well as its possible chances to become a reality and its social effects. Chapter 2

Methodology

The feasibility evaluation of the deployment of a space sun shade in the vicinity of the ﬁrst Lagrangian point requires the analysis of certain areas, common in any space mission. In the methodology chapter, the diﬀerent approaches used during the process are presented.

2.1 Initial Assumptions

In order to enable the selection of the trajectory for the mission there were some aspects that needed to be clariﬁed. As already mentioned, assuming that in a near future the human race will not have access to the manufacturing of large structures in space, it will not be feasible to launch the two large discs described in [16] from Earth. For this reason, instead of using just discs, it was decided that each one of the two shades would be composed by a certain number of smaller spacecraft, which can be put into orbit with an existing launch vehicle (or one under development). As an initial approximation, considering the total area described in [16] and that one spacecraft could have an area of 400 m2, the number of spacecraft orbiting the vicinity of the L1 point would be around 16 250 million.

Related to the travel to the sub-L1 point, the best propulsion system had to be chosen. Two options were considered at the very beginning of the research: electric propulsion and solar sailing. No other systems were taken into account because they would require to carry large amounts of propellant and thus they would greatly increase the cost of the mission. Electric propulsion is a type of low thrust space propulsion that uses electrical power to accelerate a propellant and create thrust. It has a really high speciﬁc impulse which, compared to

7 8 CHAPTER 2. METHODOLOGY

chemical propulsion, allows to create a low continuous thrust for long periods of time and with small amounts of propellant. Solar sails allow spacecraft to use solar pressure to propel themselves through space, without the need of any kind of propellant. The attitude of the sail surface controls the thrust vector, allowing the vehicle to travel in diﬀerent directions.

The ﬁnal goal of the spacecraft once in place is to cover a large area with the lowest weight possible, which gives as a result a vehicle with a design similar to a solar sail [16], even if this sail has never being considered to travel through space in previous studies. Considering this and the fact that solar sailing does not require any kind of propellant (which leads to a reduction in the launch mass compared to any other propulsion system), it was decided that the propulsion system best suited for the mission was solar sailing.

2.2 Launch

As outlined previously, it was assumed that the spacecraft will be launched from Earth. Consequently, it is necessary to study the best options to put such a large mass in orbit, regarding the type of vehicle and the orbit that this vehicle needs to reach. In addition, the launch site selection must also be examined.

2.2.1 Launcher Selection and Assumptions The selection of the launch vehicle is crucial to define the final cost of the mission, representing between fifteen and twenty-five percent of the total budget in the development of a regular space mission [18]. Moreover, in this project the launch percentage is expected to be even higher because of the large mass of the system. Therefore the driver choosing the launch vehicle for the shade was the price per kilogram.

The approximate mass expected for the system, using as reference the most optimistic of the studies treated previously, is around 1.4 × 107 tonnes [16]. Considering that historically the launcher with the largest payload capacity has been the Saturn V, which stopped working in 1973 and had a capacity of 140 tonnes, the number of launches necessary to put the shade in space will be around 105. Since the second driver during the project was time, it was considered that the reduction of the number of launches needed would mean a reduction of the time it takes to put them in orbit. This together with the fact that the price must be as low as possible, points towards the search of the CHAPTER 2. METHODOLOGY 9

Table 2.1: Launcher considered during the study. Launcher Payload to LEO (kg) Cost ($/kg) Situation Starship [19] 100 000 + 201 Under development Long March 9 [20] 140 000 - Under development SLS Block 2 [21] 130 000 8 0002 Under development SLS Block 1B [21] 105 000 8 0003 Under development Yenisei [22] 88 000 - 115 000 - Under development Falcon Heavy [23] 63 000 1 430 Operational 1 Cost for SpaceX, no information about the costumer cost yet. [24] 2 Cost estimated in 2019. [21] 3 Cost estimated in 2019. [21]

cheapest launch vehicle on the market and the one with the most payload capacity, to reduce both price and number of launches needed.

The heaviest rocket currently operational is the Falcon Heavy from the company SpaceX [23], which is able to carry around 64 tonnes to Low Earth Orbit (LEO), but there are several launchers under development with larger payload capacities expected to be operational in the next decade. Regarding the cost, as it can be seen in the Table 2.1, the cheapest is the Starship developed by SpaceX, although it must be pointed out that oﬃcial costs have not been released about this launcher. The main reason for its lower price, when compared with the rest of heavy vehicles selected in Table 2.1, is its complete reusability.

2.2.2 Target orbit Before starting the trip to the vicinity of the Lagrangian point the spacecraft must escape Earth’s gravitational sphere of influence. To do so, there are two different options to consider: the launcher injects the spacecraft directly in an escape trajectory or the spacecraft is injected in a parking orbit, from where it will escape the gravitational field using its own propulsion system.

The payload capacities in Table 2.1 are referred to LEO. If the spacecraft is to be injected in an escape trajectory, the capacity for these launchers is considerably reduced. Thus, the number of launches needed would increase as well as the cost per kilogram of each one of these launches. Consequently 10 CHAPTER 2. METHODOLOGY

Figure 2.1: Space debris distribution with altitude and inclination in 2020. Data obtained from ESA MASTER 2009. it was decided that the best option was to use a parking orbit from where the spacecraft would travel by its own means of propulsion. The next step was to select the best parking orbit. The main propulsion system of the spacecraft is a solar sail. Solar sails have a large area, which means that for low Earth orbits the atmospheric drag generated by them can not be neglected. For altitudes higher than 1000 km the acceleration generated by the solar pressure on the sail is higher than the one generated by the drag [25]. If this was not the case, the solar sail will never be able to escape, therefore, altitudes below 1000 km were dismissed. Moreover, it must be taken into account that solar sails are large areas made of extremely thin materials, which makes them especially sensible to any kind of space debris. In ﬁgure 2.1 is shown how the space debris is distributed in diﬀerent orbits. Based on this, it was decided that to minimize the possibilities of collision, the spacecraft should be injected at an altitude higher than 2000 km . From here, the solar sail would be deployed and the escape trajectory would start. It must be mentioned that although the space debris in altitudes higher than 2000 km is much fewer than in lower altitudes, the solar sail may face some problems when crossing the geostationary orbits zone. CHAPTER 2. METHODOLOGY 11

The selection of the inclination of the parking orbit was driven by: the possibility of cost reduction by using the Earth’s rotation boost and the launch window available. The reduction can be achieved by taking advantage of the Earth’s rotation when launching, which gives a boost to the vehicle and allows to carry more payload than without it. This boost increases if the vehicle is launched from a space port located close to the equator and to take the most advantage out of it, the launch azimuth must be close to 90◦. Taking into account these two characteristics the most convenient inclination for the orbit, regarding the cost reduction, must be close to zero. The reason for it can be deduced from Equation 2.1 which relates the latitude (Φ), launch azimuth (β) and inclination (i). cos i = cosΦ cos β (2.1) Given that the number of launches required to take the shade to space has been calculated to be around 105, it will be necessary to carry out several launches a day and therefore multiple space sports around the globe must be operating. To make sure that in all of them the launch window is as wide as possible, the best is to place the spacecraft in an equatorial orbit. This type of orbits has a constant launch window when launching from equatorial locations.

2.3 Trajectory

This section describes the study of the trajectory of the spacecraft once it is released in the correct target orbit. It was decided to divide it into two phases, since the dynamics of the vehicle are different in each one of them. First the spacecraft will carry out an escape trajectory to exit Earth’s sphere of influence by just using the solar sail. Once outside of the planet gravitational field, the sail will start its way to the equilibrium point close to Sun-Earth L1 point. Both phases were optimized in order to reduce the travel time, since the propellant is not a driver in the case of solar sails.

2.3.1 Reference Frames For each one of the phases diﬀerent reference frames are used to study the dynamics of the vehicle, being a total of three diﬀerent reference frames:

• Earth Centered Inertial (ECI)

• Circular Restricted 3 Body Problem (CR3BP) 12 CHAPTER 2. METHODOLOGY

• Earth Centered Sun Pointing (ECSP)

The ECI reference frame is an inertial frame centered on the Earth that does not rotate with respect to the stars. The x-axis points towards the vernal equinox, the z-axis coincides with the Earth’s rotational axis and the y-axis completes the right-handed orthogonal frame with the ﬁrst two axes such as yˆ =z ˆ × xˆ.

The CR3BP center is placed in the center of mass of the three body system, which in this case is placed on the Earth-Sun line. The x-axis points towards the Earth, the z-axis is perpendicular to the ecliptic plane and the y-axis completes the right-handed orthogonal set just as before.

Finally, the ECSP is an Earth centered system that moves with Earth rotation around the Sun. Its x-axis points towards the Sun, the z-axis is perpendicular to the ecliptic plane and the y-axis completes the right-handed orthogonal set.

2.3.2 Solar Sail Dynamics This project assumes ideal solar sails, which means that the force generated by the solar pressure on the sail is perpendicular to its surface ( nˆ being the vector in this direction). The acceleration that the solar radiation pressure induces in the sail is described as: [26]

µsun 2 ~as = β 2 (ˆrs · nˆ) nˆ (2.2) rs 20 3 −2 where µsun = 1.327 × 10 m s is the gravitational constant of the Sun, rˆs is the unit Sun-sail vector, rs is the Sun-sail distance and nˆ is the normal to the sail surface in the direction of the force. The parameter β is the solar sail lightness parameter, which is the ratio between the maximum acceleration of the vehicle due to the Solar Radiation Pressure (SRP) and the gravity of the Sun. This value is a function of the spacecraft areal density σ (in g m−2) and the optical properties of the sail Q. Being Q = 1 a perfectly reﬂecting surface and Q = 0 a surface that does not change the direction of the photons at all [16]. 1.53 · Q β = (2.3) σ CHAPTER 2. METHODOLOGY 13

The value 1.53 represents the critical loading parameter in g m−2. It is the mass to area ratio that a sail, oriented perpendicular to the sun line, should have to generate a force equal and opposite to the solar gravitational force.

The thrust vector (nˆ) can be deﬁned using two angles that describe the orientation of the solar sail with respect the CR3BP axes: the cone angle α that corresponds to the angle between the normal to the surface and the x-axis and the clock angle δ which deﬁnes the angle between the normal vector and the y-z plane. In terms of these angles, the normal vector is described with the following expression.

nˆ = cos α, sin α cos δ, sin α sin δ (2.4)

Two-Body Problem Equations The two body problem was solved when studying the escape trajectory of the solar sail, while the gravitational force of Earth was the primary force acting on it. The equations of motion of the spacecraft are written in the ECI reference frame.

¨ µ ~r = − · ~r + ~as (2.5) |~r|3 where r represents the position of the spacecraft and ~r¨ its acceleration.

Three-Body Problem Equations Once the solar sail is outside the sphere of inﬂuence of Earth the trajectory becomes a three-body problem, where the gravity of the Sun also must be taken into account. To solve this new problem, ﬁrst the state vector of the sail in the last position of the two body solution was transformed from the ECI coordinates to the CR3BP reference frame. Starting at this point, the equations of motion for the three-body problem (expressed in the CR3BP reference frame) were used to solve the movement of the spacecraft.

Given the large dimensions of the variables that these equations were going to work with, it was decided to use dimensionless variables. In order to do so, new units were introduced. The unit length chosen was the distance between the Sun and the Earth (1AU); the unit of mass was deﬁned as the sum of the mass of these two bodies such as msun + mearth = 1; the mass ratio µ = mearth/(msun +mearth) and ﬁnally, the time unit selected was 1/ω, where 14 CHAPTER 2. METHODOLOGY

Figure 2.2: Circular Restricted Three Body Problem schema [27] .

ω is the angular velocity of the Earth around the Sun.

In this reference frame and with the units mentioned, the motion of the solar sail can be described as:

¨ ˙ ~r + 2ω × ~r = ~as − ∇U (2.6) where U is representing the eﬀective gravitational potential, which can be written as:

x2 + y2 1 − µ µ U = − − ( + ) (2.7) 2 |~r1| |~r2| where the position vectors ~r1 and ~r2, that can be seen in Figure2.2, are deﬁned as ~r1 = x + µ y z and ~r2 = x − (1 − µ) y z . It must be stressed that this potential represents not only the gravitational potential but also the centripetal acceleration, included in the equation with the ﬁrst term. To use the solar sail acceleration with these new dimensionless units it needs to be rewritten as: 1 − µ 2 ~as = β 2 (ˆr1 · nˆ) nˆ (2.8) (~r1) where rˆ1 and nˆ are unit vectors. CHAPTER 2. METHODOLOGY 15

2.3.3 New Equilibrium Point The ﬁrst Lagrangian point is a location in space, laying on the Sun-Earth line, where the gravitational forces of the two bodies and the centrifugal force of the orbital motion of the third body create a stable location. Thus, a smaller mass placed in this point remains in the same relative position. When working with solar sails a new force needs to be taken into account, the solar radiation pressure. As a result, the point where a third mass is in equilibrium changes sunwards from the classical location, which is located around 1.5 × 106 km away from Earth (1/100 of the total distance between the two bodies).

To ﬁgure the new position the new force equilibrium needs to be com- puted so the total acceleration is equal to zero. At this point the sail will be perpendicular to the sunlight, the normal to the surface will be nˆ = 1 0 0. Considering this and the fact that the point will be on the x-axis, the equation to ﬁnd the location of the new equilibrium point (xe) is Equation 2.9 [16].

γ5 −(3−µ)γ4 +(3−2µ)γ3 +(1−2µ−(β+1)(1−µ))γ2 +2µγ−µ = 0 (2.9) with γ = xe − (1 − µ). As it can be seen from the equation, it is possible to change the position of the equilibrium point by selecting a certain lightness parameter for the sail. This variation will be used later on to study the area and total mass variation depending on the sail features.

2.3.4 Escape Trajectory Optimization Solar sailing provides the spacecraft with very low acceleration, which leads to that an orbital maneuver takes a long period of time. Therefore, the goal of the escape trajectory optimization is to minimize its time.

The energy per unit mass of a body orbiting around a planet is deﬁned as: 1 E = ~vT ~v + U(~r) (2.10) 2 where U(t) is the potential energy per unit mass and it has a negative value. The energy of the body remains constant and negative as long as it stays in orbit. To enable the body to escape the gravitational ﬁeld, the energy must be above zero, which can be achieved by increasing its speed. 16 CHAPTER 2. METHODOLOGY

The strategy followed to achieve the escape consists in maximizing the instantaneous rate of increase of orbital energy. This approach does not lead necessarily to the minimum time solution, but it has been shown that for the order of magnitude of solar sail acceleration the solution obtained is near minimum time [28]. The instantaneous rate of increase of the orbital energy is deﬁned in Equation 2.11 [28].

dE ˙ T T T = ~v ~v − ~gc ~v = ~as ~v (2.11) dt It can be deduced that in order to maximize it, the component of the sail acceleration along the velocity vector must be maximized in each point of the trajectory. The optimization problem was solved by Coverstone and Prussing [28] in the ECSP reference frame resulting in the following control law for the normal of the sail:

− |vy| nx = (2.12) q 2 2 2 2 vy + ξ (vy + vz )

ny = ξnx (2.13)

vz nz = ny (2.14) vy where the variable ξ is described as:

q 2 2 2 −3vxvy − vy 9vx + 8(vy + vz ) ξ = 2 2 (2.15) 4(vy + vz ) Based on this result, to compute the escape trajectory of the sail the equations of motion 2.5 deﬁned in section 2.3.2 were solved. In order to do so, everything was transformed to ECI coordinates. The simulation was stopped once the total energy of the sail reached zero, starting at this exact point the second phase of the trajectory outside the sphere of inﬂuence of Earth.

2.3.5 Trajectory to Sub-L1 Optimization The minimum-time solar sail trajectory is an optimal control problem, which can be solved by two diﬀerent methods: the indirect and the direct. For this project the direct approach was selected, as suggested in [29]. The direct methods transform the optimal control problem in a parameter optimization problem. In order to do so, the control variables are discretized by dividing the CHAPTER 2. METHODOLOGY 17

trajectory in a certain number of segments. In the paper mentioned [29], it was demonstrated that with few segments a near minimum-time solution can be accomplished. During the study it was assumed that the changes between diﬀerent angles were instantaneous, which must be taken into account when reading the ﬁnal results.

Problem Deﬁnition Any trajectory optimization problem can be described as a system of state variables (x(t)) and control variables (u(t)). The optimal control problem is generally deﬁned as:

Z tf J(x, u) = f(t, x(t), u(t))dt (2.16) t0

x˙ = f(t, x(t), u(t)), t ∈ [t0, tf ] (2.17)

r(x(t0), x(tf )) = 0 or ≥ 0 (2.18)

g(t, u(t)) ≥ 0, t ∈ [t0, tf ] (2.19) where J is the objective or cost function, x˙ are the state equations, r represents the boundary conditions (initial and final) and g stands for the path constraints defined during the trajectory. The function f represents any function depen- dant of those variables. Next each one of the functions selected to define the problem under study are presented.

• State and control variables. The state variables in this case are the position and velocity coordinates of the spacecraft. The control variables are the two angles that deﬁne the normal of the solar sail, the clock angle and cone angle, which are deﬁned in subsection 2.3.2.

• Cost function. The cost function is the function to be optimized, which here corresponds with the ﬁnal time of the trajectory.

J = tf (2.20)

• State equations. These are equations that deﬁne the system dynamics, therefore the equations of motion 2.6 deﬁned in section 2.3.2. 18 CHAPTER 2. METHODOLOGY

• Boundary conditions are usually defined as initial and final points of the trajectory. The initial point is defined by the final point of the escape trajectory, while the final point is the new equilibrium point in the Sun- Earth line. In order to facilitate the optimization process, the final point values were allowed to have a relative error of 10−5.

• Path constraints are restrictions imposed to the variables that must be respected throughout the complete trajectory, both nonlinear constraints and upper or lower bounds. Regarding the upper and lower bounds, none were defined for the state and control variables. The only bounds determined for the optimization were defined for the final time (objective function), setting the lower bound to zero and testing the upper bound in order to get a solution. One nonlinear constraint was set, in order to make sure that the reflective side of the sail is pointing towards the sun all the time. rˆ · nˆ ≥ 0 (2.21)

Multiple Shooting Parametrization Method As it was mentioned before, the optimal control problem was solved using a direct method that allows to treat the optimal control problem as an optimization problem by discretizing the control variables. A certain number of segments is deﬁned to divide the trajectory, which was chosen to be ten. For each one of these segments, the cone and clock angles have a constant value. These parameters are the optimization variables that the optimizer will change in the search of a solution. Thus, there are 10 × 2 optimization variables, two per segment. The optimization was developed using the SNOPT optimization software, which uses a sequential quadratic programming (SQP) algorithm. The software was used on MATLAB, using the interface developed by Gill and Wong [30].

2.4 Spacecraft Conﬁguration

Initially, the scope of this project did not cover the deﬁnition of the spacecraft features but, after observing how the results of its dynamics depend on it, it was decided to developed a rough description of the layout of the spacecraft. The areas in which the description is more precise are the ones related directly with the performance of the solar sail, such as the sail area, the total mass of the spacecraft and the sail material. CHAPTER 2. METHODOLOGY 19

2.4.1 Total Mass and Size Study The main driver during the whole project was the cost and therefore the total mass. This value depends on the total area (A) needed for the shade and the areal density of each one of the spacecraft (σ) that create this shade. This density can change during the mission because some of the elements can be jettisoned. For this study it was decided that this density would stay constant and therefore when examining the literature only initial densities were considered. The total mass Mtotal then becomes:

Mtotal = A · σ (2.22) The total area depends on where the new equilibrium point is located and thus, if one looks at Equation 2.9, it depends on the lightness parameter of the sail (β). This parameter is subjected to the areal density and the reflectivity of the surface facing the Sun. How the area changes with the position of the new equilibrium point can be seen in Equation 2.23, where, keeping in mind that the shades are defined to be discs, the radius needed to reduce the solar insolation a certain value ∆S is defined [16]. r dshade ∆S Rshade = Rsun (2.23) dsun S where dsun and dshade are, respectively, the distances of the Sun and the solar ∆S sail from Earth, Rsun is the Sun’s radius and S represents the percentage that the solar radiation needs to be decreased, which, as already mentioned in section 1.2, in this case has a value of 1.7% [11].

Considering these dependencies, it is possible to study how the total mass varies for different values of reflectivity and areal density. To orient the study and make the final decisions later on, some dimensions of existing solar sails or other project ideas were used as a reference; these can be found in Table 2.2.

Table 2.2: Solar sail dimensions from the literature. Solar sail Density (g m−2) Lightness parameter (β) Total area (m2) IKAROS [31] 1550 0.001 200 Light Sail 2 [32] 156 0.01 32 Sunjammer [27] 150 0.0363 1 200 Heliostorm mission [33] 14.8 ( 91) 0.0379 10 000 Angel Sun Shade [15] 4 0.0153 1 1 Density without payload. 20 CHAPTER 2. METHODOLOGY

The lower and upper limits for the areal density and the reflectivity were defined based on the latest solar sail technologies found. Although Angel [15] assumed that the areal density of the spacecraft could reach 4 g m−2, the sim- plicity of the spacecraft described in his paper does not match the one under study in this report and therefore this value was considered too low. Looking at Table 2.2 and dismissing this option, the lowest areal density of the solar sail (considering the total mass of the spacecraft) was set to be 9 g m−2. Further- more, Angel [15] discussed the minimum reflectivity achievable in a material, reaching a solution of Q ∼ 0.04, which was used as the lower bound for this variable. The outcome of the study for different combination of these two parameters can be found later on in the results section 3.1.1.

2.4.2 Mass Budget Solar sails have been deeply studied for decades but so far the only solar sails that have reached space (IKAROS [31] and Light Sail [32] ) have been test sails, with the goal of demonstrating certain solar sail related technologies. As a consequence, although these vehicles have proven that these kind of technologies can work, the mass budget of the spacecraft were not representative of a real solar sail, since they carried other propulsion systems as back up, therefore did not need a low areal density to get acceptable accelerations. Fur- thermore, all the spacecraft studied carried payloads to develop scientiﬁc mea- surements that in the case under study are not needed.

Table 2.3: Mass budget study in percentage of the total spacecraft mass and TRL. Interstellar Heliostorm Light Sail 2 IKAROS NASA Spacecraft Heliopause Mission [32] [31] study [35] Probe [34] [33] TRL 2 5+ 7 7 2 Solar sail 57 48 - - 64 assembly Thermal 4 1 - - 1 AOCS 5 11 - - 7 Power 12 5 - - 5 Structure & 10 8 - - 20 mechanisms CDH 7 15 - - 2 Payload 5 33 - - 5 CHAPTER 2. METHODOLOGY 21

The mass budget of the solar sails considered during the project can be found in Table 2.3. In the ﬁrst row it is given the Technology Readiness Level (TRL). As seen in the table, the information regarding the two solar sails with the highest TRL could not be found. Instead, several projects with no experi- mental validation or small prototype tests were used as reference.

The ﬁnal target of this study was to create a realistic mass budget for the spacecraft so, once deﬁned the total mass expected, the mass assigned for each subsystem could be approximated. Hence, it would be possible to examine if those masses were realistic with the technologies available nowadays and the ones expected to be developed in the next decades.

2.4.3 Control

Control Subsystem The solar sail must change its orientation constantly during its trajectory to the equilibrium point because it deﬁnes the direction of the thrust vector. Fur- thermore, once in the sub-L1 point, the optimal movement for the shade does not exactly follow a natural orbit, so the spacecraft will require regular attitude control of the clock and cone angles to describe the desired orbit. Therefore the spacecraft needs to have an active attitude determination and control system.

Concerning the attitude control, after selecting solar sailing as the main propulsion system in order to eliminate the use of propellant, it makes sense to follow the same reasoning in the control subsystem. Besides, the large moment of inertia of the sail means large active control torques which translate in large amounts of propellant if thrusters were to be used, or large reaction wheels [36]. Thus, the use of conventional control techniques could only be considered as backup. Consequently, it was decided that the best option was to use solar radiation pressure to control its attitude. There are two main types of techniques for attitude control using solar radiation pressure.

• Adjustment of the position of the center of pressure.

• Adjustment of the position of the center of mass.

There are two different techniques to change the position of the center of pressure. The first technique consists of changing the reflectivity of the sail, 22 CHAPTER 2. METHODOLOGY

demonstrated by IKAROS [31] which was the first solar sail to reach success- fully interplanetary space (therefore its TRL is 7). This is achieved by using Reflectivity Control Devices placed at the edges of the sail membrane that are able to generate a torque by changing its reflectivity with electricity. In this control method the torques are constrained by the reflectivity modulation and the Sun angle, resulting in a limitation of the angle change in certain positions. Furthermore, it needs to be kept in mind that these reflective devices are placed on the sail, affecting not only its orientation but also the total force generated by it.

The second technique considered is one that has been widely studied in various projects [27] but has never been tested in space, and it is the use of tip mounted vanes. These vanes are installed at the tips of the booms in order to have a large momentum arm that allows the vanes to have small areas. Each vane has two degrees of freedom, allowing a three-axis attitude control over the spacecraft. The main problem that this kind of method presents is the complexity of the conﬁguration and the deployment of the sail module.

Unlike center of pressure methods, techniques related with the displacement of the center of mass are usually completely independent from the solar sail assembly, which is an advantage since the performance of the sail is not af- fected. Nevertheless, they have one important drawback, they add more mass to the spacecraft. Some examples of these methods are the distributed mass method, which moves small masses along the booms or the bus, or the use of a gimbaled boom with a tip mass. These methods can only create pitch and yaw control because its movements can not create a torque in the perpendicular direction of the sail, thus they need to be used together with other methods in order to achieve a 3-axis attitude control.

In regard to attitude determination, the sensors must be capable of working in the vicinity of the Lagrangian point. Because of this reason, magnetometers can not be used, since their utilization is usually limited to a maximum altitude of 6000 km. Earth horizon detectors are also discarded since this type of sensors needs to be used in an orbit around the Earth. Apart from this limitation, among the rest of sensors available on the market any could be used, however, the ﬁnal sensors will be chosen looking for the minimum mass and minimum cost. CHAPTER 2. METHODOLOGY 23

Control Strategy Once each one of the spacecraft reaches the vicinity of the equilibrium point, they need to be arranged in two different groups to deploy the shadows as stated in [16], defined as two different discs. Each one of the discs must follow a certain orbit with their respective control laws. Thus, it is necessary to control a large group of spacecraft in order to achieve a certain geometry in space. The use of groups of satellites with a certain formation with one mission has been lately introduced in the space community, mainly with observation satellites.

Angel[15] already tackled this problem and he proposed a cloud of randomly placed spacecraft, completely autonomous. In his proposal each spacecraft must make sure that its facing the Sun and stay inside the cloud envelope, but the position inside of the cloud is unknown. The main reason for this strategy selection was to avoid the need of communication systems and complex station keeping requirements. Considering that in the case under study these elements are already implemented in the spacecraft in order to travel to that point using the solar sail, the use of a randomly position cloud loses most of its advantages, leading into the search of new control strategies for orbit formation.

The group of spacecraft must orbit the equilibrium point with a certain shape formation. This operation needs to be developed autonomously by the spacecraft, since trying to control from the ground such a large number (more than 100) of vehicles is not feasible [37]. A solution for this problem is the use of swarm strategies, which aim to ﬁnd a global group organization without the presence of a centralized control that allows to reach a certain goal. This is a strategy already being studied in observation satellites, since it allows to use smaller and simpler satellites to image the whole planet [38]. Swarm behaviour can be simulated implementing four basic rules in each of the in- dividuals: avoid collision (maintain a safe distance from each other), remain grouped (avoid isolation), align to the neighbor and reach the ﬁnal goal. These laws allow the spacecraft to autonomously control its position with respect to the rest of the group. Each spacecraft performs this swarm maintenance maneuvers using a certain number of the closest satellites as a reference [39]. Chapter 3

Results

As it was already mentioned previously in this report, the main goal of the project is to study the feasibility of placing a space sun shade near the first Lagrangian point. To do so, the most characteristic features of the spacecraft, the optimal trajectory and the launch have to be defined. In this section the final results for each one of these aspects obtained from the methods described before are presented.

3.1 Spacecraft Conﬁguration

After the study developed in subsection 2.4 the final features of the spacecraft could be selected. Next, each one of the aspects treated previously, such as size and mass of the spacecraft, mass budget and controls systems, are finally defined. These results enabled to compute the optimal trajectory and choose the launch option later on.

3.1.1 Total Mass and Size The total mass of the system depends on the areal density and the total area, as explained in subsection 2.4.1. At the same time, the total area depends on where the shade is placed and thus where the equilibrium point for the sail is located. As it was defined in Equation 2.9, the location of this point changes with the lightness parameter, which is defined by the reflectivity and the areal density of the sail. Therefore, it can be concluded that the total mass of the system changes with the reflectivity of the sail’s material and the areal density of the spacecraft. In order to find the combination which results in the minimum mass, this dependency was studied obtaining the graph in figure 3.1.

24 CHAPTER 3. RESULTS 25

Figure 3.1: Variation of the total mass of the system with the areal density, for a certain set of values of the reﬂectivity parameter Q. Q has a value of 0.05 for the bottom line and 1 for the one located at the top of the graph.

Figure 3.1 shows the variation of the mass with the density and the reflectivity. In the graph it is also possible to find star points that show the lowest mass achievable for each reflectivity. It can be seen that depending on the value of the reflectivity, the density of the spacecraft for the minimum mass changes. For reflectivities between 0.05 and 0.2 the minimum mass corresponds with the minimum density, whereas for reflectivities higher the minimum mass is located in higher values for the density. This takes place because the density affects the total mass in two different ways: directly by itself and indirectly through the area by changing the equilibrium point position. But this equilibrium point position also changes with the reflectivity. The total mass is proportional to the density and the area. So that, when the density increases, the mass tends to behave the same way but the area decreases, creating the opposite effect and decreasing the mass. As the reflectivity increases, the equilibrium point moves towards the Sun, increasing the area needed. For reflectivities smaller than 0.2 the most important factor when looking for the minimum mass is the direct effect of the density 26 CHAPTER 3. RESULTS

and accordingly, the minimum mass point is located in the minimum density. When the reﬂectivity reaches 0.2 and the equilibrium point moves closer to the Sun, the area becomes more important when looking for the minimum mass. This forces the minimum mass point to move to higher densities, in order to move the equilibrium point closer to the Earth and therefore decrease the area needed.

Based on these results, the minimum mass is obtained by choosing the minimum areal density and the minimum reﬂectivity, giving a ﬁnal mass of 28.5 million tonnes. However, there is something else that needs to be kept in mind and that is the performance of the solar sail. This performance is represented by the lightness parameter (β), whose values can be seen for each one of the minimum mass points in Figure 3.2. The higher the value of β, the solar sail is able to generate a greater acceleration and thus has a better performance. Consequently, the combination that results in the minimum mass corresponds as well with the worst performance of the sail.

It can be noted that the lightness parameter corresponding with the minimum mass points increases with Q, until it stabilizes at a value of 0.035 from Q ∼ 0.2 on. In view of these values, if a combination different from the one resulting in the minimum mass is to be considered in order to achieve a better sail performance, it would be reasonable to choose the first point with a lightness parameter of 0.035, since it is the one with the lowest mass inside this group. As a result, two options were under study for the definition of the final characteristics of the solar sail. The first corresponding with the minimum mass overall and the second being the one that, inside the group of minimum mass points for each reflectivity, has a lowest mass and a lightness parameter of 0.035. The definition of both points can be found in table 3.1.

Table 3.1: Options considered for the spacecraft deﬁnition. Case 1 Case 2 Density (g m−2) 9 9 Reﬂectivity 0.05 0.2 Lightness parameter (β) 0.0085 0.035 Total mass (kg) 2.85 × 1010 5.66 × 1010 Escape trajectory time (days) 1 792 582 Trajectory to L1 time (days) - 317 CHAPTER 3. RESULTS 27

Figure 3.2: Lightness parameter variation with the areal density, for a certain set of values of the reﬂectivity parameter Q. Q has a value of 0.05 for the bottom line and 1 for the one located at the top of the graph. 28 CHAPTER 3. RESULTS

Between these two options it was clear that in order to achieve the lowest cost, the minimum mass point had to be selected. Nevertheless, given the low performance of it, it was considered that a trajectory analysis of this option was necessary in order to check if the sail could travel to the vicinity of the Lagrangian point in a reasonable time. Thereafter, the trajectory analysis for each one of the options was carried out. The results regarding the time that it took for each one of the sails to describe the desired trajectory can be found in Table 3.1. This table shows that for the minimum mass case it was not possible to ﬁnd an optimal trajectory to the Lagrangian point, resulting in the elimina- tion of this option.

The number of spacecraft depends on the sail area of each one of them. This area was decided taking into account the areal density selected and the values for previous solar sail projects proposed. It had to be considered that the sail would be deployed so its size is not limited by the size of the payload fairing of the launcher. The area selected needed to be large enough so that the mass of the spacecraft was reasonable. If the area was 10 m2, the total mass would need to be 90 g, which considering the need of a deployment mechanism and the rest of subsystems (such as structure, control, thermal or communication), could be hard to achieve with the current technologies. Keeping this in mind and based on past solar sail projects, which can be found in Table 2.2, the final size of the sail was set to be 10 000 m2. Table 3.2 shows the final definition of each one of the spacecraft that forms the shade.

Table 3.2: Final deﬁnition of the solar sail main features. Density (g m−2) 9 Reﬂectivity 0.2 Lightness parameter 0.035 Area of the solar sail (m2) 10 000 Mass for one spacecraft (kg) 90 Total mass of the system (kg) 5.66 × 1010 Total area of the system (m2) 6.31 × 1012

3.1.2 Mass Budget Previously the total mass for the spacecraft was set to be 90 kg in order to achieve the desired areal density. The goal in this section was to deﬁne the mass budget expected for each one of the spacecraft subsystems. Once done, CHAPTER 3. RESULTS 29

it could be examined if the mass assigned for each subsystem, given a 90 kg spacecraft, could be achieved with current technologies. This will be discussed later on in section 5.1.

Table 3.3: Mass budget study in percentage of the total spacecraft mass. Expected weight Expected Subsystem Percentage considering sys- weight (kg) tem margin (kg) Structure 20 12.6 18 Thermal 5 3.15 4.5 Propulsion (sail 50 31.5 45 module) AOCS 5 3.15 4.5 Power 10 6.3 9 Mechanisms 2 1.3 1.8 CDH and teleme- 8 5.0 7.2 try Total 100 63 90

In Table 3.3 three columns can be found. The first one represents the percentage of the total mass that was assigned to that subsystem. The second column shows the maximum mass that the respective subsystem should have during this first phase of the design in order to comply with the mass target. Lastly, the third column shows the weight that the final design of the subsystem should have, taking into account that this mass will grow as the design evolves [40].The margin used to calculate the difference between these two columns was 30%, considering that the design process is in the System Requirements Review phase [40].

3.1.3 Control The trajectory that the solar sail needs to describe requires continuous thrust vector steering maneuvers and, as a consequence, the spacecraft must have an active three-axis attitude control system. Taking this necessity into account, as well as the technology readiness level and the beneﬁts and drawbacks of each option, all the control techniques considered in subsection 2.4.3 were evaluated. 30 CHAPTER 3. RESULTS

Change of the center of mass techniques were discarded for two reasons: the limit to two-axis control, with its consequent need of an extra control method, and their higher mass when compared with change of center of pressure techniques. Among change of the center of pressure approaches it was decided to select Reflectivity Control Devices (RCD) as the main option, which uses changes in the reflectivity in different areas of the sail to create a torque, as it can be seen in Figure 3.3. This kind of method can change the total force created by the sail when changing the reflectivity, which could mean a loss of efficiency. Nevertheless, it is the only one that has reached a TRL of seven so far [36], since the rest of methods are just concepts and have never been tested.

Figure 3.3: Schematic representation of how the Reﬂectivity Control Device works [41].

Once every solar sail is in orbit, in order to achieve the two discs configuration described in [16] the spacecraft will use a swarm behaviour as control strategy. As explained in 2.4.3, in this kind of control scheme, each vehicle performs autonomously its own maneuvers based on the position of the rest of vehicles next to it following the rules defined in the section mentioned. The first three rules are common for every swarm, but the last one, called the goal CHAPTER 3. RESULTS 31

rule, is the one that defines the final objective of the swarm. In the case under study, the final goal is the movement of the two discs formed by the swarm in the correct orbit. The spacecraft would be divided beforehand in two different groups. Once in the vicinity of the Lagrangian point, each solar sail would take its corresponding position relative to the rest of its group. At the same time, each one of the groups would be moving in the optimal orbit, pre- serving the same geometry at every moment thanks to the control laws. In principle, for the problem in hand, it was considered that in the next decades the large number of spacecraft would not entail any issue when implementing this behaviour. If this was not the case, the two swarms defined before could be divided in smaller ones, which would have a leader spacecraft that would be in charge of forming another swarm with the rest of the smaller groups.

3.2 Launch

Before starting the trajectory described in the project, the spacecraft must reach space from Earth’s surface. In this section the selection of the vehicle selected to carry out this task is presented, as well as the number of launches necessary to transport the total mass and the target orbit of these launches.

3.2.1 Launcher Selection After the analysis of the current and near-future launch vehicle market developed in subsection 2.2.1, it was decided that the lowest cost for the entire mission would correspond to the use of the Starship as main launcher. Even though the ﬁnal customer price of this vehicle is still unknown, given the initial approximations for the manufacturer cost and that currently the cheapest operational rocket belongs to SpaceX, it was decided to consider it as the best option. Furthermore, the selection of a reusable rocket has two extra advantages. The ﬁrst being that the environmental impact of each launch will be much lower since the vehicle does not need to be built from scratch each time. The second extra advantage is also related with this lack of necessity of building one rocket per launch, which means that the launch frequency will not depend on the manufacturing rate of the vehicle but only in the refurbishment time, which should be lower. 32 CHAPTER 3. RESULTS

Table 3.4: Starship main features. [19], [42] Payload capacity (kg) +100 000 (LEO), 21 000 (GTO) Payload fairing volume(m3) 650 Propellant capacity 1st stage (t) 3 300 Propellant capacity 2nd stage (t) 1 200 Cost per launch(million $/kg) 10 (2 1) 1 Operational cost. [24]

In Table 3.4 a more detailed description of the main features of the Starship is shown. This vehicle is currently under development and SpaceX plans to start operating orbital flights with it by 2020 [42]. Elon Musk, who is founder, CEO and lead designer of SpaceX, claims that the manufacturing rate for these launchers will be one hundred per year, aiming to have a fleet formed by a thousand vehicles [43] after ten years. Furthermore, the Starship design goal is to be able to carry out three flights a day per vehicle [43] .

3.2.2 Launch in Numbers In this subsection some calculations regarding the launch of the shades are presented. The whole computation was carried out considering the launch vehicle assumptions mentioned previously, assuming that SpaceX achieves its expectations on the Starship. The company claims that it will be able to launch each one of the vehicles three times a day and aims to have a fleet of 1000 ships. Based on these data and the time period for the project defined in section 1.4, according to which the shades should be operating by 2050, the results shown in Table 3.5 were calculated. For these calculations it was also assumed that the first launch would take place ten years from now, which gives a margin of twenty years for all the spacecraft to be in place.

Table 3.5: Launch deﬁnition. Years launching 20 Number of launches per day 78 Number of vehicles in operation 26 Total number of launches 566 000 CHAPTER 3. RESULTS 33

3.2.3 Target Orbit Deﬁnition The target orbit is the parking orbit in which the spacecraft will be injected to by the launcher and from where the solar sail will start its travel to the vicinity of the Lagrangian point. The lower this orbit is placed, the more payload can be carried by the launch vehicle, since as it can be seen in Table 3.4, the payload capacity of the Starship decreases considerably when changing from LEO to GTO. Therefore, looking at the study developed in 2.2.2, the lowest altitude that allows to avoid space debris and reduce the atmospheric drag force in the solar sail was set to be 2000 km. Although the deﬁnition of the maximum payload is referred to a 500 km polar orbit and 2000 km is far out of this range, given that the Starship expectations include to be able to increase its payload an additional 50 tonnes [42], for the rest of the project it was considered that the vehicle capacity to reach this altitude is the one mentioned.

In order to make the most out of the Earth’s rotation boost the launch sites must be located as close to the equator as possible. Keeping this in mind and considering that this boost increases with an azimuth angle of 90◦, the best orientation for the orbit is an equatorial orbit. This will result in the maximum velocity boost for the launcher. Moreover, there is another great advantage derived from this deﬁnition. The launch window to reach equatorial orbits from space ports with latitudes close to zero is always open. This facilitates the compliance with the launch rate requirement deﬁned in section 3.2.2. Taking into account that 78 launches will need to be carried out each day, there should be several space ports available around the globe (close to the equator) and each one of them should have its launch window open several times a day.

3.3 Final Trajectory

Once the spacecraft is in orbit it must start traveling to the new equilibrium location in the vicinity of the first Lagrangian point. As mentioned above, the propulsion system responsible of carrying out the trip is a solar sail. Hereafter in this section, the results for the optimal approach to perform the trajectory in the minimum period of time are presented. The results are divided in two different phases, in the same way as the methodology was divided, one that covers the trajectory that takes place inside the Earth’s gravitational sphere of influence and another that covers when the spacecraft is located out of this area. 34 CHAPTER 3. RESULTS

Table 3.6: Final conditions of the escape trajectory. Position (km) Velocity (m/s)

x y z vx vy vz ECI 1.37 × 106 2.55 × 105 −1.83 × 105 5.72 × 102 4.91 × 102 −3.94 × 101 CR3BP 1.51 × 109 −3.07 × 105 −2.70 × 105 6.84 × 102 2.17 × 102 −2.32 × 102

3.3.1 Escape Trajectory The initial position for the escape trajectory is the parking orbit selected in section 3.2.3, located at an altitude of 2000 km. From here the solar sail performs a low thrust maneuver, maximizing its acceleration along the velocity vector. Since the solar sail is performing a low thrust maneuver, the location of the spacecraft inside of the orbit at the beginning does not make a diﬀerence in the trajectory deﬁned.

The trajectory described by the vehicle during the maneuver is displayed in Figure 3.4, where the trajectory is represented in the ECI reference frame. The ﬁnal conditions with which the spacecraft leaves the Earth’s gravitational ﬁeld are presented in Table 3.6.

Figure 3.4: 3D view of the escape trajectory in ECI reference frame.

As it is shown in Table 3.6 the spacecraft leaves the Earth’s gravitational ﬁeld in the direction opposite to the Sun. This means that later on, during the travel to L1, the journey will be longer than expected because the solar sail must turn all the way around to reach the equilibrium point. The total time CHAPTER 3. RESULTS 35

that the sail takes to escape the sphere of influence is 537 days. In this analysis there is a continuous control law, so the thrust vector is defined differently for every time step in the integration. The values for the clock and cone angles used to define the orientation of the sail can be found in Figure 3.5. In order to see it more clearly just a few orbits were represented in the graphs.

Figure 3.5: Cone and clock angles for the ﬁrst hours of the escape trajectory.

3.3.2 Travel to Sub-L1 When the spacecraft leaves the gravitational field of the Earth, with the conditions defined in Table 3.6, the problem changes to a three body problem where the Sun needs to be taken into account. At this point the trip to the sub-L1 point starts. The time and trajectory obtained as a result of the optimization carried out in this section are not the values that correspond with putting the spacecraft in the final orbit around the sub-L1 point. The final goal used in the optimization process was the sub-L1 point with a null velocity. As a consequence, the results are an approximate description of how the trajectory would be carried out but not its final definition.

The ﬁnal solution obtained for the optimal trajectory to reach this location in space is shown in Figures 3.6 and 3.7. It is possible to see how the solar sail describes a wide loop to reach the vicinity of the Lagrangian point because its 36 CHAPTER 3. RESULTS

Figure 3.6: Travel to the sub-Lagrangian represented in CR3BP with dimensionless units.

Figure 3.7: Travel to the sub-Lagrangian represented in CR3BP with dimensionless units, XZ plane view. CHAPTER 3. RESULTS 37

Figure 3.8: Position coordinates of the spacecraft over time (in CR3BP reference frame). initial conditions where taking the sail in the opposite direction. The ﬁnal time in which the sail reached the equilibrium point was 317 days. The coordinates of the spacecrafts in each moment and its velocity are represented in Figures 3.8 and 3.9. These graphs show that the motion takes places almost in the same plane, since the displacement in the z axis is close to zero. Furthermore, it can be observed how the velocity goes to zero as the vehicle approaches the equilibrium point .

As it has been mentioned before, in order to carry out the optimization the trajectory was divided in diﬀerent segments. For each one of these segments, the cone and clock angles have constant values. The variation of the angles in each one of the segments can be found in the graphs represented in Figures 3.10 and 3.11. 38 CHAPTER 3. RESULTS

Figure 3.9: Velocity of the spacecraft over time (in CR3BP reference frame).

Figure 3.10: Cone angle variation during the trajectory to L1. CHAPTER 3. RESULTS 39

Figure 3.11: Clock angle variation during the trajectory to L1. Chapter 4

Cost Analysis

Once the technical and engineering challenges of building this kind of device were studied and evaluated in order to ﬁnish the feasibility study, a cost analysis was necessary. In this case, this was a complex task because, as for now, no private company or space agency has ever attempted a project with dimensions close to the one under study.

4.1 Launch Cost

The whole launch cost study was done assuming the use of the Starship for the whole mission in order to simplify the calculations. The Starship cost is still unknown but Elon Musk claims that the operational cost of the vehicle for SpaceX could be around US$2 million per launch [24]. Based on this value it is possible to make a rough approximation of the total cost that one launch could have for the customer.

As a private company, SpaceX does not release precise information on cost and budgets of their projects. In order to have an idea of the gross margin that the company could set for the Starship, previous Falcon 9 prices were studied. SpaceX web page has a price for the Falcon 9 of US$62 million but this price corresponds with a non reusable rocket. Musk claimed that missions with previously flown boosters were priced around US$50 million [43]. This price matches the result from the analysis made by Jefferies International LLC, which calculated the final costs and prices for the Falcon 9 reusable rocket based on the non-reusable prices, considering that a 50% of cost savings from reusing the booster were passed on to the final price [44]. Some of the results from that analysis can be found in Table 4.1.

40 CHAPTER 4. COST ANALYSIS 41

Table 4.1: Summary of cost analysis results made by Jeﬀeries [44]. Falcon 9 Falcon 9 reusable Price per launch ($M) 62 50 Direct costs ($M) 36.7 (60%) 11 (22%) First stage costs ($M) 27.5 1.8 Rest of the costs ($M) 9.2 9.2

The value of US$2 millions was decided to be considered as the direct cost of a single launch of the Starship. Based on this value, and considering that in the case of the Falcon 9 reusable rocket the direct costs represent 22% of the total price, the ﬁnal cost considered for each individual launch was set to around US$9 million. Using this as the reference value, the total costs can be calculated using the number of launches needed, which can be found in Table 3.5. The total cost for launching all the solar sails is around US$5 trillion.

4.2 Spacecraft Cost

Until last decade, the biggest constellations had been formed by groups of less than one hundred satellites. Only recently, some private companies like SpaceX, OneWeb or Amazon, have started to developed broadband internet satellite constellations formed by several thousands of satellites. This could give a closer idea to how much a satellite would cost when manufactured in large numbers, although the number from these companies are still low when compared with the large scale mass production needed for this mission.

Considering as an initial reference for this calculation the manufacturing of the Starlink constellation, SpaceX claims that the network will cost at least US$10 billion, formed by 12 000 satellites. This would give a cost per satellite of a little less than US$1 million, including the development and design of the spacecraft. Keeping in mind that the dimensions of this project is 50 000 times larger than the Starlink constellation, it was considered that this value could be considerably reduced. Furthermore, the lack of any kind of payload could also imply a reduction in the cost of the spacecraft.

Based on this information and considering approximations made by Angel [15], it was decided to consider an initial development cost of US$5 billion. 42 CHAPTER 4. COST ANALYSIS

From here, the price considered for the manufacturing of each one of the solar sails was 100US$/kg, giving a ﬁnal cost per spacecraft of US$10 000, which could be compared with the current cost of manufacturing a car. Taking into account the total number of spacecraft that must be manufactured, the production of these could cost around US$5.7 trillion , a value close to the launch cost. This total cost would be divided along the period of time in which the project is ongoing. The total cost per year, considering also the previous cost deﬁned for the launch of the spacecraft, would be of around US$540 billion per year. Chapter 5

Discussion

Previously, the mission to put a space sun shade in the first Lagrangian point was described, defining the size and configuration of the spacecraft, the trajectory to the target point and the launch phase. After presenting all the results it is necessary to analyse them. In the following chapter these results are discussed, evaluating the quality and viability of each one of them. From these assessments the final goal of the project, which is to determine the feasibility of the mission, can be defined.

5.1 Spacecraft

As a secondary objective in this report a draft of the spacecraft deﬁnition was described. Here, the mass, the areal density of the solar sail and the mass budget division for each one of the subsystems were decided.

The deﬁnition of the solar sail areal density was the most risky decision since, as explained in 2.4, solar sails with low areal density have never been tested in space, they have just being developed in research programs and tested on Earth (and therefore have a maximum TRL of 6). Still, with the quick advance of space technologies, it is to be expected for this type of propulsion to keep evolving in the upcoming years, so that a density of 9 g m−2 for the whole spacecraft could be achieved.

It must be highlighted that if the solar sail and its attitude control are ig- nored, the conﬁguration of the rest of the spacecraft needs to be very simple. In principle, there will be no payloads on board, thus, the vehicle only needs the basic subsystems in order to survive for a long period of time and

43 44 CHAPTER 5. DISCUSSION

be able to communicate with Earth and the rest of spacecraft.The communication with Earth could even be limited to certain periods of time once the shades are in place, given that it is just necessary to inform about the state of each one of them but not to control their position because it will be controlled autonomously by the spacecraft itself.

The maximum mass assigned for each one of the subsystems was defined in subsection 3.1.2. These masses must be compared with the mass of these type of subsystems nowadays in order to check its credibility. With a view to carry out this comparison, off-the-self elements for each subsystem were used as reference. This is merely an examination of the feasibility of the target masses, but it does not define the final elements for the subsystems. This would correspond to a task in the near future of the project. The weight found for the different subsystems is shown in Table 5.1. Since each element was not defined in detail the total power needed by the spacecraft was unknown but, based on other satellites traveling to the L1 point with bigger sizes like the WIND spacecraft (1250 kg and 370 W) [45] or the Aditya (around 400 kg and 400 W) [46],it was decided that 150 W should be more than enough considering the absence of payload. This value was necessary to approximate the power subsystem weight.

Some subsystems were not properly deﬁned or were marked as unknown. The reason for this is that these are more complicated to approximate without an initial design of the spacecraft. In the case of the structure, the geometry or disposition of each subsystem would be needed for it to be determined. Given the early stage of this study, these aspects are not set yet. Despite this uncertainty, it is possible to make some observations. The most common space structure materials are aluminum alloys, such as Al 6061 or composite materials, such as Carbon Fiber Reinforced Plastic with aluminum honeycomb sandwich panels. A representative number of the density of the two materials can be found in Table 5.2, since both can experience a large number of com- position variations that would change this value. Considering the properties of these, the amount of material that would be available for the structure based on the mass assigned in each of the cases can be found in the table. In order to be able to decide if these volumes would be enough for the structure, one must go through some references. A 1U CubeSat oﬀ-the-shelf structure made of Al 6061 has a volume of around 3.7 × 10−2 cm3 [53], which is a hundred times smaller than the value obtained for the aluminum alloy in the results. Looking at these values and considering that the weight of the bus without the CHAPTER 5. DISCUSSION 45

Table 5.1: Spacecraft elements for mass budget validation. Subsystem Elements Mass Star tracker 200 g [47] AOCS Sun sensors 200 g [48] Inertial Measurement Unit (IMU) 55 g [49] Solar array for 150W 425 g [50] Power Li-ion battery 1 - 2kg [51] Structure Unknown - MLI Up to structure Thermal Low absorptivity coatings Up to structure Radiators Up to structure On Board Computer 76 - 100 g [52] CDH Patch antennas Membrane 20 kg [36] Solar sail module Booms 4.5 kg [36] Reﬂectivity Control Devices 80kg

Table 5.2: Structure materials Al 6061 CFRP Al-Honeycomb Density (kg m−3) 2700 200 Material volume (cm3) 4.66 63 propulsion system should be around 35 kg, it feels safe to say that the structure mass target will not be a problem.

In the case of the thermal subsystem, as it was pointed out in Table 5.1, it was hard to approximate it without the structure and configuration definition. However, using a similar mission as reference it was possible to check its feasibility. In the HelioStorm mission [33], designed in 2006 with the goal of reaching the first Lagrangian point with a solar sail, the thermal subsystem mass was in total 3.6 kg. This value is really close to the one assigned for this subsystem in Table 3.3. Considering the technology advances already made since then and the lack of payload in the mission in hand, the final mass for the subsystem would probably be lower.

Concerning the rest of subsystems, by comparing Table 5.1 with Table 3.3 46 CHAPTER 5. DISCUSSION

it is possible to observe that the target masses would be feasible in all cases but the RCD. Most of the subsystems still have a mass margin with respect to the maximum, but it must be kept in mind that no wires or any type of con- nections between subsystems were taken into account in 5.1 . Furthermore, it needs to be considered that for the lifetime expected, there will be a need of redundancy in several of these elements.

The RCD were considered to be part of the solar sail assembly instead of being inside of the AOCS subsystem. In order to comply with the mass set for this propulsion system, these devices should have a mass lower than 10 kg, keeping in mind that part of the mass should be used for the container of the assembly and its deployment mechanisms. Considering the RCD density and surface used in IKAROS [54] and scaling their values for the project, the mass for the control method was found to be around 80 kg, which is far more than desired. This is the only element that does not comply with its mass target but, given the early stage in its design, it is to be expected that in the following decades its density will decrease considerably. Furthermore, the calculations was done considering the need to cover 9% of the area with the devices, which could also change.

Related to the control strategy followed, although the use of swarm strategies is a technology still being introduced to the space sector, it has been used in other industrial areas and therefore it should not generate any problem in the future.

5.2 Launch

The launch deﬁnition is an important part of the mission given the large mass that needs to be put up in space. This discussion mainly focuses in the possible challenges that this large number of launches could entail, both from an operational and an environmental point of view.

5.2.1 Launch in Numbers The launch results given in subsection 3.2.2 are susceptible to change over time since they depend on whether the Starship achieves SpaceX prospects or not. Furthermore, although all the calculations were done based on this launch vehicle, in the future new companies could enter the sector with better numbers. CHAPTER 5. DISCUSSION 47

All the assumptions for the Starship taken during the calculation are numbers given by the company itself but very few are final decisions, just expectations. The only number that seems to be set is the payload capacity that they are aiming to accomplish. Other figures, regarding timelines and number of vehicles, will need to be redefined in the future because currently SpaceX is still testing the ship, although they were planning to carry out the first orbital flight with the Starship the second quarter of 2020. Moreover, it must be outlined that for the calculations presented in Table 3.5 the volume of the payload fairing was not taken into account, they were done just considering the maximum mass capacity of the launcher. Thereby, it could be possible that the number of launches would need to be higher if the maximum payload mass could not be filled due to volume problems.

For the current state of space activity, the numbers given in Table 3.5 seem very high even though the number of launches is increasing each year. As stated in [55], the number of launches for the past decade has been increasing 8% per year, reaching 114 in 2018. If this trend would hold for the next thirty years, the number of launches by 2050 would be around 1400, which represents around 5% of the total number that would be needed for this project alone. The conclusion that can be drawn from these data is that, to make these results plausible, the space industry must be shaken up considerably, either by SpaceX or other companies. This seems possible given the space sector history but it is really uncertain.

5.2.2 Environmental Impact The consideration of the environmental impact of the project under study is fundamental to evaluate its implementation. The final goal of the mission is the reduction of the average global temperature to help the fight against climate change. If the development of the project caused a noticeable large effect in the Earth’s climate, it would be counteracting its objective and therefore it would not make sense to carry it out.

Historically, rocket emissions have been considered not to have a signiﬁ- cant impact in the global environment due to the low frequency of launches. As a consequence, the studies and climate simulations regarding rocket emissions are very few and mostly approximations, leaving unclear what the eﬀects of these emissions could be. The number of rocket launches has increased by 48 CHAPTER 5. DISCUSSION

Table 5.3: Carbon dioxide emissions calculations. Total propellant mass per launch 4 500 tonnes Methane mass per launch 900 tonnes Carbon dioxide emission per launch 2 475 tonnes Carbon dioxide emission in one year (77 launches per day) 70 million tonnes

8% a year in the last decade and is expected to suﬀer a greater acceleration in the following years. Because of this, the scientiﬁc community is starting to be more interested in its study [55].

The Starship propellant is formed by methane (CH4) as fuel, and liquid oxygen (LOX) as oxidizer [42]. Thus, the main products that result form its combustion are water (H2O) and carbon dioxide (CO2), but if the combustion is not complete other products appear in smaller amounts such as carbon monoxide (CO), hydrogen (H2) and Black Carbon (BC) particles. The exact quantities of each one of these products is unknown because of the lack of ex- perimental data. The two emissions that are going to be considered next are CO2 and BC, which are believed to be the ones with a higher impact.

The emissions of CO2 accumulate in the atmosphere as a whole, as any other CO2 emissions from other sources, and they have the same eﬀects to climate change [55]. For the case of the Starship, some calculations were done to approximate the amount of carbon dioxide per launch and per year, in order to be able to compare it with emissions from other sectors. These calculations were done considering a perfect combustion, which would give as products water and carbon dioxide. As it is shown in Table 5.3, the emission per year resulting from launching the sun shades would be 70 million tonnes. To put this value into context, the carbon dioxide emissions from commercial avia- tion in 2019 reached 915 million tonnes [56] and passenger cars emitted 3 600 million tonnes of carbon dioxide in 2018 [57]. Comparing the numbers, the launch of the spacecraft would represent quite a small percentage of the global emissions, although these are expected to decrease in the following years. Fur- thermore, considering that these emissions would only take place during a 20 year period and then they would be completely cut oﬀ, it seems reasonable to say that the contribution of the launches to the carbon dioxide emissions could be assumed for a greater good.

Regarding the emissions of BC particles, its eﬀects are much more uncer- CHAPTER 5. DISCUSSION 49

tain. This kind of particles concentrate in the stratosphere and around the area where the launch takes place, unlike carbon dioxide which accumulates in the whole atmosphere. BC particles have been considered good candidates for geoengineering SRM proposes since they reduce Earth’s albedo and absorb part of the solar radiation. As a result, they decrease radiation reaching the lower atmosphere which make it seem like these particles could help cooling the Earth [55]. In reality is not that simple. In fact, the only study regarding the effects of these particles in the Earth’s climate, although carried out for sub- orbital hybrid rockets, showed that the climate impact of these soot emissions 5 dominate over CO2 by a factor of 10 [55]. Rocket launches would create an unbalanced concentration of BC on the atmosphere generating different effects on a regional level. For this reason, the mean global temperature would barely change but there could be important changes of temperature in certain areas, like polar regions. Furthermore, the unbalance would change atmospheric cir- culation and ozone distribution. However, as mentioned before, the real effects of these emissions are not clear and further studies must be carried out using more detailed models.

Given that the possibility of using another launch vehicle is not out of the table, the effects of other types of propellants must be acknowledged. Any other option using a carbon based fuel would have effects really similar to the ones mentioned for the kerosene. However, another popular propellant for rocket engines is formed by liquid hydrogen (LH2) and liquid oxygen (LOX), which gives as only product water (H2O) and also hydrogen (H2) if the combustion is not complete. The effects of this combustion would be reduced to the effect of water vapour, which can have an impact in the mesosphere and the ionosphere [55]. Currently these appear to have a smaller effect in the global climate than BC or CO2 but, as mentioned before, more detailed studies need to be done in these areas in order to be sure about the climate impact of these emissions.

5.3 Trajectory Results

In subsection 3.3.2 it was mentioned that the final results do not correspond with the injection in the final orbit where the shades must be located. The reason for this is that when selecting the best position for the shades, the optimal location and movement to minimized regional climate effects given in [16] was used as reference. Although, when the dimensions of the shades were changed, the results given in the mentioned paper could not be used because 50 CHAPTER 5. DISCUSSION

the new optimal position should be recalculated. Since the optimization of the climate effects of the shade was out of the scope of this project, it was decided that considering the absence of a final orbit definition, the trajectory could be optimized using the new equilibrium point as goal. In [27] it is possible to compare the difference between the results of optimizing reaching the equilibrium point and injecting the spacecraft in a certain orbit. The paper shows that the time difference between both options differs in around two months, taking longer to reach the equilibrium point with no velocity. Based on these results, it can be concluded that the time that would result from reaching the final trajectory would probably be shorter that the one obtained in the study. This places the results of the project on the conservative side.

It must be stressed that during the trajectory deﬁnition the change between angles was considered instantaneous. This does no represent reality accurately and it means that the real time will be longer that the results obtained, since the optimal angles would take more time to be reached.

One of the most critical parts of the trajectory is the escape of the Earth’s gravitational field. Once outside of this area, the chances of the solar sail facing space debris are really low, but inside of it space debris entails a high risk. Although the initial target orbit was chosen trying to avoid it as much as possible, as it can be seen in Figure 2.1, the space debris suffers an increment when approaching the geostationary orbits area. The large dimensions of the sail increase the chances of being damaged by a piece of debris when crossing this area. This fact could limit the performance of the solar sail during the escape of the Earth’s gravitational field. Further study would be necessary in that field. In case the risk of loosing the sail would be very high, the mission might need to be changed in order to put the solar sail directly in an escape trajectory using the launcher second stage. In this way, the solar sail could be deployed once outside, avoiding the space debris but its launch cost would be much higher.

5.4 Cost

First of all, it must be emphasized that the cost calculation done previously is a rough approximation based on guesses. In the case of the launch mainly because SpaceX, being a private company, does not reveal budgets or cost be- yond those values mentioned by their executives on interviews or speeches. Regarding the cost of the manufacturing, the number is based on assumptions CHAPTER 5. DISCUSSION 51

because a space project of these dimensions has never been tackled before.

The final cost approximated for the project in section 4 was around US$10 trillion during 20 years, which gives around US$500 billion a year, even less if the number of years that the shades will be active are considered. It seems appropriate to compare the cost of the project with the cost that climate change will have for the global economy in the next decades. The cost of the effects will change depending on how much temperature rises in the future and therefore, the predictions depend on the assumptions made during the study. Burke et al. [58] projected a reduction between 15-25% in per capita output (per year) by 2100, compared to a world whose temperature stayed stable since 2000-2010. This prediction was done considering that the national commit- ments regarding climate policies stayed the same and therefore a 2.5-3◦C temperature increment would be expected by then. In order to see the magnitude of these losses it is necessary to translate these percentages into amounts of money. The transformation of these values into money is complex since the Global Domestic Product (GDP) in 2100 must be predicted and it is a variable that depends on a large number of factors. Considering five different socio- economic pathways Leimbach et al. predicted a global GDP ranging between US$309 trillion and US$906 trillion [59]. Using these data, the cost of climate change in 2100 would oscillate between US$46 and US$77 trillion, based on the most pessimistic GDP prediction, and between US$136 and US$227 trillion with the more optimistic. Thus, even with the more pessimistic forecast for the growth of the global economy, the price of the sun shades would only represent a fourth of the total losses that the global GDP will experiment in 2100 if no further actions are taken and global warming reaches 3◦C by then.

Even though the project would have a high cost, it seems affordable when compared with the cost that climate change will have for the global economy if no further actions are taken. However, the non permanent nature of this measure together with its enormous financial investment give rise to a debate: Would not it be more effective to invest this money in permanent solutions to reduce carbon dioxide emissions? In order to give an answer to this question, both options should be deeply analysed comparing their effects and chances of becoming a reality. It must be kept in mind that the goal of this geoengineering approach is to buy more time to achieve the emissions reduction goals but it does not provide a solution. Chapter 6

Conclusions

Space based geoengineering techniques have been studied for a long time from a theoretical point of view, but just a few times its practical realisation has been evaluated. This report aims to shed some light to the feasibility of this realization in the near future, considering the space sunshade approach presented in [16]. The aspects considered for the study are the size and conﬁguration of the spacecraft, the launch and the travel from a LEO to the vicinity of the ﬁrst Lagrangian point. Moreover, the cost of the whole project has been analysed.

This research has shown that it could be possible to deploy the space sunshade by 2050 but there are some challenges that must be overcome. From a technological point of view, there could be just one problem related with the mass of the control system, since the mass assumed for the RCD is too high. The rest of the technology necessary for the development of the mission is already operational or is expected to be in the near future, being the solar sail propulsion the one with the lowest TRL, with a value of 7 thanks to the deployment of IKAROS [36].

The main issue regarding the implementation of the sunshade is its size: 57 million tonnes and 6.3 trillion square meters, which translates in a volume of mass that has never been handled in the space industry before. As a consequence, the realization of the sunshade would be a challenge from a manufacturing as well as from a launching point of view.

In order to avoid fatal consequences for the planet, it has been decided that the shade should be in place by 2050. Considering the travel time from the orbit around the Earth to the Lagrangian point, this timeline would not be an

52 CHAPTER 6. CONCLUSIONS 53

issue, since the trip takes less than three years. The possible problem regarding the time goals would come from the launch capabilities. If the volume of launches were too big for the industry to manage it by the time the shades are needed to be put up in space, the project would certainly be delayed.

The trajectory analysis carried out in this report could be improved by using a diﬀerent optimization method. In this case, the control variables have been discretized and considered to change instantaneously. If these variables were considered continuous during the whole trajectory and their variation rates were taken into account, the ﬁnal solution would be closer to reality.

This project offers a first approximation to how the implementation of a space sunshade could be achieved but some refinements need to be made. A deeper understanding of the climate model used for the optimization of the sunshade configuration in [16] is necessary in order to define the final orbit in which the sunshades should be injected, since in this study it was just required for them to reach the vicinity of the new Lagrangian point. The spacecraft design must reach a more detailed description and some advances in certain subsystems must be carried out, such as the RCD. Regarding the launch phase of the mission, during the project most of the calculations have been done based on the future project of SpaceX, the Starship, however, this is not necessarily the only option. New competitors could enter the market in the following years or even the design and development of a new launcher could become part of the project. Bibliography

[1] R. Nunn et al. Ten Facts about the Economics of Climate Change and Climate Policy. Stanford Institute for Economic Policy Research and The Hamilton Project, 2019. [2] United Nations Environment Programme. Emissions Gap Report 2019. UNEP, 2019. [3] J. Shepherd et al. Geoengineering the climate. Science, governance and uncertainty. The Royal Society, 2009. isbn: 978-0-85403-773-5. [4] F. Pierce. Geoengineer the Planet? More Scientists Now Say It Must Be an Option. Mar. 29, 2019. url: https://e360.yale.edu/ features/geoengineer-the-planet-more-scientists- now-say-it-must-be-an-option (visited on 04/15/2020). [5] V.Masson-Delmotte et al. Summary for Policymakers. In: Global Warm- ing of 1.5C. An IPCC Special Report on the impacts of global warming of 1.5C above pre-industrial levels and related global greenhouse gas emission pathways, in the context of strengthening the global response to the threat of climate change, sustainable development, and eﬀorts to eradicate poverty. IPCC, 2018. [6] Alan Buis. A Degree of Concern: Why Global Temperatures Matter. url: https://climate.nasa.gov/news/2865/a-degree- of-concern-why-global-temperatures-matter/ (visited on 04/27/2020). [7] European Commission. Climate change consequences. url: https: / / ec . europa . eu / clima / change / consequences _ en (visited on 04/06/2020). [8] Paris Agreement. United Nations Treaty Collection, Chapter XXVII 7. d. url: https://treaties.un.org/pages/ViewDetails. aspx?src=TREATY&mtdsg_no=XXVI-7-d&chapter=27& clang=_en (visited on 03/28/2019).

54 BIBLIOGRAPHY 55

[9] G. Muttitt et al. The Sky Is The Limit: , Why The Paris Climate Goals Require a Managed Decline of Fossil Fuel Production. Oil Change In- ternational, 2016. [10] C.R. McInnes. “Planetary Macro-Engineering Using Orbiting Solar Re- flectors”. In: Macro-Engineering: A Challenge for the Future. Ed. by V Badescu, R.B. Cathcart, and R.D. Schuiling. Vol. 64. Water Science and Technology Library. Springer, 2006. Chap. 11, pp. 215–250. isbn: 978-1-4020-3739-9. doi: 10.1007/1-4020-4604-9. [11] C.R. McInnes. “Space-based geoengineering: Challenges and requirements.” In: SAGE Journals 224.3 (2010). doi: 10.1243/09544062JMES1439. [12] Mautner N.M. “A Space Based Solar Screen Against Climatic Warm- ing”. In: Journal of the British Interplanetary Society 44 (1991), pp. 135– 138. [13] J. Pearson, J. Oldson, and E. Levin. “Earth rings for planetary environment control”. In: Acta Astronautica 58.1 (2006), pp. 44–57. doi: 10.1016/j.actaastro.2005.03.071. [14] Struck C. “The Feasibility of Shading the Greenhouse with Dust Clouds at the Stable Lunar Lagrange Points”. In: Journal of the British Inter- planetary Society 60 (2007). [15] R. Angel. “Feasibility of cooling the Earth with a cloud of small spacecraft near the inner Lagrange point (L1)”. In: Proceedings of The Na- tional Academy of Sciences of the USA 103.46 (2006), pp. 17184–17189. doi: 10.1073/pnas.0608163103. [16] J-P. Sánchez and C.R. McInnes. “Optimal Sunshade Configurations for Space-Based Geoengineering near the Sun-Earth L1 Point.” In: PLOS ONE 10.8 (2015). doi: 10.1371/journal.pone.0136648. [17] C.R. McInnes. “Planetary macro-engineering using orbiting solar reflectors.” In: Macro-engineering: a challenge for the future (2006), pp. 215– 250. doi: 10.1007/1-4020-4604-9_11. [18] National Aeronautics and Space Administration. Major NASA Develop- ment Programs Program Cost Estimates. url: https://www.hq. nasa.gov/office/codeb/budget/LIFCY982.htm (visited on 04/09/2020). [19] Starship User’s Guide. Space Exploration Technologies Corp. Mar. 2020. 56 BIBLIOGRAPHY

[20] A. Jones. China reveals details for super-heavy-lift Long March 9 and reusable Long March 8 rockets. url: https://spacenews.com/ china - reveals - details - for - super - heavy - lift - long-march-9-and-reusable-long-march-8-rockets/ (visited on 04/02/2020). [21] Management of NASA’s Europa Mission. IG-19-019. NASA Oﬃce of Inspector General Oﬃce of Audits, 2019, p. 18. [22] Russia’s super-heavy rocket to deliver landing/launch module to Moon in 2029 – report. url: https://www.rt.com/russia/451448- russia-heavy-rocket-moon/ (visited on 04/02/2020). [23] SpaceX. Falcon Heavy. url: https://www.spacex.com/falcon- heavy (visited on 04/09/2020). [24] M. Wall. SpaceX’s Starship May Fly for Just $2 Million Per Mission, Elon Musk Says. url: https://www.space.com/spacex- starship-flight-passenger-cost-elon-musk.html (visited on 04/13/2020). [25] M.A. Peck and J.A. Atchison. “Length Scaling in Spacecraft Dynam- ics”. In: Journal of Guidance, Control and Dynamics 34.1 (2011), pp. 231– 246. doi: 10.2514/1.49383. [26] C.R. McInnes. Solar sailing. Technology, Dynamics and Mission Ap- plications. Springer, 1999. isbn: 978-1-85233-102-3. [27] J. Heiligers et al. “Sunjammer: Preliminary End-to-End Mission De- sign”. In: AIAA/AAS Astrodynamics Specialist Conference (2014). doi: 10.2514/6.2014-4127. [28] V.L.Coverstone and J.E. Prussing. “Technique for Escape from Geosyn- chronous Transfer Orbit Using a Solar Sail”. In: Journal of Guidance, Control and Dynamics 26.4 (2003), pp. 628–634. doi: 10.2514/2. 5091. [29] M. Otten and C.R. McInnes. “Near Minimum-Time Trajectories for So- lar Sails”. In: Journal of Guidance, Control and Dynamics 24.3 (2001). doi: 10.2514/2.4758. [30] P.E. Gill and E. Wong. User’s Guide for SNOPT-MATLAB:Matlab interface for nonlinear optimizer SNOPT. University of California. La Jolla, CA 92093-0112, USA, Apr. 2017. BIBLIOGRAPHY 57

[31] Herbert J. Kramer. IKAROS. url: https://earth.esa.int/ web/eoportal/satellite-missions/i/ikaros (visited on 03/24/2020). [32] The Planetary Society. Light Sail. Fly by Light for Cubesats. url: https: //www.planetary.org/explore/projects/lightsail- solar-sailing/ (visited on 03/24/2020). [33] R.M. Young. Updated Heliostorm Warning Mission: Enhancements Based on New Technology. NASA Marshall Space Flight Center, 2006. [34] A.E. Lyngvi, M.L. van den Berg, and P. Falkner. Study Overview of the Interstellar Heliopause Probe. European Space Agency, 2007. [35] J. Nosanov. Solar System Escape Architecture for Revolutionary Sci- ence. NASA Jet Propulsion Laboratory, 2013. [36] S. Gong and M. Macdonald. “Review on solar sail technology”. In: As- trodynamics 3.2 (2019), pp. 93–125. doi: 10.1007/s42064-019- 0038-x. [37] T. Conn et al. “Operating Small Sat Swarms as a Single Entity: Introduc- ing SODA”. In: 31st Annual AIAA/USU Conference of Small Satellites (2017). [38] A. Farrag, T Mahmoud, and A.Y. ElRaﬃei. “Satellite swarm survey and new conceptual design for Earth observation applications”. In: The Egyptian Journal of Remote Sensing and Space Sciences (2019). doi: 10.1016/j.ejrs.2019.12.003. [39] M. Sabatini and G.B. Palmerini. “Collective control of spacecraft swarms for space exploration”. In: Celestial Mechanics and Dynamical Astron- omy 105.2 (2009), pp. 229–244. doi: 10 . 1007 / s10569 - 009 - 9183-8. [40] O.L. de Weck. “A system approach to mass budget management.” In: AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (2006). doi: 10.2514/6.2006-7055. [41] JAXA. Small Solar Power Sail Demonstrator ’IKAROS’ Successful At- titude Control by Liquid Crystal Device. url: https://global. jaxa.jp/press/2010/07/20100723_ ikaros_ e.html (visited on 04/30/2020). [42] SpaceX. Starship. url: https://www.spacex.com/starship (visited on 04/17/2020). 58 BIBLIOGRAPHY

[43] M. Wall. Elon Musk is still thinking big with SpaceX’s Starship Mars- colonizing rocket. Really big. Jan. 18, 2020. url: https://www. space.com/elon- musk- starship- spacex- flights- mars-colony.html?utm_source=Selligent&utm_medium= email&utm_campaign=9155&utm_content=SDC_Newsletter+ &utm_term=2772300&m_i=40lmxaHOjEDBUELWb3NAUyCq% 5C%2B1o_ G6gTNF3Cprgb5oS1tG9Rsg_ %5C%2BnTFk8mq_ WXOmec3ccekIpb_ zMBn7nruCciQZQZECmGi_ LRm9SX444j (visited on 04/20/2020). [44] P.B. de Selding. SpaceX’s reusable Falcon 9: What are the real cost savings for customers? Apr. 25, 2016. url: https://spacenews. com / spacexs - reusable - falcon - 9 - what - are - the - real-cost-savings-for-customers/ (visited on 05/04/2020). [45] H.J. Kramer. WIND Solar-Terrestrial Mission. url: https://directory. eoportal.org/web/eoportal/satellite- missions/ v-w-x-y-z/wind (visited on 05/11/2020). [46] H.J. Kramer. Aditya-1. url: https://directory.eoportal. org/web/eoportal/satellite-missions/a/aditya-1 (visited on 05/11/2020). [47] Second Generation Star Tracker. ST-16RT2. Sinclair Interplanetary. 2016. [48] Coarse Sun Sensor. Bradford space. Jan. 2017. [49] Ultra High Performance Inertial Measurement Unit. Sensonor. Aug. 2019. [50] Surampudi R. et al. Solar Power Technologies for Future Planetary Sci- ence Missions. Strategic Missions and Advanced Concepts Oﬃce, Solar System Exploration Directorate ,Jet Propulsion Laboratory for Plane- tary, Science Division Science Mission Directorate, NASA, 2017. [51] Saft battery solutions for space: Reliability and performance for over 50 years. Saft. May 2019. [52] ISIS On board computer. ISIS - Innovative Solutions In Space. May 2019. [53] Endurosat. 1U CubeSat Structure. url: https://www.endurosat. com/cubesat-store/cubesat-structures/1u-cubesat- structure/ (visited on 05/14/2020). BIBLIOGRAPHY 59

[54] S. Kikuchi and J. Kawaguchi. “Asteroid de-spin and deflection strategy using a solar-sail spacecraft with reflectivity control devices”. In: Acta Astronautica 156 (2019), pp. 375–386. doi: 10.1016/j.actaastro. 2018.06.047. [55] M.N. Ross and Toohey D.W. The Coming Surge of Rocket Emissions. Sept. 24, 2019. url: https : / / eos . org / features / the - coming-surge-of-rocket-emissions (visited on 05/04/2020). [56] Air Transport Action Group. Facts and Numbers. url: https : / / www.atag.org/facts-figures.html (visited on 05/04/2020). [57] J. Teter et al. Tracking Transport. IEA, 2019. url: https://www. iea.org/reports/tracking-transport-2019. [58] M. Burke, W.M. Davis, and Diffenbaugh N.S. “Large potential reduction in economic damages under UN mitigation targets”. In: Nature 557 (2018), pp. 549–553. doi: 10.1038/s41586-018-0071-9. [59] M. Leimbach et al. “Future growth patterns of world regions – A GDP scenario approach”. In: Global Environmental Change 42 (2017), pp. 215– 225. doi: 10.1016/j.gloenvcha.2015.02.005. TRITA SCI-GRU 2020: 241