Geometry Considerations for the Radio and Plasma Waves Instrument on the ESA Jupiter Icy Moons Explorer (JUICE)

MASTER'S THESIS

Geometry Considerations for the Radio and Plasma Waves Instrument on the ESA Jupiter Icy Moons Explorer (JUICE)

Pedro Cervantes 2015

Master of Science (120 credits) Space Engineering - Space Master

Luleå University of Technology

Department of Computer Science, Electrical and Space Engineering

I would like to thank my supervisor Dr. Anders Eriksson (IRFu) for always being able to find a moment to assist and guide me during the course of this thesis. His knowledge and communication skills really helped me with the development of the project. I am also very thankful of his corrections and contribution of ideas to the document.

I also want to thank my supervisor and master program coordinator from LTU Dr.

Victoria Barabash. I really appreciate all the time and work she invested helping me find some funds to help support myself during my studies as well as finding a master thesis. The time she spend and the degree of detail in which she inspected this document is also much appreciated.

Finally, I want to express my gratitude to ESA’s Human Spaceflight and Operations Directorate and the Erasmus+ Programme of the European Union for co-funding this project.

i

Contents

Acknowledgements i

Abbreviations iv

1 Introduction 1

1.1 Introduction to the project . . . . 1

1.1.1 The JUICE Mission . . . . 1

1.1.2 The Radio Plasma Wave Instrument . . . . 2

1.2 Introduction to this document . . . . 3

2 Project Background 5 2.1 The Langmuir Probes . . . . 5

2.1.1 General principles . . . . 6

2.1.2 Bias voltage sweeps . . . . 9

2.1.3 Electric fields and waves . . . 10

2.1.4 Density fluctuations and plasma flow velocity . . . 12

2.1.5 Dust detection . . . 13

2.1.6 MIME . . . 13

2.2 Langmuir probe measurement disturbances . . . 14

2.2.1 The Shadow effect . . . 14

2.2.2 The Wake effect . . . 16

2.3 Project Objectives . . . 19

3 Model Design 20 3.1 Starting Point . . . 20

3.2 The Spacecraft Model . . . 22

3.2.1 The Spacecraft Dimensions . . . 22

3.2.2 The Langmuir Probes . . . 23

3.2.3 The Spacecraft Initial Position . . . 24

3.2.4 The Spatial Constraints . . . 25

3.3 The Shadow Model . . . 31

3.4 The Wake Model . . . 35

4 Results 41 4.1 Phase 4: Jupiter High Latitudes . . . 42

4.1.1 Shadow . . . 43

4.1.2 Wake . . . 45

ii

4.2 Phase 6: In-orbit around Ganymede . . . 47

4.2.1 Shadow . . . 49

4.2.2 Wake . . . 50

4.3 Overall Results . . . 51

4.3.1 Shadow . . . 51

4.3.2 Wake . . . 53

4.3.3 Shadow/Outside Wake . . . 54

5 Conclusions 56 5.1 Discussion of the results . . . 56

5.2 Final Remarks . . . 58

A Full results 59 A.1 Phase 1: PRM (Perijove raising maneuver) . . . 59

A.1.1 Shadow . . . 61

A.1.2 Wake . . . 63

A.2 Phase 2: EVI reduction (Energy, v

and inclination reduction) . . . 65

A.2.1 Shadow . . . 67

A.2.2 Wake . . . 69

A.3 Phase 3: Europa Phase . . . 71

A.3.1 Shadow . . . 72

A.3.2 Wake . . . 74

A.4 Phase 4: Jupiter High Latitudes . . . 76

A.4.1 Shadow . . . 77

A.4.2 Wake . . . 79

A.5 Phase 5: Transfer to Ganymede . . . 81

A.5.1 Shadow . . . 82

A.5.2 Wake . . . 84

A.6 Phase 6: In-orbit around Ganymede . . . 86

A.6.1 Shadow . . . 88

A.6.2 Wake . . . 89

A.7 Phase 6: GCO-500 . . . 90

A.7.1 Shadow . . . 91

A.7.2 Wake . . . 92

A.8 Phase 6: GCO-200 . . . 93

A.8.1 Shadow . . . 94

A.8.2 Wake . . . 95

Bibliography 96

Abbreviations

AU Astronomical Unit

DC Direct Current

ESA European Space Agency EVI Energy Vinf and Inclination GCO Ganymede Circular Orbit GEO Ganymede Elliptical Orbit JUICE JUupiter ICy Moon Explorer

LP Langmuir Probe

LP-PWI Langmuir Probe - Plasma Wave Instrument MIME Mutual IMpedance Measurements

NAC Narrow Angle Camera PRM Perijove Raising Maneuver

RPWI Radio and Plasma Wave Instrument RWI Radio Wave Instrument

SCM Search Coil Magnetometer

S/C SpaceCraft

UV UltraViolet

iv

Introduction

1.1 Introduction to the project

1.1.1 The JUICE Mission

The JUICE (JUpiter ICy moon Explorer) is a European Space Agency (ESA) mission that will send a spacecraft to the Jovian system to perform a thorough investigation of Jupiter and some of its moons, in particular of Ganymede, Callisto and Europa.

There have been numerous ground and space based observations of the Jovian system, ever since Galileo discovered the four largest moons known today as Galilean Moons.

Since then, not only ground based observations have evolved enough to shed an enormous amount of light on this system, but also space exploration has developed to the point where a celestial body that is more than 5 AU from the Sun has been visited on several occasions, particularly by the Pioneer, Voyager and Galileo missions.[ESA, 2012]

Today we have a substantial amount of information about this system. However, there are a few strong reasons that led to the desire of taking it to the next level.

First, the scientific attractiveness of being able to characterize several potential habitable worlds ”in one shot”. Ganymede, Europa and Callisto are believed to posses internal liquid water oceans which reasonably makes them the central object of study when dealing with icy worlds potential habitability.

1

Chapter 1. Introduction 2

Secondly, the Jovian system can be compared to a certain extent to the entire Solar System. The dynamics of Jupiter’s magnetosphere and the electrodynamic coupling between the planet and its satellites can be of great help for being able to understand the dynamics of larger astrophysical bodies or systems. Jupiter will also serve as an archetype for an exoplanetary gas giant, which is also a very important piece of puzzle to understand the formation of the Solar System and our own habitable world.

1.1.2 The Radio Plasma Wave Instrument

The Radio Plasma Wave Instrument (RPWI) is one of the instruments selected by ESA to fly on board of JUICE [Wahlund, 2013]. The RPWI consists of a set of sensors (Figure 1.1) that measures the near DC electric field (Langmuir Probe-Plasma Wave Instrument or LP-PWI), the electric component of plasma waves (LP-PWI and Radio Wave Instrument or RWI), magnetic field component of electromagnetic waves (Search Coil Magnetometer or SCM), radio emissions (RWI) as well as some detailed character- istics of the thermal plasma (LP-PWI) including electric conductivity.

Figure 1.1. Current baseline configuration of RPWI.[ Wahlund, 2013]

The RPWI contributes to a wide range of the mission’s science objectives, which can be divided in 5 main points [ESA, 2012]:

• Determination of the electrical conductivity, properties and dynamics of the exo- spheric cold plasma of the moons and its effects on these moons surfaces.

• Characterize the particle populations within Ganymede, Europa and Callisto exo- spheres, the induced fields coupling to their conducting subsurface oceans and its interaction with Jupiter’s magnetosphere. Investigate Ganymede’s aurora genera- tion mechanisms.

• Contribute to characterize the surface composition of both icy satellites and the role of the internal (Ganymede) and induced magnetic field in controlling surface sputtering processes, and investigating subsurface outflow processes through direct in situ measurements of the ionized component of exhaust plumes if they do exist.

• Contribute to the study processes acting in Jupiter’s magnetodisc, study the large scale coupling process between Jupiter’s magnetosphere, ionosphere and upper atmosphere and study response to solar wind variability and the role of solar wind and planetary rotations on magnetospheric dynamics.

• Contribute to the characterization of the Jovian system radiation environment and its variability over time, radio emissions and contribute to the study of the auroral footprint of the moons.

The RPWI will focus on cold plasma studies and the global understanding of how through electrodynamic and electromagnetic coupling, the momentum and energy trans- fer occur in the Jovian system.[Wahlund, 2013]

1.2 Introduction to this document

In Chapter 1 an overview and the science objectives of the JUICE mission are is pre-

sented. Some of these objectives will determine the measurements that need to be taken,

and determine the conditions for the proper geometrical arrangement of the RPWI, hence

the importance of this section.

Chapter 1. Introduction 4

Chapter 2 is dedicated to a general overview of the basic modes of Langmuir Probe operation. A qualitative explanation of how the spacecraft (S/C) wake and the shadow periods disturb the plasma environment is given. This chapter provides an insight of why different geometrical configurations and plasma disturbances are key factors to consider if plasma measurements are to be taken by the instrument. Finally, the objectives of this project are presented.

Chapter 3 covers the creation process of the simulation model from the starting point, i.e. a few points stored in a database, to a fully functional 3D simulator which is able to ascertain the position of any of the Langmuir probes and whether it is going to be in an undisturbed plasma or not.

Chapter 4 presents the simulation results, i.e. relevant plots and statistics for the whole JUICE mission. Due to the extremely repetitive nature of some results, only a couple of phases will be presented on this chapter, saving the whole series for Appendix A.

Chapter 5 contains the discussion of the results, the conclusions and other remarks.

Appendix A includes all the results omitted in Chapter 4.

Project Background

2.1 The Langmuir Probes

A Langmuir probe is a conductor used to determine the electric potential, electric tem- perature and electric density of a plasma. By introducing one or more electrodes in the plasma and varying the electric potential among the probes or between them and the spacecraft, different properties of the plasma can be obtained analyzing the mea- sured potentials and currents in each mode. The LP is a widely used instrument in space missions. The Cassini mission to Saturn and the Rosetta mission to the comet Churyomov-Gerasimenko include some of the most recent predecessors of the RPWI.

Figure 2.1. Picture of one of the Langmuir probes on board of Rosetta. Image by [Swedish Institute of Space Physics, http://www.space.irfu.se/rosetta/galleri.html].

The RPWI will include four probes, which consist of four 50 mm (diameter) identical spheres of titanium with a golden surface layer of titanium nitride. Each probe is mounted on a 200 mm long titanium stub also coated in titanium nitride, as shown in Figure 2.1. The stubs are mounted on 3 m long (approximately) booms, which are

5

Chapter 2. Project Background 6

attached to the spacecraft body. The positioning of these booms (and the probes) with respect to the spacecraft is the main issue motivating this study.

2.1.1 General principles

Assuming a spherical probe smaller than the Debye length and that the probe is at rest with respect to the plasma, the electron I

and ion current I

expressions are[H¨ oymork, 2002]:

Positive probe potential:

I

= I

(1 − χ

) (2.1)

I

= I

e

(2.2)

Negative probe potential:

I

= I

(1 − χ

) (2.3)

I

= I

e

(2.4)

where

χ

= q

V

k

T

(2.5) and

I

= −A

n

q

s

k

T

2πm

, (2.6)

where A

is the area of the probe, j is the index that denotes the corresponding particle

species, n is the number density of the surrounding plasma (number of free electrons

and ions per unit volume), q is the charge, k

is the Boltzmann constant and T is the

particle species temperature. The probe potential with respect to the plasma is given

by:

V

= V

− V

. (2.7)

In addition to electron and ion currents, a sunlit probe will also emit a photoelectron cur- rent. The solar incoming UV photons will knock out electrons from the probe provided that they carry sufficient energy to trigger this process. Then, depending on whether the probe’s potential is negative or positive, the emitted photoelectrons will be ejected away from the probe or attracted back respectively, as illustrated in Figure 2.2 (showing a positive probe). Note that in the case of the positive potential, if the emitted electron has sufficient energy it can overcome the potential and eventually escape the probe’s field. This effect is of special importance in tenuous plasmas, since the photocurrent becomes dominant for the negative potential region.

Figure 2.2. Photoelectric effect on the Langmuir probe. Image by [Swedish Institute of Space Physics, http://cluster.irfu.se/efw/ops/dummies, downloaded 2013-03-06].

Once this effect has been described, it is much easier to make sense out of the current- voltage or I-V curves and the effect that the photocurrent has on them. Figure 2.3 illustrates the difference between two I-V curve examples from the Langmuir probe instrument (LAP) on board of Rosetta.

It can be seen that the photocurrent for the negative potential reaches a constant value

fairly quickly, given that at a certain point all electrons can escape the probe regardless

of how negative the potential is, reaching a saturation point.

Chapter 2. Project Background 8

Figure 2.3. Top: I-V curve with no photoelectron current. Bottom: I-V curve with photoelectron current.[Billvik, 2005]

I

= −I

, V

< 0 (2.8)

For a positive potential the current value goes to zero very fast; while the potential

value is still small (compared to the typical energy of a photoelectron at emission),

some electrons might still have enough energy to escape the probe and still remain as a significant photocurrent value, but at some point this is not possible anymore, resulting in a null current. Also note how the photoelectron current creates a stable low impedance zone in the curve; where the slope becomes the steepest. This low impedance connection to the plasma is necessary when useful electric field measurements need to be taken. The following equation is used to describe approximately the exponential decay of the photocurrent with the increase of the potential:

I

= I

(1 + V

V

)e

−VP P

Vph

, V

> 0 (2.9)

Finally, the total current for a sunlit probe becomes:

I = I

+ I

+ I

(2.10)

To highlight the relevance of this study with respect to the Langmuir probes functioning, it is important to have a basic understanding of how these operate and their main operating modes. Keep in mind that the only goal of this description is to provide an overview of the basic parameters that can be measured by Langmuir probes as well as the physical quantities upon which these measurements depend on. For a more detailed description, see chapter 7 from [H¨ oymork, 2002] and [Merlino, 2007].

2.1.2 Bias voltage sweeps

The bias voltage sweep mode is used to estimate both ion and electron temperature as well as the densities. The bias voltage of the probe with respect to the spacecraft V

is swept over an interval from a negative to a positive value while at the same time the

current is being measured. This will generate a current function dependent on the bias

voltage, which is then represented as a current-voltage or I-V curve. As can be seen in

Equations (2.1) - (2.10) above and also illustrated in Figure 2.4, this current depends

on the plasma parameters n and T , so we can use the sweep to derive these parameters.

Chapter 2. Project Background 10

Figure 2.4. I-V curve example for electrons. Note how the slope of the curves in the linear region of the positive bias is characteristic for every pair of density and temperature values, as well as how the exponential decay with increasingly negative voltage below V = 0 depends on the electron temperature T

.[Wahlund, 2013]

The values for n

, n

, T

and T

can then be derived combining equations 2.1-2.6 and assuming that T

>> T

and m

<< m

.

2.1.3 Electric fields and waves

The variation of the electric field can be estimated by using a constant bias current on the probe. The quantity that is measured is the potential between the probe and the spacecraft, V

. The bias is chosen in order to have the resistance between the probe and the plasma as low as possible, which is the point where the I-V curve is steepest.

Due to the high sensitivity to fluctuations in the spacecraft potential for a single probe, usually two probes are used separated by a distance ~ d.

δE

= V

− V

d ' ~ δE

· ~ d (2.11)

where δE

is the measured electric field, V

is the spacecraft-probe with index i potential difference and ~ δE

is the true electric field. “In practice, the measured voltage difference will also be affected by differences between the probes and their environments, and the presence of the spacecraft can significantly change the ideal dependence on ~ δE

[Pedersen, Mozer, and Gustafsson, 1998]”

This double-probe setup has much less sensitivity to fluctuations in the spacecraft po- tential, but also requires that the changes in the potential of the field vary slowly enough in space to be able to be resolved with the chosen separation distance of the probes.

In other words, only fluctuations with wavelengths much larger than d (∼ 6 m) will be correctly measured.

The LPs allow measurements of full electric field from DC up to 1.6 MHz (measurement frequency). This range has never been possible to achieve on previous missions to outer planets, which makes it even more of a crucial key factor to be able to meet the science goals. Furthermore, it is required to have the 4 LPs extended as far as possible from each other and from the spacecraft, i.e. in a diverging configuration, since the LPs should avoid contamination from the photoelectron cloud surrounding the spacecraft and the solar panels. It is also important to keep the configuration as symmetric as possible. In addition, there are several other effects that will condition the measurement performance, i.e. photoelectron emission from the spacecraft, differential charging of large insulating surfaces, asymmetric surfaces affecting the S/C potential pattern and the plasma environment itself. It is also important that the exterior surfaces of the spacecraft as well as the solar panels are conductive to limit the disturbances.

Depending on the geometrical configuration of the LP, different magnitudes can be mea- sured. If the LP directions span a volume, the full electric field vector can be obtained.

If on the other hand all probes happen to be on a plane, it is possible to measure a

2-dimensional electric field. Then it can be used to determine the full 3-dimensional

electric field assuming that the electric field component parallel to the ambient mag-

netic field is small, which works well for low frequency plasma processes. If there is at

least two probes on a plane, it is possible to use interferometry to measure the phase

speed of waves supported by the electric field, since each pair of probes will measure

a phase different than the other pair, which is eventually used to compute the wave

vector.[RPWI-Consortium, 2013]

Chapter 2. Project Background 12

If instead of the potential difference between two probes, we introduce the spacecraft body as a third probe and measure its respective potential differences with the two probes P

and P

collinearly, the phase difference of the two signals can be used to deduce the component of the wave vector ~ k project along their common axis. Logically this setup will be sensitive to spacecraft potential fluctuations, since both differences, V

− V

and V

− V

, depend explicitly on this potential. This drawback can be easily overcome if instead of the spacecraft body we introduce two additional probes.

With two double probes the setup becomes essentially independent of V

.

All these constraints for the probes are crucial to understand the relevance of this study, since they will determine the starting point in regards of the optimal LP configuration.

2.1.4 Density fluctuations and plasma flow velocity

If a probe is biased with a positive potential V

relative to the S/C, the relative plasma density fluctuations δn/n can be obtained by sampling the current fluctuations at the probe. The resistance has to be as high as possible, making the measurements less sensitive to fluctuations in the potential. Assuming that n is proportional to the current I and that the current fluctuations are small with respect to the magnitude of the intensity, the following expression holds:

δI I = δn

n (2.12)

If instead of a single probe, one uses a pair of them separated by a distance d, they can

be used as an interferometer. The temporal delay between two signals on each probe can

be used to estimate the plasma flow velocity. If this is done with several non-coplanar

probe pairs, the full velocity vector can computed.

2.1.5 Dust detection

Another interesting application of the LP is the detection of micrometer sized dust particles. The impact between a dust particle and the surface of the spacecraft can take place at a relative velocity of a few tens of kilometers per second (due to the orbital velocities of S/C and dust particle), which in turn translates into a large impact energy.

This energy is enough to vaporize the particle and even to partially ionize the released gas, typically reaching temperatures ∼ 10

K [H¨ oymork, 2002]. This expanding wave of newly formed plasma is then detected by the probe as a δE pulse in the kHz region.

The charge collected by the probe is proportional to the mass of the original impacted dust grain and therefore it can be estimated using the relation:

Q = km (2.13)

where Q is the charge, m the mass of the dust particle and k is a constant that contains the relative velocity of the impact, the material of the impact surface, composition of the dust particle and the angle of incidence among other factors. [H¨ oymork, 2002]

2.1.6 MIME

The last example of measurement technique is the MIME (Mutual Impedance Measure-

ments). It consists of a pair of LPs transmitting a stimulating signal which is then

received by the other pair of LPs. By sweeping across different frequencies, the fre-

quency response of the plasma can be obtained. This is used to measure the complex

impedance of the plasma, which dictates what kind of wave modes can be supported by

that plasma. For example, the local electron plasma density can be calculated from the

local electron plasma resonance frequency, which is derived from a sharp peak in the

MIME frequency spectrum [RPWI-Consortium, 2013]. Since this electron density mea-

surement is determined with high accuracy, it is then used to calibrate density estimates

obtained by other subsystems/techniques.

Chapter 2. Project Background 14

2.2 Langmuir probe measurement disturbances

2.2.1 The Shadow effect

The first disturbance considered in this study will be the shadow casted over the LPs by the body and/or solar panels of the S/C. Please note that the terms shadow and eclipse will be used interchangeably in this context from now on, unless explicitly indicated otherwise.

Figure 2.5. Artist impression of a spacecraft orbiting Jupiter. Differentially lit sur- faces can be distinguished along the spacecraft. Credit: NASA

Technically speaking, the effects of the shadow affect the probe’s functioning, rather than the plasma itself. The eclipse time that a certain volume of plasma undergoes with the passage of the S/C is not enough to alter the plasma parameters in a substantial way. In other words, if we think of this eclipsed portion of the plasma as the volume

“illuminated” by the spacecraft shadow, one can see that the S/C, moving at speeds of several km/s, will be shadowing completely different parcels of plasma approximately each millisecond, assuming length scales for the LPs of a few meters.

Therefore, the main contrast of a sunlit region versus an eclipsed one is the photoelec-

tron density. The sunlit region of the spacecraft will be emitting photoelectrons, which

will form a frontal cloud of electrons. This means that from the point of view of the

instrument, the electron density is higher in this cloud than on the surrounding plasma

not affected by S/C. However, this asymmetry is neither necessarily beneficial nor in- convenient for the instrument: it actually depends on the operation mode for the probes we intend to execute at that moment.

Let us begin with the advantage of having the probe/s in sunlight. It has already been explained that a sunlit probe will emit a photoelectron current and also how this is desirable to achieve a stable low-impedance connection to the plasma if electric field measurements are to be taken. However, even in shadow one could find a region where the I-V curve is steepest. The major difference is that if there is a part of the curve dominated by I

it is independent of n, such that any possible density fluctuations will not affect the E-field measurements.

On the other hand, the mutual impedance and LP sweep measurements might benefit for being in shadow, since there is less contamination from photoelectrons. After all, a photoelectron is simply a regular electron renamed for the only purpose of indicating its source and therefore for most applications and specially from the point of view of the instrument there is no difference between them. Consequently, if the measurements we are taking are dealing with electron frequencies, they might be affected by an external source of electrons, contaminating the space plasma we want to measure. This would result in spurious electron densities.

Another undesired effect is the asymmetric illumination of two probes performing electric field measurements. A sunward facing probe will emit its electrons away from the boom, since the lit face of the sphere is in the opposite side of the boom-probe joint and also the boom’s shaft. Conversely, a probe facing away from the Sun, will have the boom in the same plane of illumination and therefore some of the photoelectrons emitted by the probe will be captured again by the boom. This will generate an asymmetric electric field in the Sun’s direction, which can lead to spurious electric field measurements [Pedersen, Mozer, and Gustafsson, 1998].

All these effects lead to the conclusion that a precise knowledge of the position of each

probe with respect to the Sun and the S/C body is of vital importance if one wants to

plan beforehand the right times to perform each type of measurement.

Chapter 2. Project Background 16

2.2.2 The Wake effect

Similarly to an aircraft in the terrestrial atmosphere, a spacecraft also generates a wake in its pass through space. However, the properties of the two fluids, air and plasma, are radically different and so is the behavior of the two wakes. Nevertheless the basic physical principle behind this effect is still the same and the same result holds under a qualitative comparison; a region of lower particle density is generated behind the vehicle’s body.

Figure 2.6. Numerical simulation of the wake behind a spacecraft. Top: XZ-plane projection. Bottom: XY-plane projection. The S/C is modeled as a box with two rectangular solar panels on each side. The relative velocity between the S/C and the plasma is along the x direction.[Sj¨ ogren, 2009]

In the simulation shown in Figure 2.6, it can be clearly seen how this density-altered

regions are very significant in size relative to the spacecraft span (35 m). Assuming the

Langmuir probes are mounted on booms of about 2-3 meters, in general there will be

periods in which at least one probe will be inside the wake, given that the length scale

of this disturbance will generally be more than a few meters.

In the case of a spacecraft traveling through plasma, the thermal speed of the ions usually cannot keep up with the velocity of the vehicle, resulting in the effect of the ions and electrons being swept away. In other words, the ions cannot refill the void left by the spacecraft in its pass fast enough to prevent the formation of a substantial wake.

The thermal speed v

can be defined as:

v

=

r 2K

T

m (2.14)

where k

is the Boltzmann constant, T is the particle species temperature and m the mass of the particle. Therefore, the intensity of the wake will strongly depend on these two parameters. Nevertheless, as far as the RPWI is concerned we are only going to be dealing with cold plasma (K

T

= 0.02 − 20 eV), where the most common species consist of various charge states of S and O [Saur et al., 1998]. Therefore, the range of ion thermal speeds that JUICE will be most likely to encounter can be estimated by taking the two opposite extreme cases:

• O

and K

T

= 20 eV:

v

= q

BT_O+

m_O+

=

q

16·1.0344·10⁻⁸

= 1.55 · 10

m/s = 15.5 Km/s

• S

and K

T

= 0.02 eV:

v

= q

BT_S+

m_S+

=

q

32·1.0344·10⁻⁸

= 347.62 m/s = 0.347 Km/s

On the other hand, the spacecraft will be orbiting Jupiter with a range of velocities v

= 4 − 14 Km/s (from SPICE kernels data). One can see that the two ranges of velocities, v

and v

have a big overlap, which would imply a very weak wake at the most, given that the thermal speed of the ions will be always in the order of the S/C velocity (except for the least energetic particles).

However, one must not forget that the plasma is corotating with Jupiter. The bulk velocity of this plasma at 10 Jupiter radii (roughly the closest approach of JUICE to Jupiter) is given by:

v

= ω · 10 · R

= 1.7610

· 10 · 71492 = 125.72 Km/s

Chapter 2. Project Background 18

where ω is Jupiter’s angular velocity in rad/s and R

is Jupiter’s radius in Km. It can be seen that even at this point, where the difference between the speed of the spacecraft and the bulk velocity of the corotating plasma is minimal, there is still one order of magnitude of difference between the two. Therefore, the effect of the spacecraft velocity to the wake can be neglected and the effect of the bulk velocity of the corotating plasma can be considered as the sole cause.

It can also be observed that v

 v

, thus it is fair to assume for the purpose of this project that a wake significant enough in size will form at all times during the trajectory of JUICE.

Another effect that has to be taken into account is the local space charge that appears in the wake. Due to the much higher thermal velocity of the electrons (since they have a much smaller mass), the ion wake will be filled by the electrons, thus creating a local charge. The thermal velocity for the electrons, for the case of the coldest plasma K

T

= 0.02 eV, is given by:

v

= q

BT_e−

m_e−

=

q

5.678·10⁻¹²

= 8.39 · 10

m/s = 83.93 Km/s

This thermal speed is in the same order of magnitude as the speed of the Jupiter coro- tating plasma. However, so far only the extreme case of JUICE’s closest approach with the encounter of the coldest part of the plasma’s temperature range has been consid- ered. During JUICE’s journey, both the electron thermal speed and the speed of the corotating plasma will be constantly changing, as the spacecraft moves closer or further away from Jupiter. Hence, the extent up to which the wake is filled with electrons will also be a variable.

Consequently, we will have a local charge in the wake that will be constantly changing, and so will the potential this charge generates. This effect will cause disturbances in the electric field that will make any attempts to make measurements futile.

Finally, these disturbances of the plasma will affect all of the LP measurement modes.

Consequently, it is going to be desirable to come up with a design where no more than

two probes are going to be inside the wake for long periods of time.

2.3 Project Objectives

This master thesis has the following goals:

• Create a mathematical code that is capable to simulate the whole trajectory of the JUICE mission, as well as the shadow and plasma wake created by the S/C in its course.

• Provide a set of useful results from the design point of view regarding the ade- quateness of any feasible Langmuir probe configuration, both custom chosen and the ones designed by the two companies competing for the S/C construction based on a prediction of wake and sunlight conditions at the probes. In other words, the results should be able to provide with hints about which configuration aspects are of importance for the instrument to contribute to the fulfillment of the science objectives described in Chapter 1.

• Extend the code to be able to be easily tailored to any other current or future mission, not only JUICE.

1Note that some objectives are constrained by the fact that the two configurations from the Consortia cannot be disclosed in this document. Therefore, even though they are still project objectives, they might not be described in this document.

Chapter 3

Model Design

3.1 Starting Point

The mathematical model of this project is based on SPICE kernels. SPICE is an in- formation system to assist scientists to plan and interpret scientific measurements and observations from space instruments, as well as to assist engineers to design the proce- dures and activities needed to conduct space exploration missions.

A kernel is the primary data set on which SPICE is based upon. It can be described as a file where a certain type of information is stored. The following description summarizes the content of each kernel, taken from [NASA, 2014]:

S- Spacecraft ephemeris, given as a function of time.

P- Planet, satellite, comet, or asteroid ephemeris, or more generally, location of any target body, given as a function of time.

The P kernel also logically includes certain physical, dynamical and cartographic con- stants for target bodies, such as size and shape specifications, and orientation of the spin axis and prime meridian.

I- Instrument description kernel, containing descriptive data peculiar to a particular scientific instrument, such as field-of-view size, shape and orientation parameters.

20

C- Pointing kernel, containing a transformation, traditionally called the ”C-matrix,”

which provides time-tagged pointing (orientation) angles for a spacecraft bus or a space- craft structure upon which science instruments are mounted. A C-kernel may also include angular rate data for that structure.

E- Events kernel, summarizing mission activities - both planned and unanticipated.

In regards of this particular project we only need the first two kernels, containing the ephemeris of spacecrafts and celestial bodies. This means that we will be using SPICE only as a target body map, which is a function of time. We can extract from SPICE all the pertaining information regarding the JUICE S/C position as well as Jupiter’s and its moons’. This is collected as a set of point data that describes the relative position of JUICE with respect to Jupiter or in general, any other body that we specify and that exists in the SPICE kernel. That is precisely the starting point: the point position of JUICE with respect to Jupiter over the specified period of time. Internally, SPICE works with a double precision value ephemeris time, however it is more convenient to convert this value to a string containing the desired date.

Figure 3.1. Trajectory (white track) of JUICE’s arrival to Jupiter, as depicted by our model’s graphical output.

The relevant part of the JUICE mission for this study starts when the S/C arrives to

Jupiter (Figure 3.1). This is scheduled to happen on 2030, January the 22nd. The first

stages of the mission upon arrival to Jupiter are not intended to be science phases, but

rather energy, velocity and orbital inclination maneuvers. Nevertheless, the geometrical

considerations of the LPs will start to be analyzed from this point onwards.

Chapter 3. Model Design 22

3.2 The Spacecraft Model

So far the spacecraft is mathematically represented by a mere point in three-dimensional space. To reach our goals, we need to build around this point a geometrical body that can sufficiently describe the relative position of the Langmuir probes with respect to the main spacecraft body, as well as the constraints that the probes are subjected to.

More specifically, the bodies that are responsible for the effects under study happen to be the same; the spacecraft body and the two solar panels. This implies that all we need to model is a three-dimensional geometry that can emulate the effects of the wake and shadow over the LPs. Therefore, we need to model the outer boundaries of the real spacecraft volume. It is then sufficient to define the spacecraft body as a cube and the solar panels as two rectangles, one on each side of the body.

3.2.1 The Spacecraft Dimensions

The simplified dimensions of these elements used for this project are the following:

• Spacecraft body: A cube with a side of 3 meters.

• Solar panels: Two flat rectangles of 17 by 2 meters each.

• Spacecraft body - Solar panels joint: The space between the two elements is 0.5 meters on each side. Note that since the contribution of this kind of frames to the wake or the shadow effects at the distance of the Langmuir probes is negligible, and therefore they are modeled by an empty space in between the two elements.

• Langmuir Probes: They all are mounted on booms in the order of 3 meters, de- pending on the different configurations.

Please note that in this chapter, the units displayed on the different plots are completely

irrelevant: their only aim is to provide the reader with an insight on how the model was

built and set up, as well as how the relative position of the S/C with respect to Jupiter

was defined in terms of angles. Jupiter is scaled 1:1, which in the plots is shown as

one Jupiter radius (Jr), while the S/C dimensions have been magnified several orders of

magnitude.

3.2.2 The Langmuir Probes

For this study, three different LP configurations were tested and compared. The first setup is based on a custom configuration, while each of the other two setups belong to their respective consortium, which are potentially in charge of building the actual JUICE spacecraft. Due to the ongoing competition between these two consortia, the explicit configuration of the LPs will not be described or displayed graphically. Then, for the purpose of this document we define three LP configurations (for the two consortia we only define a name):

1. Custom configuration:

Our custom built configuration is shown in Figure 3.2. All four probes have the geometrical root at the center of the spacecraft body and extend 4 meters from root to tip.

Figure 3.2. Position of the LP on the Custom configuration.

2. Consortium A configuration:

Langmuir probe setup proposed by Consortium A.

3. Consortium B configuration:

Langmuir probe setup proposed by Consortium B.

Chapter 3. Model Design 24

3.2.3 The Spacecraft Initial Position

We can start by arbitrarily choosing a convenient position in space for the S/C, shown in Figure 3.3:

Figure 3.3. Initial position of the JUICE spacecraft in the model, with respect to Jupiter and the Sun direction, indicated by the yellow arrow on Jupiter.

The 3 basis vectors of our tridimensional space S

are defined as follows:

• X

Axis: Along the Solar direction. In the previous image is also indicated by the yellow arrow on the planet as well as by the direction of the lighting.

• Z

Axis: Perpendicular to both the X axis and Jupiter’s orbital plane, pointing towards to the north ecliptic pole.

• Y

Axis: Completes the reference system’s right-handed trihedron.

As for the origin, it will always be defined by the planet or moon around which the S/C

is orbiting in that period of time. This coordinate system is also known as Jovian Solar

Orbital (JSO) coordinates. We also define the reference system S

, which has the same

directions as S

with the spacecraft as the origin.

3.2.4 The Spatial Constraints

Now that the reference system and the initial position of the S/C have been defined, we can introduce the constraints of the motion. For the purpose of this project, these constraints have been simplified to:

• Solar panels: Perpendicular to the Sun’s direction at all times.

• Spacecraft body: A face of the spacecraft is always pointing towards the planet or moon object of study, as if imitating the nadir pointing Narrow Angle Camera (NAC).

• Langmuir probes: The probes are rigidly rotating with the spacecraft body.

• Spacecraft body - Solar panels relative motion: All motions are coupled except along the spacecraft Y axis (see Figure 3.2), where body and panels can rotate independently.

In the actual mission, there will be periods in which the S/C is not nadir pointing, e.g.

when the high gain antenna needs to point towards Earth. However this ”fine tuning”

would end up getting lost anyways due to the current indetermination of JUICE’s differ- ent operating modes along its trajectory, and in addition, we are not interested in small periods of time, given that they will represent a small contribution to the total time a LP can potentially be in shadow and/or inside the wake.

We now must find the way to translate those constraints for the model to assimilate.

This is done through time-dependent rotation matrices. The way to code these rotations was carried out in the following way.

• First stage: The whole spacecraft rigidly rotates to engage on a nadir pointing

position, with the Sun facing side of the cube in the initial position as the chosen

nadir facing face in the final position.

Chapter 3. Model Design 26

Figure 3.4. Top: Spacecraft position vector in space. The projection vector over the

XY plane and its coordinates are also displayed.The angle φ defines the rotation to

get the S/C facing towards Jupiter’s center distance. Bottom: XY plane projection of

the spacecraft position vector. The angle θ defines the rotation to get the S/C facing

towards Jupiter’s rotation axis.

The original spacecraft reference frame S

transforms under these rotations to S

:

S

= R

· R

· S

(3.1)

where θ and φ are defined in Figure 3.4 and R

and R

are:

R

=











cos θ − sin θ 0 sin θ cos θ 0

0 0 1











R

=











cos φ 0 sin φ

0 1 0

− sin φ 0 cos φ











Finally we are left with a nadir pointing spacecraft (Figure 3.5):

Figure 3.5. S/C orientation after the first stage of rotations.

Notice that even if the solar panels can arbitrarily rotate around the S/C Y

axis, in general it will not be possible to place them completely perpendicular to the Sun’s direction. Then, we need one further constraint.

• Second stage: The whole spacecraft rigidly rotates around the nadir axis to a

position where the solar panels can achieve full perpendicularity to the Sun’s di-

rection. The mathematical condition for this is quite simple; we are looking for a

rotation around the nadir axis that leaves the axes of the solar panels with zero x

Chapter 3. Model Design 28

component on S

, i.e. contained in the plane perpendicular to the solar direction.

Then, the angle β necessary for this rotation can be obtained from:

S

= S

· R

=











S

S

S

S

S

S

S

S

S











·











1 0 0

0 cos β − sin β 0 sin β cos β











(3.2)

Notice that the column vector Y

= (S

, S

, S

) axis has a zero x component:

S

= 0 (3.3)

which is determined from the matrix multiplication (3.2) as:

S

cos β + S

sin β = 0 (3.4)

finally β can be obtained as:

tan β = − S

S

(3.5)

After this rotation, the spacecraft orientation changes to the one displayed in Figure 3.6.

• Third stage: The solar panels rotate until they are completely perpendicular to the solar direction. This time the rotations are only applied to the vectors that define the solar panels’ position, while the S/C body and the LPs remain unaltered.

From this point, we can define a third reference system S

that rotates rigidly with the solar panels. Up to now, S

has been treated identically to S

, since spacecraft and solar panels have rigidly rotated it follows that S

= S

and S

= S

. However, the moment we add an additional degree of freedom, namely a rotation around the Y

axis, we need to define yet another reference system.

Similarly as before, we obtain the necessary angle for the rotation from the con-

dition of perpendicularity. This time we impose the condition that the X

has to

be perpendicular to the original Y axis, Y

:

S

= S

· R

=











S

S

S

S

S

S

S

S

S











·











cos α 0 sin α

0 1 0

− sin α 0 cos β











(3.6)

tan α = S

S

(3.7)

Figure 3.6. S/C orientation after the second stage of rotations.

Chapter 3. Model Design 30

Figure 3.7. S/C orientation after the last rotation of the solar panels.

Finally, all the constraints have been imposed to the model. However, for illus- trative purposes all this has been done only for a single instant in time, shown in Figure 3.7. On the actual model, the spacecraft changes its position at each time, which means that the orientation should also change. Luckily the extrap- olation of the matrices and the variables (angles) to a time-dependent frame is rather trivial; it is enough to assign an extra index for each variable to account for each time step. Therefore, we can substitute all the previous equations with a time-dependent equivalent:

R

= R(t)

and ξ = ξ(t) (3.8)

where ξ is a generalized angular coordinate. Once this part of the code is done,

one can select any interval of the JUICE mission and extract any information

regarding the position and orientation of the spacecraft at any time, which is the

feature that forms the building blocks of the next steps in the project.

3.3 The Shadow Model

To create a shadow from the spacecraft is rather simple from the geometrical point of view; one can simply perform an orthogonal projection of the spacecraft volume over the plane perpendicular to the Sun’s direction. This means that we can treat the shadow as a 2-dimensional object that extends from the rear part of the spacecraft to the infinite.

Figure 3.8. Artist’s impression of the JUICE spacecraft flying-by Europa (ESA).

Therefore, we only need to find out whether the Langmuir probes are going to be inside this 2D region or not. In Figure 3.9 we can see the information extracted from the spacecraft model to run the shadow model algorithm:

These three shadow areas are defined in the code as two dimensional regions, according

to their respective time-dependent dimensions. Then, the Langmuir probes’ position vec-

tors are separated into their three spatial components and the algorithm checks whether

any of these are inside a region defined as shadow or not:

Chapter 3. Model Design 32

Figure 3.9. ZY plane projection of the S/C and the LPs (at the tips of the colored arrows) extracted from the full three-dimensional model. Three different shadow areas can be distinguished; one from the S/C body and two from each solar panel.

• Let us define the shadow region G as:

G = G

⊕ G

⊕ G

G ∈ R

(3.9)

where G

is the region pertaining to the S/C body and G

and G

to the two solar panels. The two panels are always facing towards the Sun and hence they will be rectangles of constant dimensions for all times. The S/C will also be always rectangle in this projection, however its dimension will slightly vary as it rotates with respect to the panels. Since all 3 regions are rectangles, we can define them by their specific coordinates in the plane:

G

= (L

, L

, L

, L

) G

= (L

, L

, L

, L

) G

= (L

, L

, L

, L

)

(3.10)

Note that if we take the center of the S/C as the origin of coordinates, the com-

ponents of each region will be symmetric on each axis, hence the + and - signs.

• The code does the following:

If the X component of the LP is smaller than zero (behind the S/C) and if the Y component is smaller than |L

| and the Z component is smaller than |L

|, or if the Y component of the LP is smaller than |L

| and the Z component of the LP is smaller than |L

|, then that LP is inside the shadow.

In other words, it just checks whether the point defined by the LP vector is inside the shadow region or not. The next sequence of images in Figure 3.10 shows graphically how this is performed:

Figure 3.10. Graphical representation of the JUICE spacecraft for the shadow model.

In the first image (top-left) all four probes are outside the shadow region. As the S/C

keeps rotating, two of the probes go behind the solar panels and hence, in shadow

(second and third or top-right and bottom-left respectively). Finally, on the last image

the probes get out of the shadow region.

Chapter 3. Model Design 34

Note that in Figure 3.10 the S/C and solar panels surfaces have a certain degree of transparency, therefore when the probes are behind, they are shown in a darker tone than if they would be in front or outside the shadow. Also notice that neither this fact or the units of the plots are relevant in any way for the program, the code just works with differences of relative positions of numbered-valued objects.

Finally, the code creates a new vector ~ σ

(t) for each of the 4 probes according to the following definition:

~ σ

(t) =







1 p ∈ G at t

0 p / ∈ G at t

where n is an integer index to denote a particular instant in time and p is the integer code for a certain probe, defined as:

– Green probe, p = 1 – Red probe, p = 2 – Yellow probe, p = 3 – Blue probe, p = 4

This allows us to tag each probe to ensure that the probe we are tracking at a certain instant is the same probe we have been tracking until that point, both at graphical level (color) and at code level (index).

Even though for this particular LP arrangement one could argue that not all probes need to be tracked due to symmetry reasons, the intention is to maintain the functionality of the code as general as possible. This will sustain the flexibility of the algorithm at a high enough degree so that one can input any arbitrary Langmuir probe configurations and it would still work.

Finally, this vector ~ σ

(t) will encode all the time intervals on which each one of

the probes is in shadow. Therefore, manipulating this vector one can extract all

the plots and statistics regarding the eclipse of the LPs that will be presented in

Chapter 4.

3.4 The Wake Model

The case of the wake can also be described as a shadow-like effect, i.e. as a region in the neighborhood of the spacecraft that is ”eclipsed” from particles, similarly as a shadow is an eclipse of photons. However, this falls short of a good enough comparison to consider to two effects equivalent from the geometrical point of view. An orthogonal projection is now not enough to generate the desired geometry to represent the wake, since in general, the cross section of a wake is neither going to be the same size or have the same shape as the object that is generating it. Therefore we need to establish some other assumptions to produce this model. Let’s start by defining a very generic wake that fits our case; a spacecraft traveling through a field of corotating plasma with velocity ~ v

(r, t), where this velocity is defined as the radial velocity of the plasma at a distance r from Jupiter’s center. The velocity of the S/C is neglected for these regards, and therefore ~ v

(r, t) will be the variable defining all the parameters of the wake.

For the initial guess of the geometry of the wake, existent data from a previous missions has been used, in the form of the output of a simulation.

Figure 3.11. Output of a SPIS simulation of a spacecraft in a stream of space plasma.

The smoky area behind the spacecraft represents the region where the ion density is

significantly lower than the local ambient unperturbed plasma. File from [Johansson,

2013].

Chapter 3. Model Design 36

In Figure 3.11 an attempt to a graphical representation of a three-dimensional wake is shown. By choosing appropriate colors for the different ion density values, it is possible to attain a visualization of the wake that matches with our intuitive concept of it, at least to some extent. Figure 3.12 tries to dissect further the wake, this time using a color gradient for the density values.

Figure 3.12. Same SPIS output as in Figure 3.11. The 3D wake has been reduced to three 2D cross sections with a ”cool to warm” color gradient. The red regions represent the density values of the wake that are closer to the ambient unperturbed plasma, while the colder colors stand for the lower ion density regions. File from [Johansson, 2013].

As in the previous sections of this document, the lack of quantitative information in the images is purely intended for the purpose of keeping them as general as possible. After all, we are not interested in numbers, but rather in the geometry of the wake. On one hand, the shape and dimensions of the wake can change drastically from one plasma region to another with completely different parameters. Therefore, we need again a model that is flexible enough so that this geometry can be easily edited to simulate a realistic wake for a particular set of conditions. On the other hand, even if two wakes are significantly different, they still share the same topology; an elongated region of low ion density stemming from behind the spacecraft and growing towards the direction of the incoming plasma flow.

The next step is to define an envelope of the wake region that satisfies our demands. An

intermediate simplification of the wake is shown in Figure 3.13:

Figure 3.13. Projections of the S/C and the wake envelope over the three coordinate planes. The incident plasma flow direction is indicated by the red arrows.

It can be observed how the wake envelope has been already reduced to simple geometrical curves in the previous sketch. However this geometry is still far too complicated to be able to be modeled accurately, at least as far as the scope of this project goes. Therefore it is necessary to come up with an even simpler geometry. To achieve this, let us enumerate the main requirements that the model has to comply:

• In general, the wake dimension along the plasma flow direction can vary from zero (no wake) to several meters, nevertheless for all practical purposes the wake regions that are beyond the length of the Langmuir probes can be neglected, i.e.

if one LP is inside a short wake it will also be in a longer one. Therefore we can

”cut out” the wake’s outer regions beyond the LPs reach and just ignore them in

the model, as shown in Figure 3.14.

Chapter 3. Model Design 38

Figure 3.14. First wake geometry simplification. The orange dashed lines represent the cut out plane from the part of the wake that is not within the range of the LPs length.

• By defining the previous operation in such a way, we are certain that if the boom of the Langmuir probe has a component in the flow direction it will never reach the defined boundary. Therefore, in the case that the LP is not inside the wake, it is always going to be if either one of the other two orthogonal components of the LP dimensions is larger than the perpendicular cross section of the wake.

Note that this is precisely the elliptical cross section that has not changed after

performing the previous operation, on the top right of the sketch. Hence, this

becomes the dominant curve as far as our requirements go, since every slice of the

wake in this direction will be elliptical as well, as shown in the next sketch, Figure

3.15:

Figure 3.15. Parallel wake cross sections. The green dashed lines represent different cross sections perpendicular to the flow direction.

• One last important fact to keep in mind, is that the direction of the plasma flow relative to the spacecraft orientation can be completely different from what is shown in the sketches. Those are just the most illustrative cases, but the flow can encounter the spacecraft from any angle, e.g. if the flow is perpendicular to the one presented in the sketches, then the ”wet” surface of the spacecraft would be a single square since the solar panels would be either a line or superimposed to the square. Therefore we need that our geometry somehow captures all these effects, since the dimensions of the wake will vary for every value of the angle between S/C and flow.

• Finally, we are left with the requirement of a geometry that has the following properties:

– Finite dimensions.

– Elliptical cross section perpendicular to the flow direction.

– Flexibility in its size in three dimensions to reflect wakes generated by different spacecraft orientation angles.

The easiest way to satisfy all those three requirements is to choose the 3D homologue of

the ellipse, an ellipsoid. The equation of an ellipsoid aligned with the axis of a Cartesian

coordinate system and centered at the origin is given by:

Chapter 3. Model Design 40

x

a

+ y

b

+ z

c

= 1 (3.11)

where a, b and c are the correspondent dimensions of each semi-principal axis. This implies that one can manipulate these 3 coefficients at every instant so that the size of the ellipsoid reflects as close as possible the current wake dimensions.

Another added benefit of using this approach is the mathematical simplicity of knowing whether the probe is inside the wake or not, since one only has to substitute the coordi- nates of the point probe in x, y and z and see whether or not the result is smaller than 1 or not, respectively.

The wake model is completed by a similar feature to the shadow model, vector ~ w

(t):

~ w

(t) =







1 p ∈ H at t

0 p / ∈ H at t

where n and p denote time instant and probe respectively, and H is the effective wake

region defined by the ellipsoid.

Results

The following section will present a compilation with the most relevant results to the study. To present the results in a orderly and understandable way, specially from the graphical point of view, the whole trajectory has been split into different phases, since only a few orbits can be displayed in a plot in a neat manner. For the most part, the split points are the same as the ones used by ESA to tag each milestone within every phase, unless explicitly indicated otherwise. The ”Labels” column presented on the tables at the beginning of each phase is a way to subdivide each phase even further (see Yellow book [ESA, 2012]), and here are presented with the purpose of facilitating a possible cross-check with various ESA documents.

The results can be divided into two parts: one where the code has been run for each phase individually and a second where it has been run from the first to the last phase in one go. The first set, the individual results, provides a graphical representation together with the numerical data of the output as well as a better insight on what the code does exactly. The second set contains the overall results data for the whole mission; the difference is that the output is purely numerical, since a graphical representation is not possible due to the fact that the amount of data is so large that it cannot be resolved on a standard computer display or an A4 paper sheet.

Due to the repetitive nature of the results, only two phases will be presented in this section: Phase 4 and Phase 6. The two phases take place in different orbits; Phase 4 corresponds to a Jupiter orbit while Phase 6 corresponds to a Ganymede orbit. The complete series of results by phase, including these two, will be left for Appendix A.

The overall results of the whole trajectory will also be presented in this section. The discussion of the results is saved for Chapter 5.

41

Chapter 4. Results 42

4.1 Phase 4: Jupiter High Latitudes

During this stage the inclination of the orbit will be increased up to 30

through a succession of Callisto gravity assists. This will allow the JUICE spacecraft to engage in resonance with Callisto, where they will find each other almost at the same position after every orbit. This will allow to study the unexplored high latitudes of the Jovian magnetosphere and atmosphere, as well as to fulfill the science objectives regarding the internal structure, surface and exosphere of Callisto.

Phase Labels Total time (days) Date

Jupiter High Latitudes G12, C13-C24 226 31/04/02 - 31/11/15 In Figure 4.1 the corresponding trajectory to this phase is displayed, followed by the shadow (Figure 4.2, Tables 4.1-4.6) and wake results (Figure 4.3, Tables 4.7-4.12).

Figure 4.1. Different perspectives of the JUICE orbit plot in the Jupiter inertial frame of reference. Top: 3D view. Bottom left: XY plane projection. Bottom right:

XZ plane projection. Europa, Ganymede and Callisto have been introduced in red,

blue and purple lines respectively.