LUNAR ORBITAL DEBRIS MITIGATION: CHARACTERISATION OF THE ENVIRONMENT AND IDENTIFICATION OF DISPOSAL STRATEGIES - European Space ...
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LUNAR ORBITAL DEBRIS MITIGATION: CHARACTERISATION OF THE
ENVIRONMENT AND IDENTIFICATION OF DISPOSAL STRATEGIES
P. Guardabasso(1) , S. Lizy-Destrez(1) , and M. Ansart(2)
(1)
ISAE-SUPAERO, 31400 Toulouse, France, Email: {paolo.guardabasso, stephanie.lizy-destrez}@isae-supaero.fr
(2)
Thales Alenia Space, 31037 Toulouse, France, Email: marie.ansart@thalesaleniaspace.com
ABSTRACT private actors are expressing their interest in visiting the
Earth’s moon, with the aim of exploring its surface, ex-
ploiting its resources and establishing there a permanent
There is a clear, increasing interest towards the Moon, presence of humankind. The coming years will likely see
with the idea of establishing permanent human settle- an increase of missions, with a large variety of targets,
ments on its surface and in orbit, assembling and op- masses and volumes. In particular, plans for an orbiting
erating a cislunar orbital laboratory, the Lunar Orbital station are now well established. The strongest candi-
Platform - Gateway (LOP-G), in a L2 Near Rectilinear date for its location is not a classical, keplerian orbit, but
Halo Orbit (NRHO). This new scenario will involve mul- rather a three-dimensional, periodical trajectory defined
tiple actors, including national agencies and private com- in the frame of the Earth-Moon “Three-Body Problem”
panies, which will insert and operate a high number of [16]. The cislunar space, defined as the region between
spacecraft in the cislunar space. A subject that still re- the Earth and the Moon, is in fact dominated by the gravi-
mains open and generally unregulated is the end of mis- tational influences of the two celestial bodies, which have
sion: the majority of past missions have been commanded a comparable effect on the motion of a spacecraft. This
to impact on the lunar surface, but this option might not results in a complex dynamical environment which can
be a sustainable long-term solution. In this work, the present both chaotic and periodical motion. Each three-
Circular Restricted 3-Body Problem (CR3BP) is used to body system admits in fact five equilibrium “libration”
study the dynamics of the Earth-Moon system, and sev- points Li ), around which periodical solutions, called Li-
eral families of periodic orbits are identified and their bration Point Orbits (LPOs), can be found [11].
main dynamical characteristics and behaviours described,
with the final aim of creating a cartography of the cislunar To abide to present regulations and avoid the pollution of
space. This review of CR3BP orbits could prove useful the cislunar space, future missions will require to limit
both for identifying optimal matches with future applica- their generation of debris and properly plan the disposal
tions and provide an estimation of the cislunar space util- of the spacecraft involved. In fact, cislunar debris repre-
isation and debris environment. Particular focus is given sent a risk for future lunar assets, both on orbit and on
to NRHOs since, in the coming decades, they are likely the lunar surface, as well as for Earth’s protected orbital
to become the most targeted orbits for lunar spacecraft regions and surface. Hence, knowledge of the dynamical
and therefore the origin of most artificial debris. Further- environment and of the available strategies for disposal
more, disposal strategies available in the cislunar space, is of paramount importance to mitigate the generation of
such as lunar impact and ejection towards a graveyard lunar debris, towards sustainable space exploration mis-
orbit, are reviewed and evaluated. To provide a prelimi- sions.
nary trade-off for the disposal of planned missions, sev-
eral scenarios are simulated to assess the optimal mission After an introduction on the context of the present re-
design ensuring feasibility of the chosen strategy with re- search and a review of available disposal strategies for
spect to mission requirements and its sustainability with lunar spacecraft, this paper focuses on the analysis of dis-
respect to national and international guidelines. posal manoeuvres from cislunar orbits. In Section 2, the
dynamical framework used in this analysis is presented.
The main characteristics of the cislunar environment are
Keywords: Lunar exploration, Debris, Cislunar space, reported, with attention to the Circular Restricted 3-Body
Disposal. Problem (CR3BP) model and its governing equations.
Moreover, Halo orbits are briefly discussed and the orbits
chosen for the case studies are presented. The proposed
1. INTRODUCTION methodology to analyse disposal of lunar spacecraft is
then illustrated in Section 3. Section 3.2 presents an ex-
ample of application of this methodology for two case
Lunar exploration is once again, after the last Apollo mis- studies. In Section 4, the conclusions of this research are
sion in 1972, in the spotlight. National agencies as well as drawn.
Proc. 8th European Conference on Space Debris (virtual), Darmstadt, Germany, 20–23 April 2021, published by the ESA Space Debris Office
Ed. T. Flohrer, S. Lemmens & F. Schmitz, (http://conference.sdo.esoc.esa.int, May 2021)1.1. Disposal strategies 2. DYNAMICAL MODELS
2.1. The Circular Restricted 3-Body Problem model
Several studies have addressed the problem of disposal
for Sun-Earth LPOs missions, because of their interest The CR3BP studies the motion of a particle in the com-
for astrophysics and solar observation missions [5, 1, 12]. bined gravitational field of two massive bodies [11].
In the Earth-Moon system, the available literature mainly With respect to the more general three body problem,
discusses disposal strategies for spacecraft on Near Rec- the CR3BP model is based on two simplifications: the
tilinear Halo Orbits (NRHOs), with special emphasis on two spherical massive bodies, denoted as “primaries”,
the L2 southern NRHO with a 9:2 resonance with Moon’s have circular keplerian orbits around their common cen-
synodic period [2, 6, 7]. Some works consider also other tre of mass; the third body in the dynamical system, e.g.
Halo family members [3, 4]. a spacecraft, has a negligible mass with respect to the
primaries, and can’t affect the motion of the primaries,
which makes the problem restricted.
Based on the available literature and on the history of past
missions, a cislunar spacecraft at the End Of Life (EOL) The CR3BP allows for a good understanding of the dy-
has three main options for its disposal: impact on the lu- namical behaviour of a spacecraft travelling in the Earth-
nar surface, transfer to a stable graveyard orbit or perform Moon region, and avoids the complexity and computa-
an Earth atmospheric re-entry. tional effort associated with higher fidelity models. For
this reason, it has been used to perform the preliminary
analyses discussed in this research.
The majority of past missions towards the Moon have
been either directly commanded to impact the lunar sur- The CR3BP dynamical system is conveniently described
face in a short time, or have been left in low lunar orbits, using a rotating reference frame (often referred to as
the instability of which eventually produced an impact. “synodic” frame) centred in the primaries’ common
Nevertheless, any falling spacecraft could damage histor- barycenter, with the axis x pointing towards the smaller
ical sites [10], and it might also pose a risk for future lunar primary, the axis z aligned with the angular momentum
“safety zones”, as defined in the recent Artemis accords vector of the orbiting primaries and y that completes the
[14]. Moreover, if used indiscriminately, impacts can po- right-handed frame. The resulting equations of motion,
tentially pollute areas relevant for scientific research [13] opportunely normalised with a set of characteristic quan-
with heavy materials and chemicals. Hence, it might not tities [11], are:
be a sustainable option in a long-term scenario.
∂ Ũ
ẍ − 2ẏ = −
∂x
From the cislunar space, it is possible to reach heliocen- ∂ Ũ
tric space by performing a single-impulse manoeuvre and ÿ + 2ẋ = − (1)
∂y
exploiting multi-body dynamics of the Earth, Moon and
Sun [3]. Nevertheless, to avoid a 1:1 resonance with ∂ Ũ
z̈ = −
Earth’s orbit, a second manoeuvre can be performed to ∂z
raise (or lower) the orbital energy and avoid re-entries
[1], although this possibility requires maintaining control where Ũ is an “effective” potential, taking into account
of the spacecraft until the second manoeuvre. Other po- for gravitational and centrifugal influences, defined as:
tential graveyard orbits in the cislunar space, around the
Earth or the Moon or on stable Earth-Moon LPOs, could 1 1−µ µ
Ũ = − (1 − µ)r1 2 + µr2 2 − − (2)
have the advantage of keeping the space debris at a reach- 2 r1 r2
able distance, in case a future space economy is able to
profit from the material left in orbit. where r1 = |r1 | and r2 = |r2 | are the position vectors
of the spacecraft with respect to the Earth and the Moon,
and µ = m2 /(m1 + m2 ) is the mass parameter, where
The other possibility to dispose of lunar spacecraft is to m1 and m2 are the masses of the primaries.
inject into a trajectory to re-enter Earth’s atmosphere.
This possibility has not been applied in past missions, ex- Under the above mentioned hypotheses, the CR3BP is a
cept in the case of crew vehicles or robotic sample con- conservative, time-invariant system, and it admits only
tainers returned to Earth. Current directives impose for one integral of motion:
the risk of casualty on ground to be lower than 1 in 10000
[8]. If this number cannot be achieved, a controlled re- 1 2 CJ
entry is necessary, targeting specific low-risk areas. In E= (ẋ + ẏ 2 + ż 2 ) + Ũ = − (3)
2 2
addition, an atmospheric re-entry implies the crossing of
protected Low Earth Orbit (LEO) and Geostationary Or- where CJ = −2E, called Jacobi constant, is often used
bit (GEO) regions, which poses a risk of collision for as- to differentiate between energy levels of orbits and trajec-
sets orbiting the Earth. tories.Table 1: Relevant parameters for the two L2 southern 3. DISPOSAL ANALYSIS
Halo orbits considered in this work.
T Az CJ νi A methodology is here outlined to study the disposal of
Type Ref. spacecraft from CR3BP orbits. A single, impulsive ma-
[days] [km] [-] [-]
noeuvre is applied to several initial states along a chosen
L2 NRHO 6.56 69958 3.06 93.2429 (a) orbit to perform a scan of the possible final destinations.
L2 Halo 13.79 58245 3.08 0.6845 (b) The aim is to correlate initial conditions of a spacecraft,
such as the starting position on the orbit and the initial
manoeuvre’s direction and magnitude, to its final state.
This will contribute in creating a dynamical cartography
of the cislunar space. In the following, methods used
2.2. Halo orbit families to initialise, perturb and propagate trajectories are dis-
cussed, and preliminary results are presented.
In the frame of the CR3BP model, five equilibrium points
can be defined (indicated with Li ), often called “libration” 3.1. Investigation methods
points, around which several families of periodic orbits
can be found [11]. Among these families, Halo orbits
have been already used for past mission and are a poten- First, to identify specific points on an orbit, a period frac-
tial candidate target for future applications. In particular, tion parameter θ is defined as:
NRHOs, which exists at the extremity of the family close
to the Moon, are currently the baseline for a future orbital t − t0
θ= (5)
station. T
where t0 is the time of passage at the periapsis (defined as
To compute halo orbits, first a third-order approximation the minimum distance from the Moon), and T is the or-
is used to provide an initial guess of the initial state [15]. bital period. This equal-time sampling strategy has been
This guess is then refined through an opportunely de- used to obtain the results presented. Considering t0 = 0,
fined differential correction routine until a periodic solu- it follows that θ ∈ [0, 1[, where θ = 0 corresponds to the
tion is found. The entirety of the family is then computed periapsis and θ = 0.5 to the apoapsis of the orbit.
through the process defined as continuation. There ex-
ists Halo orbits for collinear points L1 , L2 and L3 , and for Once an initial state p0 = (x0 , v0 ) =
each libration point, two families can be defined, sym- (x0 , y0 , z0 , ẋ0 , ẏ0 , ż0 ) is identified unequivocally
metrical with respect to the orbital Earth-Moon plane. with a value of θ, an instantaneous change in velocity
These are defined as “southern” and “nothern” families. ∆v is applied so that:
Along a family, it is possible to evaluate several parame- p+
0 = (x0 , v0 + ∆v) (6)
ters: the vertical extension Az , which corresponds to the
maximum value of the z component, the Jacobi constant Then, propagation is performed integrating the dynamics
CJ , defined in Equation (3), and the stability index ν, de- provided in Equation (1) using a variable step solver.
fined as [9]:
The integration is automatically stopped in case the tra-
1 1 jectory intersects the Moon, modelled as a sphere of ra-
νi = λu + (4) dius RM = 1737 km, exits from Earth’s Sphere Of Influ-
2 λs
ence (SOI) of radius RSOIE ' 0.929×106 km, or passes
behind the Earth, i.e. the x component of the trajectory’s
where λu and λs are respectively the unstable (maximum state vector crosses xE , the position of the Earth on the x
in modulus) and stable (minimum in modulus) eigenval- axis.
ues of the “monodromy” matrix of the orbit, which is the
State Transition Matrix (STM) after one orbital period. To assess the disposal options for cislunar orbits in the
CR3BP, a large scan of trajectories is initialised, per-
In the present study, two example orbits are considered: turbed and propagated until an event occurs or the to-
a “large” L2 southern Halo orbit and L2 southern NRHO tal propagation time is reached. In the frame of this re-
with a 9:2 resonance with the Moon’s synodic period. search, the initial state is perturbed in the velocity and
Relevant parameters on the two orbits are reported in Ta- anti-velocity directions, i.e. along the unit vector ûV =
ble 1, with a reference for Figures 3 and 4. These values v0 /|v0 | with a varying magnitude ∆V, resulting in a ma-
are also shown in Figure 1 along the entire family pa- noeuvre:
rameters, plotted with respect to the orbital period T . In ∆v = ±∆V ûV (7)
Figure 2, a graphical representation of the family in the
Earth-Moon system is reported, with the two case study This analysis, although limited to the velocity tangential
orbits highlighted. direction, allows to link each starting point θi and each2UELWDOSDUDPHWHUVRI/+DORRUELWV
9HUWLFDOH[WHQVLRQ -DFRELFRQVWDQW 6WDELOLW\LQGH[
Az>NP@
CJ>@
>@
/15+2 7 GD\V
/+DOR 7 GD\V
2UELWDOSHULRGT>GD\V@ 2UELWDOSHULRGT>GD\V@ 2UELWDOSHULRGT>GD\V@
Figure 1: Main parameters for the L2 Southern Halo orbit family, plotted with respect to the orbital period T . The orbits
considered in this study are highlighted with round coloured markers.
L2 NRHO (T = 6.56 days) propagation outcomes can be extrapolated for each value
L2 Halo (T = 13.79 days) of θ or ∆V, and an overall outcome probability can be
computed for each orbit.
L2
MOON Nevertheless, it is not possible to draw precise conclu-
0.05
sions on the impact latitudes and longitudes due to the
0.00 Moon’s rotation axis obliquity, which is not modelled in
the CR3BP. Some solutions exist to partially overcome
0.05 this issue [7], but they are not implemented in the present
z [-]
research, and only the occurrence of a lunar impact is
0.10
studied.
0.15
3.2. Case study analysis
0.10 In the frame of this research, an example analysis is run to
0.05 1.20
1.15 evaluate the methodology developed and identify future
y [0.00
-]
0.05 1.10 directions of research.
1.05 x [-]
0.10 1.00
Trajectories are initialised on each of the two orbits pre-
sented in Section 2.2 through 500 equally spaced values
Figure 2: Three-dimensional representation of the L2 of θ ∈ [0, 1[. They are then perturbed with 400 differ-
Southern Halo orbit family in the rotating reference ent values of ∆V ∈ [−20, 20] m/s with a step of 0.1 m/s
frame, with adimensionalised units. The orbits consid- (negative ∆Vs result in manoeuvres in the anti-velocity
ered in this study are highlighted. direction). This results in 2 × 500 × 400 = 4000 000 tra-
jectories, which are then propagated in parallel for 200
days, or until one of the stopping events is met.
manoeuvre magnitude ∆Vj to a final outcome. There is
also the possibility that none of these conditions is met Once an outcome is computed for each trajectory, a map
during the propagated time, which results in an unknown can be constructed to link them, for each orbit, to val-
outcome. As it will be seen in section Section 3.2, this ues of starting θ and manoeuvre ∆V magnitudes. An
rarely occurs with the propagation times considered. example of this analysis for the orbits considered in Sec-
tion 2.2 is presented in Figure 3. Several areas of similar
From such an analysis, it is possible to identify “clusters” behaviour can be identified, were small variations in θ
of trajectories with the same outcome, as well as zones, in and ∆V don’t change the final result. Areas where points
terms of θ and ∆V, with chaotic behaviour. The elapsed are more scattered, changing outcomes with small varia-
time of propagation before the occurrence of an event can tions of parameters, identify probable chaotic behaviour.
also be considered to judge disposal options, especially For the NRHO, reported in Figure 3a, such chaotic areas
in the frame of a cluster. Moreover, probabilities of the are observed for small values of ∆V, except for the groupTable 2: Probability of each outcome for 200 days prop- considered as well. Moreover, different directions of the
agation for two example Halo orbits. In unknown cases, disposal manoeuvre can be envisaged, expressed in the
propagation was not interrupted by an event. form of pitch and yaw angles in a Velocity Normal Bi-
Normal (VNB) frame. The use of higher fidelity models
Outcome will allow to create a more realistic cartography, in com-
parison with the results obtained with the CR3BP. This
Lunar Around would also allow for a better identification and charac-
Orbit Exit SOI Unknown
impact Earth terisation of impact locations, the coordinates of which
cannot be precisely determined by the CR3BP. More ad-
L2 NRHO 4.9% 15.0% 80.1%(a): L2 NRHO (b): L2 Halo
20 20
15 15 Passage around
Earth
10 10
5 5 Earth SOI exit
V [m/s]
V [m/s]
0 0
5 5 Moon impact
10 10
15 15 Unknown
20 20
0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00
[-] [-]
Figure 3: Outcome of propagation for the two L2 southern Halo orbits.
(a): L2 NRHO (b): L2 Halo
20 20
15 15
Time to impact [days]
10 10 150
5 5
V [m/s]
V [m/s]
0 0 100
5 5
10 10 50
15 15
20 20
0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00
[-] [-]
Figure 4: Time to impact for the two L2 southern Halo orbits.
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