Over the past few months, several moon missions have been launched, both by institutions and private companies. This new "moon race", fueled by the Artemis program, offered a recent significant achievement with India's Chandrayaan-3 landing, being the second country to achieve successful soft landing in the 21st century and the 4th in history. 

The objective of this seminar is to give an overview of astrodynamics advances applied to state-of-the-art on-going and future moon missions.

Join us for this fantastic journey to the Moon by subscribing to this upcoming COMET-ORB seminar!

This seminar can be taken remotely via the livestorm platform, or face-to-face.

Those wishing to attend in person must register not only with livestorm - which will give them access to the replay of the seminar - but also with evenium - to receive a welcome badge.

The livestorm registration link is as follows: LIVESTORM

The link for evenium registration is : EVENIUM

Schedule

• 08h45-09h00 : Welcome & Introduction - S. Locoche (ADS) & J. Laurent-Varin (CNES)
• 09h00-09h30 : Quasi-periodic Invariant Tori in Astrodynamics: Applications to Ballistic Transport in the Cislunar Space - N. Baresi (University of Surrey)
• 09h30-10h00 : Low-energy transfers in the Earth-Moon-Sun system using Elliptic-Circular problem - D. Villegas Pinto (OHB)
• 10h00-10h30 : Analysis of Distant Retrograde Orbits in the Earth-Moon System -  P. Lahoz Gaitx (ISAE-CNES)
• 10h30-10h50 : Coffee Break
• 10h50-11h20 : Cis Lunar Transfer Vehicle Mission Analysis - S. Locoche (ADS)
• 11h20-12h00: Argonaut Mission Overview - O. Dubois-Matra (ESA) + L. Bucci (ESOC)
• 12h00-13h30 : Lunch Break
• 13h30-14h00: Trajectory Design and Flight Results in Launch and Early Operation Phase for EQUULEUS mission - Y. Kawabata (University of Tokyo)
• 14h00-14h30: The astrodynamics of LUMIO, a CubeSat for observing the Lunar far side – A. Martinelli (Politecnico di Milano) 
• 14h30-14h50: Coffee Break
• 14h50-15h20: SELENA: a semi-analytical propagator for Lunar satellite orbits - C. Efthymiopoulos (University of Padova)
• 15h20-15h50: Cislunar Debris Mitigation: current status and future challenges - P. Guardabasso (Exotrail)
• 15h50-16h00: Wrap-up (J. Laurent-Varin - CNES & A. Boutonnet ESA)

(Note: the program and schedule are preliminary and might be subject to minor changes - please visit this page for the latest and most up-to-date info)

Abstracts

“Quasi-periodic Invariant Tori in Astrodynamics: Applications to Ballistic Transport in the Cislunar Space" - N. Baresi (University of Surrey)

The exploitation of Dynamical Systems Theory to the study of the motion of objects in space has led to innovative mission designs and substantial propellant savings. Recent advancements in numerical continuation techniques have enabled a new class of dynamical structures known as quasi-periodic invariant tori (QPT) to emerge as an alternative option to periodic orbits for designing and operating spacecraft missions in chaotic dynamical environments such as the Circular Restricted Three-Body Problem. QPT have the potential to significantly increase the design domain of spacecraft missions as well as unlock new, fuel-efficient transfer opportunities in the vicinity of the secondary mass, e.g., the Moon. To demonstrate these advantages, we will first overview a numerical continuation procedure to calculate families of quasi-periodic trajectories through the invariant curves of stroboscopic mappings. We will then showcase how heteroclinic connections between quasi-periodic invariant tori in the Earth-Moon system can be charted systematically by means of knot theory and the linking number, a topological property of curves in three-dimensional spaces.

"Low-energy transfers in the Earth-Moon-Sun system using Elliptic-Circular problem" - D. Villegas Pinto (OHB)

Transfers between resonant Near-Rectilinear Halo Orbits (NRHO) such as the future orbit of the Lunar Gateway – with a 9:2 synodic resonance – and Earth vicinity are investigated using a higher-fidelity Earth-Moon-Sun model known as the Elliptic-Circular problem. In this model, the Earth and the Moon move in elliptical orbits about each other and the Sun moves in a circular orbit about their barycenter. By considering the Sun’s gravity and the Moon’s eccentricity, we are able to include the most significant perturbations of the cislunar environment and better approximate the real dynamics of the system. In turn, these perturbations mean that the periodic resonant NRHOs of the Circular Restricted Three-Body Problem (CR3BP) are replaced by two-dimensional quasi-periodic resonant tori. Making use of the tori’s hyperbolic invariant manifolds, we obtain low-energy trajectories that link Earth vicinity and the NRHOs and naturally produce what are also known as Weak Stability Boundary (WSB) transfers.

“Analysis of Distant Retrograde Orbits in the Earth Moon System” -  P. Lahoz Gaitx (ISAE-CNES)

The study of Distant Retrograde Orbits has been a subject of interest from the proposal of the Asteroid Redirect Robotic Mission by NASA, but it has been the development of the Artemis Program and the fulfilment of its first mission what has led to new studies on the subject. The presented work explores the characteristics of DROs and their applications for their potential use in the development of future interplanetary missions. First, a complete characterization of the DRO family and its bifurcations in the Earth-Moon system is presented. Then, the use of manifolds of neighbouring period tripling DROs is evaluated as a possible methodology to design connection trajectories with the Earth. Moreover, these natural trajectories, studied in a Patched-CR3BP model with the Sun-Earth system, offer the possibility to find cheap escape trajectories from the Lunar vicinity. This work is finally completed with a study of the station-keeping cost and the analysis of the trajectory of Artemis‑I

“Cis-Lunar Transfer Vehicle Mission Analysis”  - S. Locoche (ADS)

Discussions between ESA and NASA identified the development and deployment of a lunar orbital platform gateway concept, called the Gateway, as an intermediate step towards human deep space travel. In order to fulfil the new exploration objectives, the study of a Cis-Lunar Transfer Vehicle concept has been performed at Airbus Defence and Space under the supervision of ESA. A mission analysis that has been conducted to support preliminary system design, payload mass estimation and mission timeline for the investigated mission architecture and for the system trade-offs. In particular, launch, transfer and phasing options are designed and optimized in a high-fidelity model. The feasibility and robustness of these options under realistic operational requirements are analysed and the overall mission performance is assessed and traded providing a broad scope of future transfer options for a cargo mission to the Gateway.

“Argonaut Mission Overview" - O. Dubois-Matra (ESA)

Argonaut is an ESA project to provide Europe with autonomous access to the Moon surface. This lunar lander is being designed for a series of missions with many options for its payloads – from cargo and infrastructure delivery to scientific operations. Launched on an Ariane 6 rocket, Argonaut will be able to land at any region of the Moon. The ESA mission analysis results for the launch windows, Earth-Moon transit, lunar orbit insertion and landing will be presented.

“Trajectory Design and Flight Results in Launch and Early Operation Phase for EQUULEUS mission" - Y. Kawabata (University of Tokyo)

EQUULEUS (EQUilibriUm Lunar-Earth point 6U Spacecraft) is a 6U CubeSat developed by the University of Tokyo and the Japan Aerospace Exploration Agency (JAXA). The spacecraft was launched on November 16, 2022 as one of the ten secondary payloads onboard NASA's Space Launch System launch vehicle. The destination of EQUULEUS is an Earth-Moon L2 (EML2) near-rectilinear quasi-Halo orbit.

EQUULEUS has three mission objectives: 1) demonstrate the orbital maneuvering capabilities of a nano-satellite in the cis-lunar environment, 2) observe the magnetosphere plasma, and 3) grasp the size and spatial distribution of solid objects in the cis-lunar space.

After the launch, EQUUELUS was inserted into a lunar transfer orbit. The closest approach to the Moon was about five days after the launch. If EQUULEUS could not perform the Delta-V operation before the lunar closest approach, EQUULEUS would escape from the Earth region and could not come back anymore. We successfully finished the planned initial checkout operations and delta-V operations precisely in the Launch and Early Operation Phase (LEOP). As a result, EQUULEUS was inserted into the nominal trajectory toward EML2 as planned.

The presentation will include an overview of the EQUULEUS mission and the results of the trajectory design based on the actual launch window provided by NASA. In addition, the achievements of the operations and orbital maneuvers in LEOP will be focused on.

“The astrodynamics of LUMIO, a CubeSat for observing the Lunar far side" – F. Topputo (Politecnico di Milano)

Meteoroids constantly impact the Earth–Moon system, posing risks to space assets and threatening the life on the Earth. By studying lunar surface impacts, detailed information regarding meteoroid magnitudes, velocities, and distributions can be obtained, improving models and validating meteoroid impact studies. The LUMIO CubeSat mission aims to observe and characterize meteoroid impacts on the lunar far side, enhancing lunar situational awareness and complementing Earth-based observations. This study discusses the mission design and analysis of LUMIO, with a focus on utilizing weak stability boundaries (WSB) for a cost-effective transfer to the operative halo orbit. Leveraging WSB offers advantages such as reducing propellant requirements and increasing launch opportunities. Furthermore, technical considerations and the potential of WSB to enhance the feasibility and efficiency of CubeSat missions, including LUMIO, in the future are highlighted.

“SELENA: a semi-analytical propagator for Lunar satellite orbits" - C. Efthymiopoulos (University of Padova)

Joint work with K. Tsiganis, C. Yanez, I. Gkolias, M. Gaitanas in the framework of the CNES research activity "Semi-Analytical Theory of a Lunar Artificial Satellite".

The talk will summarize the main features of the semi-analytical theory and corresponding propagator (SELENA) developed for the integration of lunar satellite orbits over secular timescales. SELENA is the analogue, for lunar satellite orbits, of CNES semi-analytical propagator STELA (see https://www.connectbycnes.fr/en/stela) of Earth satellite orbits.

As regards the theory behind semi-analytical propagation, a main difference between SELENA and STELA stems from the fact that the Moon's rotation frequency is smaller than the Earth's one by a a factor about 1/28. This implies that, contrary to STELA, the perturbative treatment of the Moon's tesseral harmonics, aiming to eliminate short-period terms from the equations of motion, can be carried out in so-called "closed form", i.e., without series expansions in the orbital eccentricity. To this end, SELENA uses a variant of the classical relegation algorithm of Deprit and collaborators. 

Similarly, the fact that the Earth and Moon are locked in the 1:1 (synchronous) spin-orbit resonance implies that the perturbative treatment of the third body tidal terms in the equations of motion can also be carried out via a variant of the relegation algorithm. 

Besides the semi-analytical theory behind SELENA, the talk will describe the tool (software + GUI) developed to support various functionalities of the semi-analytical propagation, as well as various precision estimates obtained through orbital running campaigns. Details on all the above arguments can be found in SELENA's final report published in ArXiV 2309.11904v1

Cislunar Debris Mitigation: current status and future challenges - P. Guardabasso (Exotrail)

With the increasing interest towards the Moon, the rise of new exploration programs, and private actors' involvement, a solid and consistent debris mitigation approach should be adopted to avoid creating a hostile environment. Nevertheless, this is a challenging task, as more complex mission designs emerge in the dynamical environment of cislunar space, broadly defined as the region of Earth-Moon gravitational influence.

After an overview of past, present and future missions targeted at the Moon, this works first presents he translation of periodical solutions found in the Circular Restricted Three-Body Problem (CR3BP) model to a Sun-Earth-Moon higher fidelity model. A dataset of suitable initial conditions is hence created.

The problem of cislunar debris is tackled first by analysing the aftermath of spacecraft fragmentation, currently the primary mechanism of debris generation in space. Such an event is positioned in several starting locations, providing an overview of its short- and long-term effects on the cislunar space. Then, possible debris mitigation strategies are discussed, identifying end-of-life disposal solutions for active spacecraft. Pictorial maps are proposed to assess the availability and robustness of such solutions, searching for families of trajectories with similar shapes and outcomes instead of chaotic behaviours