Detecting gravity anomalies in asteroids: application to Hera’s radio science

BACKGROUND: An accurate estimation of the density distribution of asteroids is of great interest for both planetary science and defense. Knowing the internal density of an asteroid will unlock our understanding of their formation, improve our knowledge of the gravity environment around them and enhance the safety of spacecraft-asteroid proximity operations. Asteroids are the result of impacts between celestial objects, thus, gravity anomalies in asteroids can occur. Indeed, the Moon is characterised by such anomalies (mascons) which can affect the orbit stability of a spacecraft.

AIM and SCOPE: The scope of this project is to investigate a novel approach in detecting gravity anomalies in asteroids through the inverse gravity problem. A combination between traditional measurements of gravity-induced accelerations, experienced by a spacecraft, with the information of the dynamical system theory is yet to be explored. Traditional methods to estimate the asteroids’ internal density distribution include the fitting of gravity coefficients from a chosen gravity model combined with the gravity accelerations experienced by a spacecraft. Several inverse constrained optimisation methods have been explored such as least-squares, Bayesian, neural network, and genetic algorithms. This project will investigate novel machine learning approaches to the inverse problem with constraints from the information of the dynamical systems theory (e.g., inverse problem from equilibrium points detection) which differ from traditional approach that makes use of solely gravity-induced accelerations. The aim of the thesis is to develop a strategy for autonomous radio science operations, thus developing the onboard software that enables a spacecraft or CubeSats (a 10x10x10cm small size spacecraft) to self-estimate the internal grain density distribution of asteroids. This study will enable, for example, a generalised strategy for determining sequences of spacecraft’s close-proximity ascending operations (e.g., hovering, orbit) for estimating asteroids’ internal structure as a function of their physical properties (e.g., class, size, spin-ratio). Ultimately, the project should answer the research question “Which generalised radio science methodology will enable a self-driven spacecraft to perform onboard autonomous detection of asteroids’ gravity anomalies and reconstruction of their internal structure for several asteroids’ class?”

RESEARCH PLAN: The PhD student will have a primary supervisor from the SoE, Dr Stefania Soldini, expert in radio science and planetary defense missions, a second supervisor from Physics, Prof Monica D’Onofrio, expert in ML applications to large datasets in particle physics and AI explainability methods, and a primary supervisor from ESA, Dr Dario Izzo, head of the ESA’s Advanced Concepts Team (ACT) (ESTEC – European Space Research and Technology Centre, Netherlands), responsible of ESA’s geodesyNets software. The geodesyNets software solve the gravity inversion problem by using a neural network. The proposed plan includes:

1.The PhD student will spend the first six-month in Liverpool familiarising with asteroids’ gravity models and performing a thorough review and comparison in performance of several inverse methods that include machine learning.

2.The student is then expected to spend at least 1-year at ESTEC in the ACT group for the development of the theory and methods to use AI for solving the inverse gravity problem for Didydmos binary asteroid system and other asteroids and to support the development of geodesyNets. In particular, by comparing the mascons model with the neural density fields.

3.The last phase of the PhD will be completed in Liverpool where the methodology will be generalised to several class of asteroids.

RESEARCH ENVIRONMENT: You will work within a vibrant and rapidly growing community of space researchers in the Aerospace Division of the School of Engineering and the Physics Department at the University of Liverpool. This project is in strict collaboration with the European Space Agency (ESA) to support the Hera mission. The project is partially funded by the ESA-OSIP call. You are expected to spend 12 months at the ESA/ESTEC facility in the Netherlands. The student will also be involved in the Hera’s dynamics working group meetings where Dr Soldini is a team member. This would guarantee the student access to expert in planetary science and asteroids formation, and valuable real-time data. The student will also have the unique opportunity to propose and lead a specific mission phase of the Hera mission. Through the student’s computation and analysis, it will be possible to estimate the best trajectory path for gravity estimation for Hera spacecraft and its two CubeSats. Access to a new 60m2 facility for hardware-in-the loop testing of mission operations is also available led by Dr Soldini.

REQUIRED SKILLS: We are seeking candidates with a minimum of 2:1 (or equivalent) master’s degree in Astrophysics, Applied Mathematics, Aerospace Engineering, Computer Science or any other related subject. Experience in one of more of the following areas is required: A strong background in applied math, modeling and simulation, and a good understanding of optimisation methods. Excellent coding skills in one computing language e.g., Python or MATLAB or C++. Strong communication and team working skills are essential as well. Knowledge of machine learning and GNC is beneficial.

We want all of our staff and Students to feel that Liverpool is an inclusive and welcoming environment that actively celebrates and encourages diversity. We are committed to working with students to make all reasonable project adaptations including supporting those with caring responsibilities, disabilities or other personal circumstances. For example, If you have a disability you may be entitled to a Disabled Students Allowance on top of your studentship to help cover the costs of any additional support that a person studying for a doctorate might need as a result.

We believe everyone deserves an excellent education and encourage students from all backgrounds and personal circumstances to apply.

Applicant Eligibility

Candidates will have, or be due to obtain, a Master’s Degree or equivalent from a reputable University in an appropriate field of Engineering. Exceptional candidates with a First Class Bachelor’s Degree in an appropriate field will also be considered.

Application Process

Candidates wishing to apply should complete the University of Liverpool application form [How to apply for a PhD – University of Liverpool] applying for a PhD in Aerospace Engineering and uploading: Degree Certificates & Transcripts, a CV, covering letter and two academic references.