Camilla Colombo

• Doctor of Philosophy in Aerospace Engineering
• Professor (Associate) at Politecnico di Milano

This paper investigates the long-term evolution of spacecraft in Highly Elliptical Orbits (HEOs). The single averaged disturbing potential due to luni-solar perturbations and zonal harmonics of the Earth gravity field is written. The double averaged potential is also derived in the Earth-centered equatorial system. Maps of long-term evolution are c...

Small fragments are rarely included in the evolution of the debris population as their number is so large that the computational time would become prohibitive. However, they also can be dangerous to operational satellites, so it is important to study their contribution to the collision probability. This work proposes an analytical method to propaga...

This article presents the design of the end-of-life disposal of spacecraft in Highly Elliptical Orbits through Earth re-entry. The effect of luni-solar perturbations can be enhanced through impulsive maneuvers to move the spacecraft on a trajectory that will naturally evolve in the long-term towards Earth re-entry. The dynamics is propagated throug...

This paper investigates the effect of planetary oblateness and solar radiation pressure on the orbits of high area-to-mass spacecraft. A planar Hamiltonian model shows the existence of equilibrium orbits with the orbit apogee pointing towards or away from the Sun. These solutions are numerically continued to non-zero inclinations and considering th...

Autonomous spacecraft proximity operations represent a key enabler for future mission architectures such as in-orbit servicing, active debris removal, object inspection, and in-orbit assembly. This work addresses safety concepts for the relative trajectory guidance design applicable to challenging proximity operations in the close-range domain. The...

Space Eye (SpEye) is a two-satellite technology demonstration mission aimed at validating crucial technologies and methodologies essential for advanced on-orbit inspection and formation-flying. This initiative holds significant relevance for the development of future operational nano-satellite capabilities and missions. The primary objective of the...

The increase in the number of orbiting objects, being them controllable or uncontrollable, is expected to significantly affect space operations in the near future. This is particularly true in the Low Earth Orbit (LEO) region, where the population of debris is increasing because of new fragmentation, while, at the same time, the advent of large con...

Space is one of the last frontiers of scientific exploration and, now more than ever, it is also a valuable economic and strategic resource. The exponential increase in academic and industry’s focus on space, empowered by the usage of CubeSats, has inevitably increased the amount of in-orbit objects. As space projects become more and more ambitious...

The growth of Earth-orbiting objects represents a major concern for the safety of space operations. Despite the adopted mitigation measures, the increase of the number of space debris poses a threat to space missions in terms of risk of collisions among fragments and active satellites. Since not all these events can be predicted in advance, the ear...

The population of objects in space faced an unforeseeable growth in the last decades. Therefore, it is now imperative to reiterate the debris mitigation guidelines and reconsider the approach to the debris proliferation problem. Different counteractions are available to deal with the situation. However, how to efficiently combine and apply these me...

Current projections of the in-orbit objects’ population show that even an effective implementation of mitigation measures may not be sufficient to counteract the proliferation of space debris. Hence, remediation actions are also under consideration and various Active Debris Removal (ADR) techniques and mission scenarios are currently investigated....

Orbital uncertainty propagation tasks have become the computational bottleneck in many astronomical and astrodynamical applications: Monte Carlo-based strategies lie at the state of the art, given the high non-linearity of the dynamics. For this reason, several methods to mitigate the computational intensity of such problems have been studied. On o...

The study of the dynamics of flybys is featured in several space-mission-related applications, spanning from the design of interplanetary orbits to the computation of impact probabilities with given celestial bodies in planetary protection and defense tasks. While patched-conics, two-body models suffice in accuracy for trajectory planning cases, co...

Scientific interest in asteroids and their physical characteristics is growing. These bodies provide insights into the primordial solar system and represent a valuable source of metals, silicates, and water. Several missions over the past few years have aimed to improve and better identify the main properties of these poorly known celestial bodies....

Given the growing number of planned missions and satellite launches, it is clear the cislunar orbital domain gained great interest from both industries and space agencies in the last few years. The chaotic dynamics that characterise this area of space set new challenges that have not been considered for near-Earth space. An increasing number of spa...

Over the past decade, the number of space debris has steadily increased. Consequently, the risk of collision between debris and active satellites has also increased, threatening the safety of space operations. Therefore, it is crucial to characterise fragments as soon as possible after their formation, to gather information about the fragmentation...

Space utilisation faced unforeseeable changes in the last decades. However, the policy definition for debris mitigation has not matched the rapid growth of the inert population on orbit. The interdisciplinary framework proposed in the GREEN SPECIES project, funded by the European Research Council, aims at providing scientific support to the reactiv...

Neglecting small fragments in space debris evolutionary models can lead to a significant underestimation of the collision risk for operational satellites. However, when scaling down to the millimetre range, the debris population grows to over a hundred million objects, making deterministic approaches too computationally expensive. On the contrary,...

In recent years, the interest in proximity operations to uncooperative and non-collaborative objects has been growing and and demanding for specific technology advances to tackle these challenging cases of in-orbit servicing and removal missions. Indeed, these architectures hold a crucial role in guaranteeing future sustainable and efficient space...

Lethal untrackable debris objects pose the highest risk to the sustainability of the space environment, and thus, shall be included in the assessment of the long-term effect of mitigation and remediation measures to the space debris problem. The introduction of centimetre-sized particles in the debris evolutionary models represents a challenge from...

Low-thrust propulsion systems are widely used in space missions due to their high specific impulse and reduced propellant consumption. However, current research focuses on eliminating drifts in low-thrust maneuvers, resulting in high operational costs for daily station-keeping. This study aims to achieve autonomous station-keeping by exploiting lon...

This paper presents an improved alpha shape-based linear interpolation method, and an improved binning method within the continuum method framework for accurate and efficient planar phase space long-term density propagation. The density evolution equation is formulated for the continuum density propagation under the influence of the solar radiation...

A convenient formalism for the design of resonant flyby trajectories is the B-plane, where postencounter orbits with target resonance conditions or semimajor axes can be analytically mapped. This framework has been developed by many authors starting from the classical Öpik’s theory for close encounters, but it still relies on the approximation of c...

This paper studies the bifurcation case for the planar phase space long-term density propagation problem, and presents an improved multi-segment continuum method for accurate and efficient long-term density propagation, by introducing the multi-segment method to the alpha shape triangulation-based linear interpolation method. The density evolution...

In this paper we will show the computation of the space debris index through the THEMIS tool. The debris index can be computed in different orbital regions: Low Earth Orbit, Medium Earth orbit, Geostationary, and Geostationary Transfer orbit through the careful selection of the phase space domain where the fragment cloud propagation and the effects...

The first large constellations have been launched in recent years, and new ones are planned. This new trend is leading to an increase in the number of objects orbiting around the Earth [1], crowding some regions of the orbital space. While the introduction of such a large number of spacecrafts will bring social and economic benefits, for example to...

Excluding the untrackable debris objects, when establishing mitigation measures for the space debris problem, results in an underestimation of the actual threat. However, the inclusion of such small fragments into debris evolutionary models is an enormous challenge from a computational point of view. To address this problem, the model COMETA (Conti...

In recent years, missions such as JAXA's Hayabusa2 and NASA's OSIRIS-Rex have visited Near Earth Asteroids, explored their environments, and collected samples from these primordial Solar System bodies. Their physical composition is largely unknown and challenging to predict from ground observations. That is why sample collection from such bodies is...

The space community is moving forward the development of in-orbit servicing and removal technologies to enable the circular economy in space and improve the future space missions' scientific and commercial return and space environment exploitation. The exploitation of nanosatel-lites to perform proximity operation represents a further opportunity t...

The Radiation Environment Monitor for Energetic Cosmic rays (REMEC) is one of the missions selected by ESA in the frame of Czech ambitious missions programme to conduct phase 0, A, B studies of missions built and operated by Czech companies and research organizations. REMEC is a microsatellite proposed to be placed outside of Earth's magnetosphere...

The maturity of electric propulsion has welcomed new parties to populate space at significantly cheaper costs. This is responsible for an increasingly congested space traffic but also for the possibility of mitigating the more frequent close encounters by resorting to collision avoidance manoeuvres with little impact on the mission lifetime. Tradit...

Neglecting small fragments in space debris evolutionary models can lead to a significant underestimation of the collision risk for operational satellites. However, when scaling down to the millimeter range, the debris population grows to over one million objects, making deterministic approaches too computationally expensive. On the contrary, probab...

Several analysis tasks feature the propagation of large sets of trajectories, ranging from monitoring the space debris environment to assessing the compliance of space missions with planetary protection policies. The increasingly stringent accuracy requirements inevitably make high-fidelity analyses become more computationally intensive, easily rea...

In this paper the operational tool for the computation of the space debris index that will be released through a web-based front end by the end of 2023. The development of the software THEMIS is the results of an effort of Politecnico di Milano and Deimos UK within a project funded by the European Space Agency to track the health of the space envir...

In the last decades, the growing in-orbit population of resident objects has become one of the main concerns for space agencies and institutions worldwide, and several Space Surveillance and Tracking (SST) related initiatives have been promoted to tackle this issue. Indeed, the presence of the so-called space debris may jeopardise the operative mis...

This paper presents a new analytical procedure to model the umbra generated during an eclipse considering an oblate ellipsoid of rotation as occulting body and a conical shadow. The method is based on purely geometrical considerations and results in the analytical definition of the entry and exit points from the conical shadow starting from the kno...

In this paper an analytical and a semi-analytical technique to compute low thrust Collision Avoidance Manoeuvres (CAMs) are presented and tested against a large dataset of Conjunction Data Messages (CDMs). Such CDMs simulate real conjunctions and they are derived from a screening against a background Two-Line Element population in different orbit s...

The high non-linearity of the Cartesian equations of the orbital motion represents a limit for the computational efficiency of high-fidelity numerical simulations. The implicitly straightforward interface with physical forces and perturbing accelerations has made the Cartesian formulation the most popular dynamics description in numerical simulatio...

This work presents the model of an ejecta cloud distribution to characterise the plume generated by the impact of a projectile onto asteroids surfaces. A continuum distribution based on the combination of probability density functions is developed to describe the size, ejection speed, and ejection angles of the fragments. The ejecta distribution is...

The permanent power loss and the deviation of the trajectory of satellites impacted by centimetre and sub-centimetre sized debris have highlighted the need of taking into account such small fragments in the evolutionary models of the debris population and in the assessment of the in-orbit collision risk. When scaling down to the centimetre-millimet...

The continuously growing number of objects orbiting around the Earth is expected to be accompanied by an increasing frequency of objects re-entering the Earth’s atmosphere. Many of these re-entries will be uncontrolled, making their prediction challenging and subject to several uncertainties. Traditionally, re-entry predictions are based on the pro...

The orbital propagation of large sets of initial conditions under high accuracy requirements is currently a bottleneck in the development of space missions, e.g. for planetary protection compliance analyses. The proposed approach can include any force source in the dynamical model through efficient Picard-Chebyshev (PC) numerical simulations. A two...

The sustainability of the space around the Earth is becoming an increasingly important issue in the space sector. Indeed, given the introduction of large constellations that place many satellites in specific orbital regions and the occurrence of breakup events (e.g., the CZ-6A breakup occurred on the 12 th of November 2022) that increase the backgr...

A popular intermediary in the theory of artificial satellites is obtained after the elimination of par-allactic terms from the J 2-problem Hamiltonian. The resulting quasi-Keplerian system is in turn converted into the Kepler problem by a torsion. When this reduction process is applied to unbounded orbits, the solution is made of Keplerian hyperbol...

In recent years low-thrust propulsion has become an alternative to chemical propulsion for many different applications. Hence, it becomes necessary to have accurate and fast methods to improve the uncertainty realism of the propagated orbits to improve the measurement correlation process and to allow a more accurate estimation of collision probabil...

Autonomous spacecraft proximity operations represent a key enabler for future mission architectures such as in-orbit servicing, active debris removal, objects' inspection, and in-orbit assembly. This work addresses safety concepts for the relative trajectory guidance design applicable to challenging proximity operations in the close-range domain. T...

The extension of debris evolutionary models to any orbital regime beyond low-Earth orbit is crucial to assess the future evolution of the space environment and define mitigation measures. However, when extending the continuum approach to any non-linear dynamics, the bottleneck is given by the computational cost. This paper proposes a novel approach...

The orbital propagation of large sets of initial conditions under high accuracy requirements is currently a bottleneck in the development of space missions, e.g. for planetary protection compliance analyses. The proposed approach can include any force source in the dynamical model through efficient Picard-Chebyshev (PC) numerical simulations. A two...

This work presents the model of an ejecta cloud distribution to characterise the plume generated by the impact of a projectile onto asteroids surfaces. A continuum distribution based on the combination of probability density functions is developed to describe the size, ejection speed, and ejection angles of the fragments. The ejecta distribution is...

ESA’s Soil Moisture and Ocean Salinity (SMOS) mission, together with NASA’s Soil Moisture Active Passive (SMAP) mission, are both providing a wealth of information to the user community for a wide range of applications. Although both missions are still operational, they have significantly exceeded their design life time. For this reason, ESA is loo...

This work presents a mission concept for in-orbit particle collection for sampling and exploration missions towards Near-Earth asteroids. Ejecta is generated via a small kinetic impactor and two possible collection strategies are investigated: collecting the particle along the anti-solar direction, exploiting the dynamical features of the L$_2$ Lag...

This work presents a mission concept for in-orbit particle collection for sampling and exploration missions towards Near-Earth asteroids. Ejecta is generated via a small kinetic impactor and two possible collection strategies are investigated: collecting the particle along the anti-solar direction, exploiting the dynamical features of the L2 Lagran...

Exploration missions to other planets have to satisfy planetary protection requirements to limit the probability of impacts between mission-related objects and celestial bodies, with the goal of reducing the risk of contaminating them with biological material coming from Earth. The verification of these requirements can become a lengthy and computa...

This paper presents an improved methodology for long-term uncertainty propagation in nonlinear dynamics by combining techniques of initial multi-directional splitting and adaptive entropy-based splitting during the propagation within the Gaussian mixture model framework. An initial multi-directional splitting technique applied to the directions par...

This work presents a new mission concept for sample collection missions around asteroids. Starting from the heritage of mission Hayabusa2, a kinetic impactor is used to generate fragments, which are then collected in orbit. The work discusses the feasibility of the mission, possible collection strategies, and the preliminary concepts of operations.

This work presents the Starling2.0 debris evolutionary model, a fully probabilistic tool which aims to predict the future evolution of the space debris environment. The background debris population is mapped into a phase space density function and propagated according to the continuity equation. The probability of collision with uncontrolled orbiti...

This paper proposes a continuity equation-based debris’ evolutionary model for the long-term propagation of fragments’ clouds under atmospheric drag, J2 perturbation, solar radiation pressure and third-body perturbation. In particular, it focuses on enhancing the computational efficiency of the dynamical model. This purpose is achieved by cutting...

The paper describes the design and modelling of an on-orbit mission experiment for testing a novel engine technology in Space. The goal is to assess the novel engine thrust profile through an on-orbit reverse engineering approach. The simulation tool developed at Politecnico di Milano is initially designed to propagate the free attitude dynamics of...

This work presents a sensitivity analysis of ejecta models used to model impact events onto small bodies in the Solar System. The application in exam is focused on kinetic impacts on Near Earth Asteroids to study the possibility of collecting the generated fragments in orbit, thus avoiding landing or touchdown operations. The sensitivity analysis s...

Space planetary missions' analysis with low-thrust propulsion includes orbit raising and de-orbiting manoeuvres which can involve multiple revolutions resulting in a spiralling motion of the satellite. The launch of large constellation satellites is increasing the number of satellites launched per month and the design of their trajectory to be posi...

The population of objects in space has increased dramatically over recent decades. Space debris now represents the majority of objects in space resulting from inactive satellites, breakups, collisions and fragmentations. It has become a concern for institutions all over the world and, as such, it has led to the fostering of several programmes to co...

The orbital propagation of large sets of initial conditions under high accuracy requirements is currently a bottleneck in the development of space missions, e.g. for planetary protection compliance analyses. The proposed approach can include any force source in the dynamical model through efficient Picard-Chebyshev (PC) numerical simulations. A two...

Formation flying missions have increased their importance thanks to the better performances that can be achieved with a distributed system of satellites. One of the most demanding challenges linked to the formation flying missions is the formulation of a robust control plan. Due to the recent developments in electrical propulsion, controllers that...

In the context of future L-band missions, the need to improve the spatial resolution with respect to the ESA's Soil Moisture and Ocean Salinity (SMOS) mission should be addressed for future follow-on studies with a range of applications over land and oceans. Since November 2009, SMOS has been producing global maps of soil moisture and sea surface s...

An analytical solution is presented that captures the bulk of the dynamics of close flybys about oblate celestial bodies. The solution is obtained by perturbations. More specifically, an infinitesimal contact transformation is found that reduces the perturbed hyperbolic Keplerian motion to a hyperbolic Kepler problem with varied angular momentum. I...

In the context of space sustainability and space traffic coordination and management, it is important to define an internationally recognised and accepted approach to measure the Space capacity, defined as the quantity and type of missions/objects that the Space environment can sustain. In parallel to the study on how the capacity can be measured,...

In recent years low-thrust propulsion has become a credible alternative to standard chemical propulsion for many different applications, ranging from orbital transfers to maintenance of small satellites in LEO. Despite the extensive effort that has been put into development of guidance algorithms for low-thrust systems, only few works have consider...

Satellite eclipse determination is one of the most important tasks to be analyzed in the preliminary design of a planetary space mission. Indeed, the duration of the eclipse is a driver for the sizing of the batteries that must be used when solar energy is not available. Many analytical and numerical algorithms based on several assumptions exist bo...

This work presents a methodology for the computation of particle fluxes around asteroids as they are generated by a kinetic impact on the asteroid surfaces. The methodology combines the dynamical propagation of small fragments in a perturbed environment with the modelling of impact crater phenomena. The particle fluxes allow the estimation of the n...

A popular intermediary in the theory of artificial satellites is obtained after the elimination of parallactic terms from the J2-problem Hamiltonian. The resulting quasi-Keplerian system is in turn converted into the Kepler problem by a torsion. When this reduction process is applied to unbounded orbits the solution is made of Keplerian hyperbolae....

Like any industry, space activities generate pressures on the environment and strives towards more sustainable activities. A consensus among the European industrial stakeholders and national agencies in the Space sector is emerging on the need to address eco-design through the prism of the environmental Life Cycle Assessment (LCA) methodology. Whil...

At a time when space debris are already a growing issue in the space sector, the deployment of large constellations, made of hundreds to thousands of satellites, is of concern from an environmental point of view. In the next decade, the space sector will undergo a considerable change as the population of active satellites is about to quintuple. Thi...

The detection of flybys in the numerical propagation of interplanetary trajectories is a key aspect to enable planetary protection analyses. Their much faster dynamics, compared to the pure heliocentric motion, hinders the development of advanced orbital integrators: regularisation-based approaches and variation of parameters implementations are ex...

This paper compares the continuum evolution for density equation modelling and the Gaussian mixture model on the 2D phase space long-term density propagation problem in the context of high-altitude and high area-to-mass ratio satellite long-term propagation. The density evolution equation, a pure numerical and pointwise method for the density propa...

This paper presents an analytical model for collision probability assessments between de-orbiting or injecting space objects and satellite constellations. Considering the first to be subjected to a continuous tangential acceleration, its spiraling motion would result in a series of close approaches in the proximity of a constellation. The proposed...

This paper compares the continuum evolution for density equation modelling and the Gaussian mixture model on the 2D phase space long-term density propagation problem in the context of high-altitude and high area-to-mass ratio satellite long-term propagation. The density evolution equation, a pure numerical and pointwise method for the density propa...