Andrea Milani, Professor at the University of Pisa, passed away suddenly on 28 November 2018, at age 70. Born in Florence, Italy, on 19 June 1948, Milani became a major figure in the celestial mechanics community, as recognized by the Division on Dynamical Astronomy of the AAS, which named him the 2010 recipient of its prestigious Brouwer Award. Although a meeting had just been held in Pisa in early September 2018 to celebrate his 70th birthday and imminent official retirement, it was clear that Milani intended to remain active in research as an Emeritus Professor and a senior scientist with the company SpaceDyS, which develops software for space-science applications. But chaos, which Milani studied so much in the solar system, also rules human life: the future is unpredictable. The community of planetary dynamicists mourns the loss of one of its most eminent members.
To understand the magnitude of the loss, let’s turn back and outline the major achievements of Milani’s almost 50-year-long activity. In the 1980s, Milani was among those who changed our understanding of the solar system, from the view inherited from the Enlightenment times of a perfectly ticking clockwork, to the modern view of a more complex, irregular and ever-evolving machinery. His contribution was both analytic, with studies on normal forms, small divisors and resonant dynamics, and numerical, with the development of integrators with an accurate control of the accumulation of errors. As an example, Milani and his collaborators studied in detail the complex dynamical evolution of Pluto and showed that it is affected by three levels of resonances: the mean motion resonance with Neptune, the Kozai resonance, and a super-resonance among the secular precession rates of Pluto and Neptune, ultimately responsible for the positive Lyapunov exponent (indicating chaotic motion) earlier detected by Sussman and Wisdom (Science 248 (1988): 433-437).
The asteroid belt proved to be a more fertile playground than the planets themselves to study chaos and its consequences. Among the many contributions of Andrea Milani on chaotic dynamics in the asteroid belt, I would like to recall three. With A. Nobili, Milani showed that some asteroids can have a small Lyapunov exponent (i.e., a strongly chaotic motion) but remain confined in a neighborhood of their original orbit for the age of the solar system. Only in two degrees of freedom can regular trajectories bound chaotic motion, so this result was not expected for the evolution of an asteroid in the full planetary system. We now know that “stable chaos” can be understood with the theory developed by the Russian mathematician N. N. Nekhoroshev. At the opposite end of the spectrum of possible dynamical behaviors, Milani and P. Farinella, another giant of planetary science at the University of Pisa who prematurely passed away, found an asteroid on the brink of being removed: the asteroid is in the chaotic region surrounding a powerful resonance, which will eventually eject it from the asteroid belt within an expected timescale of 10 My.
The existence of bodies with a dynamical lifetime much shorter than the age of the solar system was a real puzzle at the time. We know now that this is due to a non-gravitational force, called the Yarkovsky effect, pushing asteroids from regular orbits into chaotic zones. In another paper, Milani and Farinella demonstrated that chaotic dynamics can cause the slow dispersal of asteroid families. Knowing the chaotic diffusion rate from numerical simulations and the current orbital dispersal, they estimated an upper bound of 50 My for the age of the Veritas family. They called this approach chaotic chronology. Such a young age for an asteroid family was a surprising result (we know now that the age of the family is only 8 My), showing that the structure of the asteroid belt is changing on geological times not only as a consequence of chaotic dynamics, but also of collisional events.
The topic of asteroid families is central in Milani’s scientific activity. It’s fair to say that Milani did not just provide relevant contributions in this field: he founded the field himself! The identification of asteroid families requires the calculation of quantities that do not change significantly during the dynamical evolution of the asteroids, provided they are not in chaotic diffusion. These quantities are called proper elements. Before Milani, proper elements were calculated with analytic schemes limited to first order in the masses of the planets and/or low degree in eccentricity and inclination. Then families were identified visually as apparent clumps in proper element space. With Z. Knezevic, Milani developed a perturbation approach to the computation of proper elements up to order two in the planetary masses and degree 4 in eccentricities and inclinations, with an innovative iterative algorithm to minimize the error in the determination of the proper frequencies.
Throughout the years, Milani and Knezevic maintained a databased in Pisa, named AstDys, with updated proper elements for all known asteroids. Armed with this database, with colleagues in the Observatory at Turin, Milani searched for asteroid families using a rigorous cluster analysis, which identifies clumps of asteroids above statistical significance level. Then, in a number of papers, Milani and his collaborators (mostly students) studied the structure of the families, their interactions with resonances, their spreading due to the Yarkovsky effect, their ages, etc. He also pioneered coupling proper elements with physical properties (albedo, colors) to achieve a more reliable identification of family members. Today, the study of asteroid families is a major field in planetary science involving many tens of researchers, from theorists to observers and experimentalists. Without Milani kick-starting this field with his mathematical approach to proper elements, the landscape of planetary science would be very different today.
Milani was also interested in applied science. As a mathematician, he was looking at rigorous optimized algorithms to solve problems, whereas others were just employing brute-force calculations. Thus, he introduced innovative approaches in space geodesy, orbital determination, and the calculation of collision probabilities of specific asteroids with the Earth given their orbital uncertainties. Today, the most effective algorithms for impact monitoring, both in Pisa and at the Jet Propulsion Laboratory, are of Milani’s origin or heritage.
I am 18 years younger than Andrea Milani, so when I was just entering the field, Milani was already an established professor. I remember my apprehension — shared by my young colleagues and never fully extinguished with time — seeing Milani stand up at the end of my talk (he always stood when asking a question) and begin, “I would like to point out....” That usually meant trouble to come. Working on similar subjects, he and I had over our careers some scientific debates, which, both being Italian, could become quickly very animated and loud. But Milani never took any of these personally and even after the hottest exchanges the relationships quickly returned to calm and friendly. And the few times when further results showed Milani’s ideas to be incorrect, he would admit it openly and move on, which reflects on his scholarly honor.
I like to imagine that he joins his mentor Giuseppe Colombo, whom he admired so much, and that they both will watch the journey to Mercury of the recently launched BepiColombo mission of the European Space Agency. The mission, devoted to Colombo’s memory, was strongly supported by Milani, who also helped devise the Mercury Orbiter Radio- science Experiment (MORE) that is onboard the spacecraft. Enjoy the show, Andrea. You deserve it.