Artificial spin-up and fragmentation of sub-kilometre asteroids

The article demonstrates the feasibility of artificially increase the spin rate of asteroids about 200 m in diameter beyond the limit in which they begin to disrupt. In the proposed concept a tethered satellite of less than a few tens of kilometres length anchored to the asteroid surface is employed as a mean to exchange angular momentum with the celestial body and increase its spin rate. Simple calculations based on angular momentum and energy conservation show that a 200 m diameter asteroid can be spun-up to critical rotation speed in less than one year with current technology.The scheme can be utilized as a unique scientific tool to characterize the asteroid internal structure and composition.     

Experimental and theoretical burning of solid rocket propellants near the pressure deflagration limit

Burning of composite solid rocket propellants near the pressure deflagration limit (PDL) was studied experimentally in two different test chambers. The propellant tested was a nonmetallized ammonium perchlorate-based composite propellant (AP 84/CTPB 16). Measurements were taken of the regression rate, oscillations frequency and flame luminosity. Self-sustained oscillations were detected near the PDL that matched reasonably well the predictions of the analytical nonlinear stability theory and of the numerically solved nonlinear mathematical model. Both experimental and numerical results show the burning rate oscillations near the PDL due to statically unstable burning, that is the only combustion regime possible below a certain pressure. When pressure is further reduced the amplitude of the oscillations increases and their frequency decreases, until extinction follows abruptly below a pressure that corresponds to the PDL.     

Planetary Defense From Space: Part 2 (Simple) Asteroid Deflection Law

A system of two space bases housing missiles for an efficient Planetary Defense of the Earth from asteroids and comets was firstly proposed by this author in 2002. It was then shown that the five Lagrangian points of the Earth–Moon system lead naturally to only two unmistakable locations of these two space bases within the sphere of influence of the Earth. These locations are the two Lagrangian points L1 (in between the Earth and the Moon) and L3 (in the direction opposite to the Moon from the Earth). In fact, placing missiles based at L1 and L3 would enable the missiles to deflect the trajectory of incoming asteroids by hitting them orthogonally to their impact trajectory toward the Earth, thus maximizing the deflection at best. It was also shown that confocal conics are the only class of missile trajectories fulfilling this “best orthogonal deflection” requirement.The mathematical theory developed by the author in the years 2002–2004 was just the beginning of a more expanded research program about the Planetary Defense. In fact, while those papers developed the formal Keplerian theory of the Optimal Planetary Defense achievable from the Earth–Moon Lagrangian points L1 and L3, this paper is devoted to the proof of a simple “(small) asteroid deflection law” relating directly the following variables to each other:

(1) the speed of the arriving asteroid with respect to the Earth (known from the astrometric observations);

(2) the asteroid's size and density (also supposed to be known from astronomical observations of various types);

(3) the “security radius” of the Earth, that is, the minimal sphere around the Earth outside which we must force the asteroid to fly if we want to be safe on Earth. Typically, we assume the security radius to equal about 10,000 km from the Earth center, but this number might be changed by more refined analyses, especially in the case of “rubble pile” asteroids;

(4) the distance from the Earth of the two Lagrangian points L1 and L3 where the defense missiles are to be housed;

(5) the deflecting missile's data, namely its mass and especially its “extra-boost”, that is, the extra-energy by which the missile must hit the asteroid to achieve the requested minimal deflection outside the security radius around the Earth.

This discovery of the simple “asteroid deflection law” presented in this paper was possible because:

(1) In the vicinity of the Earth, the hyperbola of the arriving asteroid is nearly the same as its own asymptote, namely, the asteroid's hyperbola is very much like a straight line. We call this approximation the line/circle approximation. Although “rough” compared to the ordinary Keplerian theory, this approximation simplifies the mathematical problem to such an extent that two simple, final equations can be derived.

(2) The confocal missile trajectory, orthogonal to this straight line, ceases then to be an ellipse to become just a circle centered at the Earth. This fact also simplifies things greatly. Our results are thus to be regarded as a good engineering approximation, valid for a preliminary astronautical design of the missiles and bases at L1 and L3.

Still, many more sophisticated refinements would be needed for a complete Planetary Defense System:

(1) taking into account many perturbation forces of all kinds acting on both the asteroids and missiles shot from L1 and L3;

(2) adding more (non-optimal) trajectories of missiles shot from either the Lagrangian points L4 and L5 of the Earth–Moon system or from the surface of the Moon itself;

(3) encompassing the full range of missiles currently available to the USA (and possibly other countries) so as to really see “which missiles could divert which asteroids”, even just within the very simplified scheme proposed in this paper.

In summary: outlined for the first time in February 2002, our Confocal Planetary Defense concept is a simplified Keplerian Theory that already proved simple enough to catch the attention of scholars, popular writers, and representatives of the US Military. These developments would hopefully mark the beginning of a general mathematical vision for building an efficient Planetary Defense System in space and in the vicinity of the Earth, although not on the surface of the Earth itself!We must make a real progress beyond academic papers, Hollywood movies and secret military plans, before asteroids like 99942 Apophis get close enough to destroy us in 2029 or a little later.     

Assessing and minimizing collisions in satellite mega-constellations

We aim to provide satellite operators and researchers with an efficient means for evaluating and mitigating collision risk during the design process of mega-constellations. We first introduce a novel algorithm for conjunction prediction that relies on large-scale numerical simulations and uses a sequence of filters to greatly reduce its computational expense. We then use this brute-force algorithm to establish baselines of endogenous (intra-constellation), or self-induced, conjunction events for the FCC-reported designs of the OneWeb LEO and SpaceX Starlink mega-constellations. We demonstrate how these deterministic results can be used to validate more computationally efficient, stochastic techniques for close-encounter prediction by adopting a new probabilistic approach from Solar-System dynamics as a simple test case. Finally, we show how our methodology can be applied during the design phase of large constellations by investigating Minimum Space Occupancy (MiSO) orbits, a generalization of classical frozen orbits that holistically account for the perturbed-Keplerian dynamics of the Earth-satellite-Moon-Sun system. The results indicate that the adoption of MiSO orbital configurations of the proposed mega-constellations can significantly reduce the risk of endogenous collisions with nearly indistinguishable adjustments to the nominal orbital elements of the constellation satellites.     

SETI,extrasolar planets search and interstellar flight: When are they going to merge?

The SETI Permanent Study Group (abbreviated SETI PSG) of the International Academy of Astronautics (IAA), with web site: http://www.setileague.org/iaaseti/index.html, is one of the few international venues where, as of 2006, scientists with different backgrounds and from all over the world can meet and discuss recent advances in the scientific, technical and societal aspects of SETI. In particular, the Pe?ek Lecture that traditionally opens in October every year the SETI 1 Session of the International Astronautical Congress (IAC), is intended to describe the updated state-of-the-art in SETI and related fields with the accent on science and technology rather than on the societal consequences of a contact with ET. We have thus come to the conclusion that a Pe?ek Lecture devoted to the interplay between SETI and the rapidly evolving field of the Search for Extrasolar Planets (or Exoplanets) would be quite up-to-date, especially in view of the over 200 exoplanets rapidly discovered in the 11 years between 1995 and 2006. Moreover, besides SETI and Exoplanets, there is a third field of scientific investigation that, although not as mature as the former two fields in terms of experimental research, is striving ahead among many theoretical difficulties but might really change the course of human history when becoming reality: this is the theory (so far) of Interstellar Flight, that would one day enable us to travel across the vast interstellar distances initially by virtues of probes only, and later “in person”.The present Pe?ek Lecture is trying to compare the different grow rate and the (now small) overlap in between these three apparently “unrelated” fields. And even if we can hardly find any answer in these “dark ages” we live, let us at least raise the question: “When are SETI, Exoplanet Searches and Interstellar Flight going to merge in the future of Humankind?”.     

The data compression problem for the “GAIA” astrometric satellite of ESA

Space-based astrometry has a great tradition at ESA. The first space-based astrometric satellite in history, “Hipparcos”, was launched by ESA in 1989 and, in spite of orbital problems, was able to accomplish almost all of its tasks until it was finally shut down in 1993. The results of the Hipparcos mission were published by ESA in 1997 in the form of six CD-ROMs: the Hipparcos Catalogue contains 118,218 entries with median astrometric precision of around 1 milliarcsec, and specific results for double and multiple systems. In practice, Hipparcos drew for the first time the three-dimensional “map” of the spherical region of the Galaxy surrounding the Sun and having a radius of roughly 1,000 light years.

Then, in 1995, ESA launched the study of a new astrometric satellite, named “GAIA” and about a hundred times more powerful than Hipparcos, i.e. with median astrometric precision of around 10 microarcsec. This new satellite is intended to measure the parallaxes of over 50 million stars in the Galaxy, at least for the brightest stars, and this would mean to “draw” the three-dimensional map of the whole Galaxy, reaching out even to the Magellanic Clouds, 180,000 light years away.

The team of European scientists and engineers now designing GAIA, however, is facing hard technological difficulties. One of these is the design and coding of radically new and ultra-powerful mathematical algorithms for the on-board compression of the 50-million-stars data that GAIA will send to Earth from its intended geostationary orbit. Preliminary estimates of the raw data rates from the GAIA focal plane, in fact, are of the order of a few Gigabits per second. To reduce the data stream to the envisaged telemetry link of 1 Megabit per second, on-board data compression with a 1 to 1,000 ratio is the target. Clearly, this is far beyond the capabilities of any lossless compression technique (enabling compression ratios of 1 to some tens), and so some “wise” lossy compression mathematical procedure must be adopted.

In this paper a GAIA-adapted lossy data compression technique is presented, based on the Karhunen-Loève Transform (KLT). The essence of this method was already used by NASA for the Galileo mission when the large antenna got stuck and the mission was rescued by re-programming the on-board computer in terms of the KLT. That transform was officially named ICT — “Integer Cosine Transform” — by the NASA-JPL team led by Dr. Kahr-Ming Cheung. But the KLT here described for GAIA will of course differ from the JPL one in many regards, owing to the advances in computer technology.

Finally, estimates are also given about the possibility of using the KLT for onboard data compression in case GAIA is going to be put into orbit around the Lagrangian point L2 of the Earth-Sun system, and, above all, in case the number of stars to be observed is actually raised from 50 millions to one billion, as ESA currently appears to be likely to pursue.     

Galactic outflows and the pollution of the galactic environment by supernovae

We here explore the effects of the SN explosions into the halo of star-forming galaxies like the Milky Way. Successive randomly distributed and clustered SNe explosions cause the formation of hot superbubbles that drive either fountains or galactic winds above the galactic disk, depending on the amount and concentration of energy that is injected by the SNe. In a galactic fountain, the ejected gas is re-captured by the gravitational potential and falls back onto the disk. From 3D non-equilibrium radiative cooling hydrodynamical simulations of these fountains, we find that they may reach altitudes up to about 5 kpc in the halo and thus allow for the formation of the so called intermediate-velocity-clouds (IVCs) which are often observed in the halos of disk galaxies. The high-velocity-clouds that are also observed but at higher altitudes (of up to 12 kpc) require another mechanism to explain their production. We argue that they could be formed either by the capture of gas from the intergalactic medium and/or by the action of magnetic fields that are carried to the halo with the gas in the fountains. Due to angular momentum losses to the halo, we find that the fountain material falls back to smaller radii and is not largely spread over the galactic disk. Instead, the SNe ejecta fall nearby the region where the fountain was produced, a result which is consistent with recent chemical models of the galaxy. The fall back material leads to the formation of new generations of molecular clouds and to supersonic turbulence feedback in the disk.     

Application of time-variable process noise in terrestrial reference frames determined from VLBI data

In recent years, Kalman filtering has emerged as a suitable technique to determine terrestrial reference frames (TRFs), a prime example being JTRF2014. The time series approach allows variations of station coordinates that are neither reduced by observational corrections nor considered in the functional model to be taken into account. These variations are primarily due to non-tidal geophysical loading effects that are not reduced according to the current IERS Conventions (2010). It is standard practice that the process noise models applied in Kalman filter TRF solutions are derived from time series of loading displacements and account for station dependent differences. So far, it has been assumed that the parameters of these process noise models are constant over time. However, due to the presence of seasonal and irregular variations, this assumption does not truly reflect reality. In this study, we derive a station coordinate process noise model allowing for such temporal variations. This process noise model and one that is a parameterized version of the former are applied in the computation of TRF solutions based on very long baseline interferometry data. In comparison with a solution based on a constant process noise model, we find that the station coordinates are affected at the millimeter level.