Related papers: A Method for Calculating Collision Probability Bet…
This paper presents formulae for calculation the solid angle of intersecting spherical caps, conical surfaces and polyhedral cones.
We propose factor graph optimization for simultaneous planning, control, and trajectory estimation for collision-free navigation of autonomous systems in environments with moving objects. The proposed online probabilistic motion planning…
Space debris is a major problem in space exploration. International bodies continuously monitor a large database of orbiting objects and emit warnings in the form of conjunction data messages. An important question for satellite operators…
Analytical approximations are commonly employed in the initial trajectory design phase of a mission to rapidly explore a broad design space. In the context of an asteroid deflection mission, accurately predicting deflection is crucial to…
In this paper, a new parametrization of the relative motion between two satellites orbiting a central body is presented. The parametrization is based on the nodal elements: a set of angles describing the orbit geometry with respect to the…
Typically, when estimating the prior transit probability, one assumes a uniform distribution for the cosine of the inclination angle i of the companion's orbit, which yields the familiar estimate of ~R_*/a. However, the posterior transit…
The problem deals with an exact calculation of the intersection area of a circle arbitrary placed on a grid of square shaped elements with gaps between them (finite fill factor). Usually an approximation is used for the calculation of the…
In the realm of computer-aided design (CAD) software, the intersection of B-spline surfaces stands as a fundamental operation. Despite the extensive history of surface intersection algorithms, the challenge of handling complex intersection…
Transits on single stars are rare. The probability rarely exceeds a few per cent. Furthermore, this probability rapidly approaches zero at increasing orbital period. Therefore transit surveys have been predominantly limited to the inner…
In Dark Matter direct detection we are facing the situation of some experiments reporting positive signals which are in conflict with limits from other experiments. Such conclusions are subject to large uncertainties introduced by the…
Most meteorites are fragments from recent collisions experienced in the asteroid belt. In such a hyper-velocity collision, the smaller collision partner is destroyed, whereas a crater on the asteroid is formed or it is entirely disrupted,…
We perform N-body simulations of young triple systems consisting of two low-mass companions orbiting around a significantly more massive primary. We find that, when the orbits of the companions are coplanar and not too widely separated, the…
We consider a rigid body acted upon by two forces, a constant force and the collective force of interaction with a continuum of particles. We assume that some of the particles that collide with the body reflect elastically (specularly),…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
In this paper, the third in the series, we continue our study of combinatorics in chaotic Newtonian dynamics. We study the chaotic four-body problem in Newtonian gravity assuming finite-sized particles, and we focus on interactions that…
We introduce a formalism for the calculation of the time of arrival t at a detector of particles traveling through interacting environments. We develop a general formulation that employs quantum canonical transformations from the free to…
In this paper we complete the program initiated by the first and second authors and rigorously derive a Boltzmann-type equation that incorporates higher order collisions among gas particles. More precisely, starting from a finite…
The interest in the problem of small asteroids observed shortly before a deep close approach or an impact with the Earth has grown a lot in recent years. Since the observational dataset of such objects is very limited, they deserve…
Particle interactions are key elements of many dynamical systems. In the context of systems described by a Boltzmann equation, such interactions may be described by a collision integral, a multidimensional integral over the momentum-phase…
Near-Earth objects (NEOs) have the potential to cause extensive damage and loss of life on Earth. Advancements in NEO discovery, trajectory prediction, and deflection technology indicate that an impact could be prevented, with sufficient…