Related papers: Packing Moons Inside the Earth
Clumsy packing is considered an inefficient packing, meaning we find the minimum number of objects we can pack into a space so that we can not pack any more object. Thus we are effectively spacing out the objects as far apart as possible so…
Motivated by recent measurements of the free-floating planet mass function at terrestrial masses, we consider the possibility that the solar system may have captured a terrestrial planet early in its history. We show that $\sim 1.2$…
This review paper is devoted to the problems of sphere packings in 4 dimensions. The main goal is to find reasonable approaches for solutions to problems related to densest sphere packings in 4-dimensional Euclidean space. We consider two…
The giant impact hypothesis is the dominant theory of how the Earth-Moon system was formed. Models have been created that can produce a disk of debris with the proper mass and composition to create our Moon. Models have also been created…
Advances in robotics and additive manufacturing have become game-changing for the prospects of space industry. It has become feasible to bootstrap a self-sustaining, self-expanding industry at reasonably low cost. Simple modeling was…
A surprisingly large amount of information on our solar system can be gained from simple measurements of the apparent angular diameters of the sun and the moon. This information includes the average density of the sun, the distance between…
The Space Interferometry Mission (SIM) will make precise astrometric measurements that can be used to detect planets around nearby stars. We have simulated SIM observations and estimated the ability of SIM to detect planets with given…
[abridged] In the typical giant-impact scenario for the Moon formation most of the Moon's material originates from the impactor. Any Earth-impactor composition difference should, therefore, correspond to a comparable Earth-Moon composition…
The lunar geological record contains a rich archive of the history of the inner Solar System, including information relevant to understanding the origin and evolution of the Earth-Moon system, the geological evolution of rocky planets, and…
In this small review we present the actual state the knowledge about weighting black holes. Black holes can be found in stellar binary systems in our Galaxy and in other nearby galaxies, in globular clusters, which we can see in our and…
In the classic circle packing problem, one asks whether a given set of circles can be packed into a given container. Packing problems like this have been shown to be $\mathsf{NP}$-hard. In this paper, we present new sufficient conditions…
A subset of the sphere is said short if it is contained in an open hemisphere. A short closed set which is geodesically convex is called a cap. The following theorem holds: 1. The minimal number of short closed sets covering the $n$-sphere…
Let $S$ be a set of $n$ points in the unit square $[0,1]^2$, one of which is the origin. We construct $n$ pairwise interior-disjoint axis-aligned empty rectangles such that the lower left corner of each rectangle is a point in $S$, and the…
About half of all known stellar systems with Sun-like stars consist of two or more stars, significantly affecting the orbital stability of any planet in these systems. Here we study the onset of instability for an Earth-type planet that is…
It is commonly believed that the most efficient way to pack a finite number of equal-sized spheres is by arranging them tightly in a cluster. However, mathematicians have conjectured that a linear arrangement may actually result in the…
Using over 89 million astrometric observations of 349,737 numbered minor planets, an attempt was made to determine the masses of 230 of them by simultaneously solving for corrections to all orbital elements and the masses. For 132 minor…
We develop a model to describe the properties of random assemblies of polydisperse hard spheres. We show that the key features to describe the system are (i) the dependence between the free volume of a sphere and the various coordination…
Applying semi-classical Quantum Mechanics, the vacuum fluctuations within a star are determined, assuming a constant mass density and applying a monopole approximation. It is found that the density for the vacuum fluctuations does not only…
Packing problems, which ask how to arrange a collection of objects in space to meet certain criteria, are important in a great many physical and biological systems, where geometrical arrangements at small scales control behaviour at larger…
The problem of the formation of the Moon is still not explained satisfactorily. While it is a generally accepted scenario that the last giant impact on Earth between some 50 to 100 million years after the starting of the formation of the…