Related papers: Packing Moons Inside the Earth
All 4 giant planets in the Solar System host systems of multiple moons, whereas the terrestrial planets only host up to 2 moons. The Earth can capture small asteroids as temporary satellites, which begs the question as to how many moons…
A brief report on recent work on the sphere-packing problem.
Given a set $P$ of $n$ points in the plane, where $n$ is even, we consider the following question: How many plane perfect matchings can be packed into $P$? We prove that at least $\lceil\log_2{n}\rceil-2$ plane perfect matchings can be…
The Earth-Moon system is unusual in several respects. The Moon is roughly 1/4 the radius of the Earth - a larger satellite-to-planet size ratio than all known satellites other than Pluto's Charon. The Moon has a tiny core, perhaps with only…
The Earth's comparatively massive moon, formed via a giant impact on the proto-Earth, has played an important role in the development of life on our planet, both in the history and strength of the ocean tides and in stabilizing the chaotic…
Contrary to popular belief, the global positioning problem on earth may have more than one solutions even if the user position is restricted to a sphere. With 3 satellites, we show that there can be up to 4 solutions on a sphere. With 4 or…
The classical sphere packing problem asks for the best (infinite) arrangement of non-overlapping unit balls which cover as much space as possible. We define a generalized version of the problem, where we allow each ball a limited amount of…
Each of the giant planets within the Solar System has large moons but none of these moons have their own moons (which we call ${\it submoons}$). By analogy with studies of moons around short-period exoplanets, we investigate the…
A sphere packing of the three-dimensional Euclidean space is compact if it has only tetrahedral holes, that is, any local maximum of the distance to the spheres is at equal distance to exactly four spheres. This papers describes all the…
Magic squares have been well explored here on Earth [1], but there appears to have been little-to-no examination of $\textit{lunar}$ magic squares. Some kinds of magic squares exist on the moon (i.e. under lunar arithmetic) but not on Earth…
Satellite formation is a natural by-product of planet formation. With the discovery of nu- merous extrasolar planets, it is likely that moons of extrasolar planets (exomoons) will soon be discovered. Some of the most promising techniques…
We show that for a transiting exoplanet accompanied by a moon which also transits, the absolute masses and radii of the star, planet and moon are determinable. For a planet-star system, it is well known that the density of the star is…
We point out that by comparing the total mass (in gravitational units) of the earth-moon system, as determined by lunar laser ranging, with the sum of the lunar mass as independently determined by its gravitational action on satellites or…
How good is our universe at making habitable planets? The answer to this depends on which factors are important for life: Does a planet need to be Earth mass? Does it need to be inside the temperate zone? are systems with hot Jupiters…
During the last few years several new results on packing problems were obtained using a blend of tools from semidefinite optimization, polynomial optimization, and harmonic analysis. We survey some of these results and the techniques…
In the Colored Bin Packing problem a set of items with varying weights and colors must be packed into bins of uniform weight limit such that no two items of the same color may be packed adjacently within a bin. We solve this problem for the…
Earth is unusual in bearing life, and in having a large moon. A number of authors have suggested a possible connection between the two, e.g. through lunar stabilisation of the earth's obliquity, or through the effects of the oceanic tides.…
Two decades ago, astronomers began detecting planets orbiting stars other than our Sun, so-called exoplanets. Since that time, the rate of detections and the sensitivity to ever-smaller planets has improved dramatically with several…
Of the few thousand discovered exoplanets, a significant number orbit in the habitable zone of their star. Many of them are gas giants lacking a rocky surface and solid water reservoirs necessary for life as we know it. The search for…
Compact packings are specific packings of spheres which can be seen as tilings and are good candidates to maximize the density. We show that the compact packings of the Euclidean space with two sizes of spheres are exactly those obtained by…