Related papers: Measuring Mountains on the Moon
Future Moon bases will likely be constructed using resources mined from the surface of the Moon. The difficulty of maintaining a human workforce on the Moon and communications lag with Earth means that mining will need to be conducted using…
We point out that the mass of the cosmos on gigaparsec scales can be measured, owing to the unique geometric role of the maximum in the areal radius. Unlike all other points on the past null cone, this maximum has an associated mass, which…
The Gaia mission is expected to provide highly accurate astrometric, photometric, and spectroscopic measurements for about $10^9$ objects. Automated classification of detected sources is a key part of the data processing. Here a few aspects…
The size of the diameter of the Sun has been debated for a very long time. First tackled by the Greek astronomers from a geometric point of view, an estimate, although incorrect, has been determined, not truly called into question for…
We describe a geometrical method for tracing a planet's orbit using its velocity hodograph, that is, the path of the planet's velocity. The method requires only a straight edge, a compass, and the help of the hodograph. We also obtain…
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.…
In this paper we will do the following: (1) show how to geometrically define multiplication, using only basic plane geometry, independently of area and any notion of similar triangles; (2) prove all the properties of multiplication using…
We construct measure which determines a two-variable mean in a very natural way. Using that measure we can extend the mean to infinite sets as well. E.g. we can calculate the geometric mean of any set with positive Lebesgue measure. We also…
A measure for the description of the chirality of triangles is introduced. The measure $X\delta$ is zero for triangles with at least one mirror axe, i.e. equilateral or isosceles triangles, and positive or negative for scalane, i.e. left or…
A discussion of the solar diameter and its variations must be linked to the limb darkening function (LDF). We introduce a new method to perform high resolution astrometry of the solar diameter from the ground, through the observations of…
Algorithms for the computation of the forward and inverse geodesic problems for an ellipsoid of revolution are derived. These are accurate to better than 15 nm when applied to the terrestrial ellipsoids. The solutions of other problems…
A fully geometric procedure of quantization that utilizes a natural and necessary metric on phase space is reviewed and briefly related to the goals of the program of geometric quantization.
Inspired by a formula of Stern that relates scalar curvature to harmonic functions, we evaluate the mass of an asymptotically flat $3$-manifold along faces and edges of a large coordinate cube. In terms of the mean curvature and dihedral…
We introduce the general-relativistic definition of Lunar Coordinate Time (TCL) based on the IAU 2000 resolutions that provide a framework for relativistic reference systems. From this foundation, we derive a transformation equation that…
The Moon appears bright in the sky as a source of energetic neutral atoms (ENAs). These ENAs have recently been imaged over a broad energy range both from near the lunar surface, by India's Chandrayaan-1 mission (CH-1), and from a much more…
The incircle of a triangle touches the sides of the triangle in three points. It is well known that the lines from these points to the opposite vertices meet at a point known as the Gergonne point of the triangle. We use a computer to…
We present early results from a project to measure the sky-averaged (global), redshifted $21\,$cm signal from the Epoch of Reionisation (EoR), using the Murchison Widefield Array (MWA) telescope. Because interferometers are not sensitive to…
In order to make accurate inferences about the solar interior using helioseismology, it is essential to understand all the relevant physical effects on the observations. One effect to understand is the (complex-valued) ratio of the…
To understand the physics of sunspots, it is important to know the properties of their magnetic field, and especially its height stratification plays a substantial role. There are mainly two methods to assess this stratification, but they…
The variation of the solar diameter is the subject of hot debates due to the possible effect on Earth climate and also due to different interpretations of long period solar variabilities, including the total solar irradiance. We shortly…