arXiv subjects

Martín Avendaño

Publications and source records attributed to Martín Avendaño.

3 recordsLinked to original sources

arXiv2026

Revisiting Aristarchus's method to estimate the ratio of the distances from Earth to the Sun and the Moon

In this article we revisit Aristarchus' ancient experiment to determine the ratios between the Earth-Moon and Earth-Sun distances. We present here the construction of a simple instrument, basically a tube that, by projecting its shadow, that allows one to estimate the Sun-Earth-Moon angle at the moment of first (or last) quarter. The simplicity of its construction and the accuracy of the measurements obtained may come as a surprise. We discuss the complexities involved in determining the exact moment of first quarter, based on the shape of the elliptical shadow projected on the Moon. Finally, we analyze and implement a strategy that allows us to approximate the measurement of this angle and estimate its value using observations that can be performed twice a month, and more accurately a couple of times during the year. We place Aristarchus' problem in its historical context and detail the physical and mathematical topics that can be developed and motivated through this experiment, in addition to carrying out a very thorough analysis of the errors associated with this measurement.

physics.pop-ph↗

arXiv2020

Efficient search of optimal Flower Constellations

We derive an analytical closed expression to compute the minimum distance (quantified by the angle of separation measured from the center of the Earth) between any two satellites located at the same altitude and in circular orbits. We also exploit several properties of Flower Constellations (FCs) that, combined with our formula for the distance, give an efficient method to compute the minimum angular distance between satellites, for all possible FCs with up to a given number of satellites.

astro-ph.IM↗

arXiv2010

Faster p-adic Feasibility for Certain Multivariate Sparse Polynomials

We present algorithms revealing new families of polynomials allowing sub-exponential detection of p-adic rational roots, relative to the sparse encoding. For instance, we show that the case of honest n-variate (n+1)-nomials is doable in NP and, for p exceeding the Newton polytope volume and not dividing any coefficient, in constant time. Furthermore, using the theory of linear forms in p-adic logarithms, we prove that the case of trinomials in one variable can be done in NP. The best previous complexity bounds for these problems were EXPTIME or worse. Finally, we prove that detecting p-adic rational roots for sparse polynomials in one variable is NP-hard with respect to randomized reductions. The last proof makes use of an efficient construction of primes in certain arithmetic progressions. The smallest n where detecting p-adic rational roots for n-variate sparse polynomials is NP-hard appears to have been unknown.

math.NT↗