Estimating the Moon-to-Earth Radius Ratio with a Smartphone, a Telescope, and an Eclipse

Caerols, Hugo; Asenjo, Felipe A.

doi:10.1119/10.0002071

Cited by 6 publications

(7 citation statements)

References 6 publications

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“…The real values of the crater's diameters d C are small compared to the diameter of the Moon 2R M , where the Moon's radius is R M = 1, 737.4 km [16]. As a side note, although this parameter is well known, its value can be estimated in several simple manners, such as using smartphone photos of a lunar eclipse [4]. For cases such as these craters, the geometry of the crater can be considered Euclidean, and the proportions between the distances linear.…”

Section: Small Distances Flat Geometry and Proportionalitymentioning

confidence: 99%

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Using smartphone photographs of the Moon to acquaint students with non-Euclidean geometry

Caerols,

Carrasco,

Asenjo

2021

Preprint

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Although they are sometimes considered problematic to grasp by students, the concepts behind non-Euclidean geometry can be taught using astronomical images. By using photographs of the Moon taken with a smartphone through a simple telescope, we were able to introduce these concepts to high-school students and college newcomers. By recognizing different Moon geological structures within the photograph, we teach students how to calculate distances of mountain ranges or areas of craters on the Moon's surface, introducing the notions of geodesics and spherical triangles. Furthermore, students can empirically see that the correct estimations for the actual values cannot be obtained using flat geometry. Instead, by using three-dimensional curved geometry, precise estimates of lengths and areas of geological elements in the Moon can be computed with less than 4% error. These procedures help students understand, concretely, non-Euclidean geometry concepts.

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Section: Small Distances Flat Geometry and Proportionalitymentioning

confidence: 99%

“…With this software, we can calculate how large the diameter of the craters and the Moon's radius is the photograph on a centimeter scale. A detailed procedure to obtain those values can be found in [4].…”

Section: Small Distances Flat Geometry and Proportionalitymentioning

confidence: 99%

Using smartphone photographs of the Moon to acquaint students with non-Euclidean geometry

Caerols,

Carrasco,

Asenjo

2021

Preprint

Self Cite

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“…The Moon has been the object of admiration since antiquity and corresponds to one of the celestial bodies that are best observed from Earth, getting excellent photographs of its phases with amateur telescopes and smartphones [1]. The Moon can also be an excellent object to make different astronomical calculations and measurements in order to prove the powerfulness of physics and mathematics [2]. For example, selenography can be used to introduce non-Euclidean geometries to undergraduate students [3].…”

Section: Introductionmentioning

confidence: 99%

Measuring the elliptical form of the Moon’s terminator curve and its illuminated area by direct and indirect methods

Caerols,

Asenjo,

Ponce

2023

Phys. Educ.

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Because solar light, from Earth perspective, a curve is drawn in Moon’s surface that separates its dark side from the illuminated one. This curve is known as the terminator curve. In this article we prove, using direct and indirect methods, that the terminator curve corresponds to an ellipse. This is demonstrated using mathematical concepts and photographs of the Moon that are analysed with a geometrical software. Using this information, we also show how to calculate the illuminated fraction area of the Moon depending on its day of rotation. We obtain excellent approximations regarding the values given by computational systems. We discuss the results of considering the Moon as a flat disk or like a sphere. We analyse the technical difficulties of the process and the mathematical tools needed for more precise calculations. We also put in context this demonstration of the ellipticity of the terminator curve for any interior planet illuminated by a central star of any planetary system, seen from a outsider planet, the case in which the phases are more noticeable. Finally we extend the previous calculations to analyse the illuminated percentage of the inner planets Mercury and Venus, obtaining excellent results in the case of Venus.

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“…In this context, the role of science education and, specifically, astronomy teaching, is fundamental to promote the acknowledgment of scientific research methods and their use as a tool to understand the current world [11][12][13][14][15][16][17][18][19][20]. Accordingly, we present a physical modeling activity that allows students to determine the differences between a disk and a sphere using pure scientific criteria.…”

Section: Introductionmentioning

confidence: 99%

The Moon, a disk or a sphere?

Duarte,

Mota,

de Carvalho

et al. 2021

Preprint

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In this paper, we present a physical modeling activity whose objective is to allow students to determine the differences between a disk and a sphere using pure scientific criteria. Thereunto, we reproduce the Sun-Earth-Moon system with low-cost materials and compare the illumination effects on the Moon considering two possible shapes for it (a sphere and a disk). The analysis is based on the shape of the Terminator line produced in each case as a function of the illumination angle. The results obtained are first discussed and then applied so that one can interpret the observed patterns in the illumination effects of other celestial bodies, such as Venus or even the Earth. Thereby, the activity can be very useful to unmask the unscientific idea of Flat Earth. The entire activity is easily replicable and it may be useful to promote a more realistic view of science and its methods.

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Estimating the Moon-to-Earth Radius Ratio with a Smartphone, a Telescope, and an Eclipse

Cited by 6 publications

References 6 publications

Using smartphone photographs of the Moon to acquaint students with non-Euclidean geometry

Using smartphone photographs of the Moon to acquaint students with non-Euclidean geometry

Measuring the elliptical form of the Moon’s terminator curve and its illuminated area by direct and indirect methods

The Moon, a disk or a sphere?

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