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Numerical Model of Perturbated Earth’s Satellite Orbit
Saneliso Vuyo Makhanya,
Wei-Hsi Liao
Issue:
Volume 5, Issue 1, March 2019
Pages:
1-14
Received:
14 October 2018
Accepted:
25 January 2019
Published:
15 February 2019
Abstract: The study aimed to develop a two-dimensional numerical model of a perturbed Earth’s satellite orbit under the influence of the Moon. The first step was to model, numerically, the Earth-satellite orbit. The interaction was assumed to be first order. The basis of the model was that for two-dimensional motion, influence in the radial direction does not affect the motion in the tangential direction and vice versa. Based on this, the satellite’s motion was decomposed into radial and tangential directions. The trajectory was segmented into time intervals and the curve swept over each interval was approximated as a straight line with the assumption that acceleration in each interval was constant. Equations of constant accelerated motion were used to describe the motion of the satellite over each interval. When the model results were compared with the exact solution, for an elliptical orbit, they matched perfectly well over the entire orbit with a maximum relative error of 0.079%. When it was tested for other orbits, circular, hyperbolic, etc., it retained all of them according to theoretical predictions. The model was then extended to incorporate the effects of the Moon by launching the satellite at quarter, half and three-quarter distance from Earth to Moon. A circular orbit was used to model the effects of the Moon. The acceleration results of the model were compared with theoretical predictions. The corresponding errors in the acceleration for the three positions of launch were 0.019% and 0.20%. This showed that this model is applicable for predicting perturbated satellite orbit and it can be applied with any extra force to describe perturbated orbit of the satellite. It can also be used to model the trajectory of projectile motion, of which the exact solution is incapable of generating. Since this model gives the speed of the satellite at any instant, it can be applied when the orbit needs to be changed as it can be used to compute the required new speed.
Abstract: The study aimed to develop a two-dimensional numerical model of a perturbed Earth’s satellite orbit under the influence of the Moon. The first step was to model, numerically, the Earth-satellite orbit. The interaction was assumed to be first order. The basis of the model was that for two-dimensional motion, influence in the radial direction does no...
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Duality Occurrences: Physical Origin of Wave Functions
Issue:
Volume 5, Issue 1, March 2019
Pages:
15-19
Received:
23 January 2019
Accepted:
2 March 2019
Published:
21 March 2019
Abstract: The quantum mystery began with the probabilistic interpretation of the wave function. However, this usefulness is definitive in Quantum Mechanics while the suspense continues. The present paper aims to investigate the origin of such a mystery. Hence, considering a relativistic charged particle in quantum vacuum, it appeared that: (i) from a classical association, this electromagnetismself-consistent derives from the usual wave function, which corresponds to the scalar nature in addition to the vector one. (ii) Such duplicity is only justifiable when the related gauge fields describe fermions, in accordance with the previous theory of duality field-matter. This occurrence then corresponds to the appearance of bosons at cell intersections in vacuum lattice, whatever is the field. (iii) From the related gauge couplings, the scalar function must have an unknown vector companion. Both appear as originating the related conservation laws on one side. On the other side, specific variations of the field front would explain their physical origin. (iv) Moreover, both define an original gauge field to which that of law conservation is sensible. (v) Due to definition validity in any reference system, their possible quantization should lead to that of scalar and vector fields of stationary states. At last, the results highlight the connection between waves and fields associable to any object, emphasizing the field unification framework.
Abstract: The quantum mystery began with the probabilistic interpretation of the wave function. However, this usefulness is definitive in Quantum Mechanics while the suspense continues. The present paper aims to investigate the origin of such a mystery. Hence, considering a relativistic charged particle in quantum vacuum, it appeared that: (i) from a classic...
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High School Students’ Language Related Struggles with Contextualized Differential Equations
Issue:
Volume 5, Issue 1, March 2019
Pages:
20-31
Received:
10 January 2019
Accepted:
15 March 2019
Published:
18 April 2019
Abstract: Upon observing with concern that the majority of high school students experienced severe language related difficulties when solving contextualized differential equations, the researcher then decided to investigate the kinds of such challenges and their impact on students’ learning of differential equations. A sample of 10 mathematics students was selected from one urban high school in one province in Zimbabwe. Written tasks and follow up interviews were employed as data collection tools for the study. Content analysis technique was applied to the written responses and interview transcriptions to obtain a revealing picture of how the kinds of the language related challenges interfere with the growth of mathematical content. The study revealed that the students struggled with interpreting and formulating differential equations from given mathematical situations. Further, interpretation of given initial conditions posed a challenge to the learners. A major consequence of these language related challenges was that the students could not generate complete solutions and lack of interplay between conceptual and procedural fluency was one of the insights generated from this study with regards to the learning of differential equations. The study findings have important implications for instruction in high school mathematics lessons such as the need to develop and foster the students’ abilities to engage in adaptive reasoning and use multiple modes of presenting content in order to promote students’ understanding of contextualized differential equations.
Abstract: Upon observing with concern that the majority of high school students experienced severe language related difficulties when solving contextualized differential equations, the researcher then decided to investigate the kinds of such challenges and their impact on students’ learning of differential equations. A sample of 10 mathematics students was s...
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Heating Effects Induced in a Finite Silver Selenide Slab by a Modelled Laser Internal Source Using the Hyperbolic Heat Conduction (HHCE) Model in Dimensionless Domain
Mohamed Abdelhady Kamel El-Adawi,
Safaa Abdelfattah Shalaby,
Hoda Saad Al-Fanakh
Issue:
Volume 5, Issue 1, March 2019
Pages:
32-37
Received:
11 March 2019
Accepted:
16 April 2019
Published:
20 May 2019
Abstract: Lasers of high power densities are useful for a variety of material processing techniques. Laser heating of a finite homogeneous Silver Selenide slab is studied according to the hyperbolic heat conduction model. Laplace Integral transform technique is used to get the solution. This material suffers phase transition from semiconductor to metallic phase at 403 K. It has vital technological applications. The obtained temperature field makes it possible to determine the time required to initiate phase transition or melting. The functional dependence of the obtained functions is revealed. Different laser power densities are considered as illustrative examples.
Abstract: Lasers of high power densities are useful for a variety of material processing techniques. Laser heating of a finite homogeneous Silver Selenide slab is studied according to the hyperbolic heat conduction model. Laplace Integral transform technique is used to get the solution. This material suffers phase transition from semiconductor to metallic ph...
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