Application of GUI Matlab in physics: Planetary motion (Kepler’s Law)

AbstractIn this series of papers I attempt to provide an answer to the question how the Babylonian scholars arrived at their mathematical theory of planetary motion. Papers I and II were devoted to system A theory of the outer planets and of the planet Venus. In this third and last paper I will study system A theory of the planet Mercury. Our knowledge of the Babylonian theory of Mercury is at present based on twelve Ephemerides and seven Procedure Texts. Three computational systems of Mercury are known, all of system A. System A1 is represented by nine Ephemerides covering the years 190 BC to 100 BC and system A2 by two Ephemerides covering the years 310 to 290 BC. System A3 is known from a Procedure Text and from Text M, an Ephemeris of the last evening visibility of Mercury for the years 424 to 403 BC. From an analysis of the Babylonian observations of Mercury preserved in the Astronomical Diaries and Planetary Texts we find: (1) that dates on which Mercury reaches its stationary points are not recorded, (2) that Normal Star observations on or near dates of first and last appearance of Mercury are rare (about once every twenty observations), and (3) that about one out of every seven pairs of first and last appearances is recorded as “omitted” when Mercury remains invisible due to a combination of the low inclination of its orbit to the horizon and the attenuation by atmospheric extinction. To be able to study the way in which the Babylonian scholars constructed their system A models of Mercury from the available observational material I have created a database of synthetic observations by computing the dates and zodiacal longitudes of all first and last appearances and of all stationary points of Mercury in Babylon between 450 and 50 BC. Of the data required for the construction of an ephemeris synodic time intervals Δt can be directly derived from observed dates but zodiacal longitudes and synodic arcs Δλ must be determined in some other way. Because for Mercury positions with respect to Normal Stars can only rarely be determined at its first or last appearance I propose that the Babylonian scholars used the relation Δλ = Δt −3;39,40, which follows from the period relations, to compute synodic arcs of Mercury from the observed synodic time intervals. An additional difficulty in the construction of System A step functions is that most amplitudes are larger than the associated zone lengths so that in the computation of the longitudes of the synodic phases of Mercury quite often two zone boundaries are crossed. This complication makes it difficult to understand how the Babylonian scholars managed to construct System A models for Mercury that fitted the observations so well because it requires an excessive amount of computational effort to find the best possible step function in a complicated trial and error fitting process with four or five free parameters. To circumvent this difficulty I propose that the Babylonian scholars used an alternative more direct method to fit System A-type models to the observational data of Mercury. This alternative method is based on the fact that after three synodic intervals Mercury returns to a position in the sky which is on average only 17.4° less in longitude. Using reduced amplitudes of about 14°–25° but keeping the same zone boundaries, the computation of what I will call 3-synarc system A models of Mercury is significantly simplified. A full ephemeris of a synodic phase of Mercury can then be composed by combining three columns of longitudes computed with 3-synarc step functions, each column starting with a longitude of Mercury one synodic event apart. Confirmation that this method was indeed used by the Babylonian astronomers comes from Text M (BM 36551+), a very early ephemeris of the last appearances in the evening of Mercury from 424 to 403 BC, computed in three columns according to System A3. Based on an analysis of Text M I suggest that around 400 BC the initial approach in system A modelling of Mercury may have been directed towards choosing “nice” sexagesimal numbers for the amplitudes of the system A step functions while in the later final models, dating from around 300 BC onwards, more emphasis was put on selecting numerical values for the amplitudes such that they were related by simple ratios. The fact that different ephemeris periods were used for each of the four synodic phases of Mercury in the later models may be related to the selection of a best fitting set of System A step function amplitudes for each synodic phase.

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Controlling Film Thickness Distribution by Magnetron Sputtering with Rotation and Revolution

Coatings ◽

10.3390/coatings11050599 ◽

2021 ◽

Vol 11 (5) ◽

pp. 599

Author(s):

Handan Huang ◽

Li Jiang ◽

Yiyun Yao ◽

Zhong Zhang ◽

Zhanshan Wang ◽

...

Keyword(s):

Magnetron Sputtering ◽

Film Thickness ◽

Multilayer Film ◽

Thickness Distribution ◽

Parabolic Cylinder ◽

Particle Model ◽

Planetary Motion ◽

X Rays ◽

X Ray ◽

Sputtering System

The laterally graded multilayer collimator is a vital part of a high-precision diffractometer. It is applied as condensing reflectors to convert divergent X-rays from laboratory X-ray sources into a parallel beam. The thickness of the multilayer film varies with the angle of incidence to guarantee every position on the mirror satisfies the Bragg reflection. In principle, the accuracy of the parameters of the sputtering conditions is essential for achieving a reliable result. In this paper, we proposed a precise method for the fabrication of the laterally graded multilayer based on a planetary motion magnetron sputtering system for film thickness control. This method uses the fast and slow particle model to obtain the particle transport process, and then combines it with the planetary motion magnetron sputtering system to establish the film thickness distribution model. Moreover, the parameters of the sputtering conditions in the model are derived from experimental inversion to improve accuracy. The revolution and rotation of the substrate holder during the final deposition process are achieved by the speed curve calculated according to the model. Measurement results from the X-ray reflection test (XRR) show that the thickness error of the laterally graded multilayer film, coated on a parabolic cylinder Si substrate, is less than 1%, demonstrating the effectiveness of the optimized method for obtaining accurate film thickness distribution.

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On the Prediction of Solar Cycles

Solar Physics ◽

10.1007/s11207-020-01760-7 ◽

2021 ◽

Vol 296 (1) ◽

Author(s):

V. Courtillot ◽

F. Lopes ◽

J. L. Le Mouël

Keyword(s):

Solar Activity ◽

Solar Cycle ◽

Transfer Function ◽

Singular Spectrum Analysis ◽

Activity Cycle ◽

Solar Activity Cycle ◽

Planetary Motion ◽

Data Sets ◽

Solar Cycles ◽

Jovian Planets

AbstractThis article deals with the prediction of the upcoming solar activity cycle, Solar Cycle 25. We propose that astronomical ephemeris, specifically taken from the catalogs of aphelia of the four Jovian planets, could be drivers of variations in solar activity, represented by the series of sunspot numbers (SSN) from 1749 to 2020. We use singular spectrum analysis (SSA) to associate components with similar periods in the ephemeris and SSN. We determine the transfer function between the two data sets. We improve the match in successive steps: first with Jupiter only, then with the four Jovian planets and finally including commensurable periods of pairs and pairs of pairs of the Jovian planets (following Mörth and Schlamminger in Planetary Motion, Sunspots and Climate, Solar-Terrestrial Influences on Weather and Climate, 193, 1979). The transfer function can be applied to the ephemeris to predict future cycles. We test this with success using the “hindcast prediction” of Solar Cycles 21 to 24, using only data preceding these cycles, and by analyzing separately two 130 and 140 year-long halves of the original series. We conclude with a prediction of Solar Cycle 25 that can be compared to a dozen predictions by other authors: the maximum would occur in 2026.2 (± 1 yr) and reach an amplitude of 97.6 (± 7.8), similar to that of Solar Cycle 24, therefore sketching a new “Modern minimum”, following the Dalton and Gleissberg minima.

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Self-assembly and novel planetary motion of ferrofluid drops in a rotational magnetic field

Microfluidics and Nanofluidics ◽

10.1007/s10404-014-1472-1 ◽

2014 ◽

Vol 18 (5-6) ◽

pp. 795-806 ◽

Cited By ~ 11

Author(s):

Ching-Yao Chen ◽

Hao-Chung Hsueh ◽

Sheng-Yan Wang ◽

Yan-Hom Li

Keyword(s):

Magnetic Field ◽

Self Assembly ◽

Planetary Motion ◽

Rotational Magnetic Field

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Machinability Evaluation of Inclined Planetary Motion Milling System for Difficult-to-Cut Materials

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.656-657.320 ◽

2015 ◽

Vol 656-657 ◽

pp. 320-327 ◽

Cited By ~ 3

Author(s):

Hidetake Tanaka ◽

Toma Yoshita

Keyword(s):

Cutting Tool ◽

Rotation Axis ◽

Tool Geometry ◽

Planetary Motion ◽

Orbital Drilling ◽

Drilling Technique ◽

Cutting Model ◽

Cutting Experiments ◽

Tool Rotation ◽

The Revolution

CFRP and Titanium alloy, which are known as difficult-to-cut materials have been widely used as structural material in aviation industries. The orbital drilling is one of an effective drilling technique for the industries. However this technique has some disadvantages such as increase of cutting force due to cutting with tool center point, inertial vibration generated by revolution and high installation cost. In order to improve the disadvantages, we have invented a new drilling technique which is called inclined planetary motion milling. The inclined planetary motion milling and the planetary mechanism drilling has two axes of cutting tool rotation axis and revolution axis. Cutting tool rotation axis of the orbital drilling is moved parallel to the revolution axis in eccentric. On the other hand, in the case of the inclined planetary motion milling, eccentric of the cutting tool rotation axis is realized by inclination of a few degrees from the revolution axis. Therefore, the movement of eccentric mechanism can be reduced by comparison with the orbital drilling because inclined angle is smaller than eccentricity of the cutting tool tip. As a result, eccentric mechanism can be downsized and inertial vibration is reduced. In the study, a geometrical cutting model of inclined planetary motion milling was set up. The theoretical surface roughness of the inside of drilled holes by use of two types cutting tool geometry were calculated based on the model. And cutting experiments using the new prototype for CFRP were carried out in order to evaluate the effect on machinability with change of cutting point atmosphere. In addition, optimal cutting condition was derived according to cutting experiments for titanium alloys utilizing the orthogonal array.

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