The total solar eclipse prediction by using Meeus Algorithm implemented on MATLAB

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1 Journal of Physics: Conference Series PAPER OPEN ACCESS The total solar eclipse prediction by using Meeus Algorithm implemented on MATLAB To cite this article: A Melati and S Hodijah 2016 J. Phys.: Conf. Ser View the article online for updates and enhancements. This content was downloaded from IP address on 27/04/2018 at 21:11

2 The total solar eclipse prediction by using Meeus Algorithm implemented on MATLAB A Melati, S Hodijah Physics Department, Faculty of Science and Technology, UIN Sunan Kalijaga Yogyakarta, Jl. Maksda Adisucipto No. 1, Yogyakarta, Indonesia asih.melati@gmail.com Abstract. The phenomenon of solar and lunar eclipses can be predicted where and when it will happen. The Total Solar Eclipse (TSE) phenomenon on March 09th, 2016 became revival astronomy science in Indonesia and provided public astronomy education. This research aims to predict the total solar eclipse phenomenon from 2016 until We Used Besselian calculations and Meeus algorithms implemented in MATLAB R2012b software. This methods combine with VSOP087 and ELP algorithm. As an example of simulation, TSE prediction on April 20th, 2042 has 0.2 seconds distinction of duration compared with NASA prediction. For the whole data TSE from year of 2016 until 2100 we found seconds differences compared with NASA prediction. 1. Introduction Total solar eclipse (TSE) is not a sign of human mortality and natality. As a matter of fact, it has a predetermined time as the appearance of the hilal as said by Islamic phylosopher Shaykh al-islam Ibn Taimiyah. The eclipse on March 9th, 2016 was clearly visible in many parts in Indonesia, including Central Sulawesi and Ternate. It was becomes special momentum and astronomy euphoria. The high interest of public indicates that most of Indonesian people eager to learn astronomy. This euphoria was different from TSE phenomenon in 1983 which enormous people were anxious. This research aims to predict next TSE using Meeus Algorithm. Meeus Algoritm could predict maximum duration of TSE [1][2]. We simulated TSE from year of 2016 until 2100 using MATLAB R2012b software. 2. TSE calculation based on Meeus Algorithm To calculate or predict solar eclipse, we need to know Besselian Elements according to the date of the solar eclipse. The Besselian elements of unification algorithms are VSOP87 (for the Sun) and ELP (for the Moon). The method was developed by Friedrich Wilhelm Bessel in 1842 and was repeatedly refined since then. The basic idea of the method is that the Besselian elements describe the motion of the lunar shadow on a suitably chosen, so called fundamental plane. The fundamental plane crosses the centre of the Earth and is perpendicular to the axis of the shadow cone. The Besselian elements shown in figure 1 below[3][5]. Where observer plane is an observer on the Earth's surface. L 1 is a radius of the penumbra cone in the fundamental plane, L 2 is the radius of umbra cone in the fundamental plane, L 1' is the radius of penumbra cone in observer plane on the Earth's surface, L 2' is the radius of umbra cone in observer plane on the Earth's surface, f 1 is angle between the penumbra cone and the shadow axis of Moon's, f 2 is angle between the umbra cone and the shadow axis of Moon's. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by Ltd 1

3 Start Input Data : Besselian element based on date and year TSE on No Calculate Latitude, Longitude, Azimuth and Altitude of Sun, Radius Ratio between Moon dan Sun, Path, Duration of solar eclipse, and area Error occur? Yes or No? Output Data : Latitude, Longitude, Azimuth and Altitude of Sun, Radius Ratio between Moon dan Sun, Path, Duration of solar eclipse, and area Result analyzing Conclusion Figure 1. Description Besselian element in the from of image ( archast/solec/solec.html). End Figure 2.Flow chart of TSE predictions. In the case of a central eclipse, the type of the eclipse can be determined by the following rules: if u < 0, the eclipse is total; if u > , it is annular; if u is between 0 and , the eclipse is either annular or annular-total. u represents radius of the Moon s umbral cone in the fundamental plane. In the latter case, the ambiguity is removed as follow 0, > 0 (1) If u <, the eclipse is annular-total; otherwise it is the annular one. In the case of a partial solar eclipse, the greatest magnitude is attained at the point of the surface of the Earth which comes closest to the axis of shadow. The magnitude of the eclipse at that point is 1,5433 u 0,5461 2u (2) 2

4 represents the least distance from the axis of the Moon s shadow to the center of the Earth, in units of the equatorial radius of the Earth [4]. 3. Methods Prediction steps of a total solar eclipse are presented in the form of a flow chart shown figure Result and discussion Based on our TSE predictions there are ± 68 total solar eclipse that will occur from year of 2016 to 2100 (see figure 3, prediction of the total solar eclipse on April 20 th, 2042) using Besselian element illustrated on Table.1 Table 1. Besselian Element for TSE on April 20 th, 2042[5] Figure 3. Simulation TSE Predictions Display on April 20 th, 2042 Using MATLAB Software Figure 4. Graph Geographic Region or position through which the Total Solar Eclipse on April 20 th,

5 Figure 5. Geographic Region or position through which the Total Solar Eclipse on April 20 th, Figure 4 and 5 shows TSE coverage on 20 April The TSE will be observed in Indian Ocean, then across Jambi town and southern Sumatra, Java Sea, Bangka and Belitung Island, Java Sea, the city of Pontianak, West Kalimantan, then across Malaysia, South China Sea, Brunei, Sabah-Malaysia, the Philippines and ended up in the North Pacific Ocean. The longest duration of totality based on the algorithm is 4 minutes 51 seconds. All of the obtained TSE are different compared with NASA prediction. NASA prediction will have 0.2 seconds longer duration than our research. Based on the results that have been obtained, simulation TSE predictions with Besselian method combined with VSOP87 (for the Sun) and ELP (for the Moon) algorithms on MATLAB software could be used as reference for the next total solar eclipse predictions until 2100[4]. Our results show seconds longer duration of totality compared with the results from NASA [6] Acknowlegment We would like to thank Astronic Study Club Sunan Kalijaga Islamic State University for support this research, Dr Rinto Anugraha lecturer Physics Department Gajah Mada University and Anggara Dwi for helping operate several label programming. References [1] Lewis Isabel M 1931 American Astronomical Society [2] Meeus J 2003 J. British Astronomical Association 113 (6): [3] Gautschy R 2012 Canon of Solar Eclipse from 2501 BC to 1000 AD (Swiss: Swiss National Science Foundation) [4] Meeus J 1998 Astronomical Algorthms second edition (Virginia, USA: Willmann Bell) p [5] Meeus J 1989 Elements of Solar Eclipses (Virginia, USA: Willmann Bell) p 150 [6] Espenak F and Meeus J 2009 Five Millenium Catalog of Solar Eclipses: to (2000 BCE to 3000 CE)-Revised NASA/TP p. A-164 4