The 2016-2100 total solar eclipse prediction by using Meeus Algorithm implemented on MATLAB

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The 2016-2100 total solar eclipse prediction by using Meeus Algorithm implemented on MATLAB
Journal of Physics: Conference Series

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The 2016-2100 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. 771 012039

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The 2016-2100 total solar eclipse prediction by using Meeus Algorithm implemented on MATLAB
International Symposium on Sun, Earth, and Life (ISSEL)                                                        IOP Publishing
Journal of Physics: Conference Series 771 (2016) 012039                                    doi:10.1088/1742-6596/771/1/012039

The 2016-2100 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

                     E-mail: 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 2100. We Used Besselian calculations
                     and Meeus algorithms implemented in MATLAB R2012b software. This methods combine with
                     VSOP087 and ELP2000-82 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 0.04-0.21 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 ELP2000-
82 (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. L1 is a radius of the
penumbra cone in the fundamental plane, L2 is the radius of umbra cone in the fundamental plane, L1' is
the radius of penumbra cone in observer plane on the Earth's surface, L2' is the radius of umbra cone in
observer plane on the Earth's surface, f1 is angle between the penumbra cone and the shadow axis of
Moon's, f2 is angle between the umbra cone and the shadow axis of Moon's.

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Published under licence by IOP Publishing Ltd                         1
The 2016-2100 total solar eclipse prediction by using Meeus Algorithm implemented on MATLAB
International Symposium on Sun, Earth, and Life (ISSEL)                                                IOP Publishing
Journal of Physics: Conference Series 771 (2016) 012039                            doi:10.1088/1742-6596/771/1/012039

                                                                        Start

                                                              Input Data : Besselian
                                                              element based on date
                                                              and year TSE on 2016-
                                                                       2100                           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

                                                                        End

        Figure 1. Description                    Figure 2.Flow chart of TSE predictions.
        Besselian element in the from
        of image
        (http://www.gautschy.ch/~rita/
        archast/solec/solec.html).

    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 > +0.0047, it is annular; if u is between 0 and +0.0047, 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, 00464 1   2 > 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
The 2016-2100 total solar eclipse prediction by using Meeus Algorithm implemented on MATLAB
International Symposium on Sun, Earth, and Life (ISSEL)                                     IOP Publishing
Journal of Physics: Conference Series 771 (2016) 012039                 doi:10.1088/1742-6596/771/1/012039

 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 2.

4. 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 20th, 2042) using Besselian element illustrated
on Table.1
                        Table 1. Besselian Element for TSE on April 20th, 2042[5]

     Figure 3. Simulation TSE Predictions Display on April 20th, 2042 Using MATLAB Software

 Figure 4. Graph Geographic Region or position through which the Total Solar Eclipse on April 20th,
                                              2042.

                                                     3
International Symposium on Sun, Earth, and Life (ISSEL)                                 IOP Publishing
Journal of Physics: Conference Series 771 (2016) 012039             doi:10.1088/1742-6596/771/1/012039

 Figure 5. Geographic Region or position through which the Total Solar Eclipse on April 20th, 2042.

   Figure 4 and 5 shows TSE coverage on 20 April 2042. 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 ELP2000-82 (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 0.04-0.21 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 6 265 – 266
[2] Meeus J 2003 J. British Astronomical Association 113 (6): 343-348
[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 379-
        388
[5] Meeus J 1989 Elements of Solar Eclipses 1951-2200 (Virginia, USA: Willmann Bell) p 150
[6] Espenak F and Meeus J 2009 Five Millenium Catalog of Solar Eclipses: -1999 to +3000 (2000
        BCE to 3000 CE)-Revised NASA/TP-2009-214174 p. A-164

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