ATTEMPTS TO REPRODUCE NICOLAUS COPERNICUS EXPERIMENTS NCU, Torun, Poland Andrzej Strobel, Jozefina Turlo

ATTEMPTS TO REPRODUCE NICOLAUS COPERNICUS EXPERIMENTS

NCU, Torun, PolandAndrzej Strobel, Jozefina Turlo

Plan of presentation

I. IntroductionI. Introduction

II. Historical background II. Historical background

III. Orginal experiment of Nicolaus III. Orginal experiment of Nicolaus Copernicus, Copernicus, Olsztyn, 1517Olsztyn, 1517

IV. Reproductions of Nicolaus Copernicus IV. Reproductions of Nicolaus Copernicus experiments in Torun, 2010experiments in Torun, 2010

V. Mathematical description of the resultsV. Mathematical description of the results

VI. Summary, remarksVI. Summary, remarks

VII. PublicationsVII. Publications

I. IntroductionAstronomy as interdisciplinary subject:

1.Subdisciplines as: astrophysics, astrometry, radioastronomy, mechanics of sky, astronomic spectroscopy, astrochemistry, planetology, astrobiology, cosmology, astronautics. 2. ”Interdisciplinary thinkers” in the past: e.g. Leonardo da Vinci, Nicholas Copernicus, Galileo Galilei, René Descartes, Isaac Newton, Wolfgang Goethe, Albert Einstein …

II. Historical backgroundII. Historical background• Parents: Barbara Watzenrode, Mikolaj Kopernik

• Born on 19 February 1473, at St. Anna Street 15/17, Torun

• Elementary school - St. Johns Parish School, Torun

• Secondary school – not known exactly but probably in Wloclawek

• 1491 – 1495 – University study in Krakow

• 1496 – 1503 – University studies in Bologna (canon law), Padova

(medicine, astronomy, Greek), Ferrara (PhD in canon law)

Torun Krakow Padova

II. Historical backgroundII. Historical background• 1503 – return to Poland (Lidzbark – manor of Lukasz Watrzenrode)

• 1510 – ed. „Comment about hypotheses of celestial movements”

• 1512 – 1515 – Tower of Frombork, sun and other planets

observations, experiments due to „the calendar reform”

• 1516 – Olsztyn Castle – administration of church property and

defense against Teutonic Order

• 1517 – Construction of astronomical table (sun callender) at the

wall of Olsztyn Castle gallery

• 1543 – Frombork: „The Revolutionibus” and death of Copernicus

Lidzbark Olsztyn Frombork

III. Orginal experiment of Nicolaus III. Orginal experiment of Nicolaus Copernicus, Olsztyn, 1517Copernicus, Olsztyn, 1517

The main goals of Copernicus experiment The main goals of Copernicus experiment were:were: • Perform Sun observation and irregular Perform Sun observation and irregular

motion of Earth.motion of Earth.• Answer the question of Pope Leon X Answer the question of Pope Leon X

concerning possibility to change the concerning possibility to change the obeyed obeyed

callendar (1513).callendar (1513).• Define the moment of Spring equinox, Define the moment of Spring equinox, which which

was movable at that time - there was was movable at that time - there was diffrence diffrence

between callendar year (365 and ¼ between callendar year (365 and ¼

day) and real period of Earth motion day) and real period of Earth motion around the around the

Sun (365 days 5h 48’ 46’’). Sun (365 days 5h 48’ 46’’).

This difference was equal around 11 This difference was equal around 11 minutes!minutes!

• Calculate the lenght of astronomical year Calculate the lenght of astronomical year measured as the distance between two measured as the distance between two equinoxes (Spring or Autumn).equinoxes (Spring or Autumn).

The first observation Copernicus made in The first observation Copernicus made in Frombork (1513-1515), later in Olsztyn, Frombork (1513-1515), later in Olsztyn, 1517.1517.


Location of Copernicus mirror at the Olsztyn CastleLocation of Copernicus mirror at the Olsztyn Castle


This is original astronomical table plotted by Copernicus on This is original astronomical table plotted by Copernicus on the wall of Olsztyn Castle gallery in 1517. the wall of Olsztyn Castle gallery in 1517.

In the Figure, parallelly to (the red) linear curve we can In the Figure, parallelly to (the red) linear curve we can recognize some letters from the word: recognize some letters from the word: AEQUINOCTIUMAEQUINOCTIUM (equinox). The other curves (blue) are the parts of paraboles. (equinox). The other curves (blue) are the parts of paraboles.

The arabic numbers 10,15,20 describe The arabic numbers 10,15,20 describe length position of the length position of the SSun on the eclipticun on the ecliptic. The black lines describe the hour of . The black lines describe the hour of observations.observations.

IV. Reproduction of Nicolaus IV. Reproduction of Nicolaus Copernicus experiments in Torun, 2010 Copernicus experiments in Torun, 2010

Methodology of work:

•Consecutive steps of the collective work of supervisors, teachers and students were as follows:

•Study of the available literature, •Description of Case studies, •Writting the scenario of lesson based on the Case studies, •Preparation of instruments and ppt presentation, •Conduction of pilot lesson and reflection, •Corrections and dissemination of the results.

•Furthermore, two M.Sc. degree works were supervised: •Active methods for motivation students towards the effective

lerning of physics with the use of History elements •Development of inquiry – interactive methods of teaching based

on Witelo and Copernicus studies.

There are the results of Ms. Witkowska observations made in There are the results of Ms. Witkowska observations made in the Institute of Physics of NCU in 17th February to 4th May the Institute of Physics of NCU in 17th February to 4th May 2010. She used simple mirror with diameter 2 cm and screen 2010. She used simple mirror with diameter 2 cm and screen 2,5m x 1,5m. 2,5m x 1,5m.


The contribution of Nicolaus Copernicus observations to the reform of calendar• Target groups.

Lesson for students from lower secondary school at the advaced level (13-16).• Operational aims. Student:

1. knows properties of light – rectilinear propagation and reflection, 2. understands the function of mirror and reflection - gnomonic method, 3. knows the creation of shadow and its everyday aplications, 4. conducts the experiment of N. Copernicus on astronomical table.

• Fundamental lesson - conclusions, reflections, remarks.

Introductory lesson to explain interdisciplinary character of Copernicus experiment (elements of physics, astronomy, geography, history, philosophy). Planning observations, working groups, elaboration of results.

• Historical introduction on famous Copernicus observations.

The results of students where compared with the Copernicus observations, improvements for the next experiment on finding of equinoxes.


The contribution of Nicolaus Copernicus observations to the reform of calendar

Experimental setup of mirror

The group of observers with teacher


Mirror at the window View of the mark

Marks at the ceiling

The contribution of Nicolaus Copernicus observations to the reform of calendar

Plot showing the results of student observations made from 18th February

to 22nd April 2010 in the Secondary School sepervised by Ms. Czerwinska.

The red linear curve in the middle indicate the vicinity of Spring equinox.


V. Mathematical decription of the V. Mathematical decription of the results results

1. Graphical model of virtual motion of sun on a cone


2. Description of conical plane


3. Cone in the cartesian coordinates and ceiling projection

z’ = z + h

x = x’y = y’


4. After linear translation along axis z by distance „–h” – distance from projection plane to the mirror plane (center of coordination system is placed in the center of mirror):

z’ = z + h

x = x’y = y’

5. After rotation of system around axis x by „900-φ” (axis z overlap axis of Earth rotation):

x’ = xy’ = ysinφ - hcosφz’ = hsinφ + ycosφ


6. After substitution of transform coordinate to the cone equation and conversions we obtain the „rabbit” track in the form:

y2(cos2φ-tg2δsin2φ)+hysin2φ[1+tg2δ]+h2(sin2φ-tg2δcos2φ)-x2tg2δ=0

7. We can consider the specific cases:a) Pole: φ=900, sinφ=1, cosφ=0, equation 6:

-y2tg2δ+h2-x2tg2δ=0 /tg2δ

x2+y2=h2/tg2δ

Circle with the radius R = h/tgδ


7. We can consider the specific cases:b) Equator: φ=00, sinφ=0, cosφ=1, tgδ=0 (for equinox δ=0) equation 6:

y2=0

Linear curve overlap with axis x

c) Equator: φ=0, outside equinox δ≠0 euqtion 6:

y2-h2tg2δ-x2tg2δ=0 /h2tg2δ

y2/h2tg2δ – x2/h2=1

Canonical equation of hyperbole


7. We can consider the specific cases:d) Equinox δ=0, φ≠0 (moderate latitudes) equation 6:

y2cos2φ+2sinφcosφhy+h2sin2φ=0

(ycosφ+hsinφ)2=0

y=-htgφ

Linear curve parallel to the axis x


We would like to add that:

1. The issue raised by the described Case study is connected with the Polish core curriculum in:

• History – Europe and the Mediterranean world in the Middle Ages,• Geography – Earth as a part of the Universe,• Physics – Solar System, propagation of light (reflection and refraction, nature of light)• Philosophy – representatives of ancient philosophy: Aristotle,• Regional knowledge – elements of history and representatives.


We would like to add that:

2. The lessons based on this topic have additional advantages for students, they:

• are learning about the main concepts and physical phenomena,• are learning responsibility,• are recognizing the knowledge development and acquire physical and technical skills,• are recognizing the historical background of experiment,• experience interdisciplinary integration,• developing their personality and the way of collaboration.

VII. Publications 1. The solar calendar of Nicolaus Copernicus, Part I, Z.Turło, A. Witkowska, J. Turło, Nauczanie

Przedmiotów Przyrodniczych, 29, 2009. pp. 9-17.2. The solar calendar of Nicolaus Copernicus, Part II, A. Witkowska, Nauczanie Przedmiotów

Przyrodniczych, 30, 2009. pp. 25-29.3. The solar calendar of Nicolaus Copernicus, Part III, M. Czerwińska, Nauczanie Przedmiotów

Przyrodniczych, 30, 2009. pp. 30-40.

Thank You for your attention!

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ATTEMPTS TO REPRODUCE NICOLAUS COPERNICUS EXPERIMENTS NCU, Torun, Poland Andrzej Strobel, Jozefina Turlo