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background="../../../../../ASTRONOMIA/i_grandi_astronomi/Keplero/tre_leggi_keplero/stars_fissa.gif" lang=IT link=blue vlink=purple style='tab-interval:35.4pt'> <div class=WordSection1> <p class=MsoNormal><a href="../../../../../ASTRONOMIA/i_grandi_astronomi/i_grandi_astronomi.html#keplero"><span style='mso-fareast-font-family:"Times New Roman";mso-no-proof:yes;text-decoration: none;text-underline:none'><img border=0 width=39 height=25 id="_x0000_i1034" src="../../../../../ASTRONOMIA/i_grandi_astronomi/Keplero/tre_leggi_keplero/indietro.gif" alt="Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: D:\backup disco E\03_II_SESTANTE_SITO\ASTRONOMIA\i_grandi_astronomi\Keplero\tre_leggi_keplero\indietro.gif"></span></a><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> <p class=MsoNormal><o:p>&nbsp;</o:p></p> <div align=center> <table class=MsoNormalTable border=0 cellpadding=0 width=1150 style='width: 862.5pt;mso-cellspacing:1.5pt;background:black;mso-background-themecolor:text1; mso-yfti-tbllook:1184;mso-padding-alt:0cm 5.4pt 0cm 5.4pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><b style='mso-bidi-font-weight:normal'><i style='mso-bidi-font-style:normal'><span style='font-size:18.0pt;color:#00B0F0'><o:p>&nbsp;</o:p></span></i></b></p> <p class=MsoNormal align=center style='margin-bottom:6.0pt;text-align:center'><span style='mso-no-proof:yes'><img border=0 width=794 height=58 id="_x0000_i1033" src="intestazione_01.gif" alt="Descrizione: Descrizione: D:\backup disco E\03_II_SESTANTE_SITO\en\ASTRONOMIA\i_grandi_astronomi\Keplero\tre_leggi_keplero\intestazione_01.gif"></span><b style='mso-bidi-font-weight:normal'><i style='mso-bidi-font-style:normal'><span style='font-size:18.0pt;color:#00B0F0'><o:p></o:p></span></i></b></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><b style='mso-bidi-font-weight:normal'><i style='mso-bidi-font-style:normal'><span style='font-size:18.0pt;color:#00B0F0'><o:p>&nbsp;</o:p></span></i></b></p> <p align=center style='text-align:center'><span lang=EN-GB style='color:gray; mso-ansi-language:EN-GB'>Download Java: click here if demos below cannot be visualized</span><span lang=EN-GB style='color:gray;mso-ansi-language:EN-US'> </span><span lang=EN-US style='mso-ansi-language:EN-US'><br> </span><a href="http://java.sun.com/getjava/download.html" target="_blank"><span style='mso-no-proof:yes;text-decoration:none;text-underline:none'><img border=0 width=112 height=47 id="_x0000_i1032" src="http://www.ac-ilsestante.it/astronomia/i_grandi_astronomi/Keplero/tre_leggi_keplero/javagetitnow.gif" alt="Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: Descrizione: http://www.ac-ilsestante.it/astronomia/i_grandi_astronomi/Keplero/tre_leggi_keplero/javagetitnow.gif"></span></a><span lang=EN-US style='color:gray;mso-ansi-language:EN-US'><o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span class=SpellE><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-size:18.0pt;color:#00B0F0;mso-ansi-language:EN-GB'>Kepler s</span></i></span><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-size:18.0pt; color:#00B0F0;mso-ansi-language:EN-GB'> data </span></i><i style='mso-bidi-font-style: normal'><span lang=EN-GB style='font-size:18.0pt;color:#FFC000;mso-ansi-language: EN-GB'>: <span class=SpellE>Tycho s</span> observations, the model of the Sun and the model of the planets</span></i><i style='mso-bidi-font-style:normal'><span lang=EN-US style='font-size:18.0pt;color:#FFC000;mso-ansi-language:EN-US'><o:p></o:p></span></i></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='color:#EEECE1;mso-themecolor:background2;mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><b style='mso-bidi-font-weight: normal'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:#00B0F0;mso-ansi-language:EN-US'>Kepler</span></b><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'> has very few reliable things, </span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:#FFC000;mso-ansi-language:EN-US'>the measures in longitude of Mars relative to Earth with the uncertainty of a couple of  primes </span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'>, </span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:#00B0F0; mso-ansi-language:EN-US'>the theory of the Sun </span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>(or equivalently, of the Earth) of Tycho Brahe. Given the low eccentricity, the model of the Sun (Earth) will be more easily validated for both the longitude and distance.<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>Generations of astronomers studied the motion of the sun with sundials, so that it is known with great precision.<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:white; mso-themecolor:background1;mso-ansi-language:EN-US'>For the ancient model of the Sun (Earth) is a simple eccentric circle</span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>.<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>It is easy to theoretically calculate the distance in terms of percentage change of the deferent. Specifically, to measure, one could observe the Sun's diameter, but the great sundials (a hole in the ceiling of the church) will come in later periods. Kepler will use a more indirect method.<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>At the end he will find a simple model, that gives consistent results for the orbit of the Earth, it will be valid for the calculation of longitudes, and for the distance.</span><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='color:#EEECE1;mso-themecolor:background2;mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal align=center style='text-align:center'><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif";color:white; mso-ansi-language:EN-GB'>Synthesis: <span class=msonormal0><b style='mso-bidi-font-weight:normal'>« </b></span></span><span class=msonormal0><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif";color:red; mso-ansi-language:EN-GB'>New Astronomy </span></b></span><span class=msonormal0><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif";color:white; mso-ansi-language:EN-GB'>» 1609 </span></b></span><span class=msonormal0><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:white;mso-ansi-language:EN-GB'>- </span></span><span class=msonormal0><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt; font-family:"Arial","sans-serif";color:#00B0F0;mso-ansi-language:EN-GB'>Johannes Kepler</span></b></span><span lang=EN-GB style='font-size:11.0pt;font-family: "Arial","sans-serif";color:white;mso-ansi-language:EN-GB'>  translated by William H. Donahue&quot;</span><span lang=EN-GB style='font-size:10.0pt; mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-US'> </span><span lang=EN-US style='font-size:10.0pt;mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US'><o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='color:#EEECE1;mso-themecolor:background2;mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='color:#EEECE1;mso-themecolor:background2;mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='color:#EEECE1;mso-themecolor:background2;mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='color:#EEECE1;mso-themecolor:background2;mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='color:#EEECE1;mso-themecolor:background2;mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='color:#EEECE1;mso-themecolor:background2;mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='color:#EEECE1;mso-themecolor:background2;mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span class=SpellE><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-size:18.0pt;color:#00B0F0;mso-ansi-language:EN-GB'>Tycho s</span></i></span><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-size:18.0pt; color:#00B0F0;mso-ansi-language:EN-GB'> Earth-Sun(Sun-Earth) model </span></i><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-size:18.0pt; color:#FFC000;mso-ansi-language:EN-GB'>: a simple eccentric</span></i><i style='mso-bidi-font-style:normal'><span lang=EN-US style='font-size:18.0pt; color:#FFC000;mso-ansi-language:EN-US'><o:p></o:p></span></i></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='color:black;mso-themecolor:text1;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:1'> <td style='padding:.75pt .75pt .75pt .75pt'> <p align=center style='text-align:center'><span style='font-size:10.0pt; mso-fareast-font-family:"Times New Roman"'> <applet code="CabriJava.class" width="1100" height="500" align="middle" ARCHIVE="CabriJava.jar"> <PARAM NAME=file VALUE="tycho_1.fig"> <PARAM NAME=lang VALUE="en"> <PARAM NAME=bgcolor VALUE="#000000"> <PARAM NAME=autocontrol VALUE="true"> <PARAM NAME=spring VALUE="point 18 size -1,0 "> </applet> </span></p> </td> </tr> <tr style='mso-yfti-irow:2'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><span style='mso-fareast-font-family:"Times New Roman"'>&nbsp;<o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:3'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language: EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span class=SpellE><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-size:18.0pt;color:#00B0F0;mso-ansi-language:EN-GB'>Tycho s</span></i></span><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-size:18.0pt; color:#00B0F0;mso-ansi-language:EN-GB'> </span></i><i style='mso-bidi-font-style: normal'><span lang=EN-GB style='font-size:18.0pt;color:#FFC000;mso-ansi-language: EN-GB'>planetary model</span></i><i style='mso-bidi-font-style:normal'><span lang=EN-US style='font-size:18.0pt;color:gray;mso-ansi-language:EN-US'><o:p></o:p></span></i></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-GB'>In </span><b style='mso-bidi-font-weight: normal'><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:#00B0F0;mso-ansi-language:EN-GB'>the <span class=SpellE>Tychonic</span></span></b><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-GB'> </span><b style='mso-bidi-font-weight: normal'><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:#00B0F0;mso-ansi-language:EN-GB'>planetary model </span></b><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-GB'>an <span class=SpellE>equant</span> point was foreseen, from which motion was seen as uniformly circular (a classical vision: </span><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:#FFC000;mso-ansi-language:EN-GB'>the circle, was a symmetrical perfect figure</span><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-GB'>). This meant that the planet, seen from the Sun (A), had no uniform motion, but originated from a hypothetical uniform motion about the <span class=SpellE>equant</span>.</span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:4'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><span lang=EN-US style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <table class=MsoNormalTable border=0 cellpadding=0 width=1000 style='width:750.0pt;mso-cellspacing:1.5pt;mso-yfti-tbllook:1184;mso-padding-alt: 0cm 5.4pt 0cm 5.4pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal align=center style='text-align:center'><span lang=EN-US style='mso-fareast-font-family:"Times New Roman";mso-ansi-language:EN-US'><span style='mso-spacerun:yes'> </span></span><span style='mso-fareast-font-family: "Times New Roman";color:black;mso-themecolor:text1'>.</span><span style='mso-fareast-font-family:"Times New Roman"'><span style='mso-spacerun:yes'>            </span></span><span style='mso-no-proof: yes'><img border=0 width=210 height=304 id="_x0000_i1031" src="schema%20ticonico%20pianeta.jpg" alt="Descrizione: Descrizione: D:\backup disco E\03_II_SESTANTE_SITO\en\ASTRONOMIA\i_grandi_astronomi\Keplero\tre_leggi_keplero\schema ticonico pianeta.jpg"></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom: 6.0pt;margin-left:35.4pt;text-align:justify'><b style='mso-bidi-font-weight: normal'><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt; font-family:"Arial","sans-serif";color:white;mso-ansi-language:EN-GB'>C  </span></b><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt;font-family: "Arial","sans-serif";color:#0070C0;mso-ansi-language:EN-GB'> is the </span><span class=SpellE><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt;font-family:"Arial","sans-serif"; color:white;mso-ansi-language:EN-GB'>equant</span></b></span><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt;font-family: "Arial","sans-serif";color:#0070C0;mso-ansi-language:EN-GB'>  motion is uniformly circular<o:p></o:p></span></p> <p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom: 6.0pt;margin-left:35.4pt;text-align:justify'><b style='mso-bidi-font-weight: normal'><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt; font-family:"Arial","sans-serif";color:white;mso-ansi-language:EN-GB'>A</span></b><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt;font-family: "Arial","sans-serif";color:#0070C0;mso-ansi-language:EN-GB'><span style='mso-spacerun:yes'>  </span></span><b style='mso-bidi-font-weight: normal'><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt; font-family:"Arial","sans-serif";color:white;mso-ansi-language:EN-GB'> </span></b><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt;font-family: "Arial","sans-serif";color:#0070C0;mso-ansi-language:EN-GB'> is the mean </span><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt; mso-bidi-font-size:12.0pt;font-family:"Arial","sans-serif";color:white; mso-ansi-language:EN-GB'>Sun</span></b><span lang=EN-GB style='font-size: 11.0pt;mso-bidi-font-size:12.0pt;font-family:"Arial","sans-serif"; color:#0070C0;mso-ansi-language:EN-GB'> for Tycho, the true Sun for Kepler<o:p></o:p></span></p> <p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom: 6.0pt;margin-left:35.4pt;text-align:justify'><b style='mso-bidi-font-weight: normal'><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt; font-family:"Arial","sans-serif";color:white;mso-ansi-language:EN-GB'>B</span></b><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt;font-family: "Arial","sans-serif";color:#0070C0;mso-ansi-language:EN-GB'> </span><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt; mso-bidi-font-size:12.0pt;font-family:"Arial","sans-serif";color:white; mso-ansi-language:EN-GB'> </span></b><span lang=EN-GB style='font-size: 11.0pt;mso-bidi-font-size:12.0pt;font-family:"Arial","sans-serif"; color:#0070C0;mso-ansi-language:EN-GB'> is the orbit s </span><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt; mso-bidi-font-size:12.0pt;font-family:"Arial","sans-serif";color:white; mso-ansi-language:EN-GB'>centre</span></b><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt;font-family:"Arial","sans-serif"; color:#0070C0;mso-ansi-language:EN-GB'> <o:p></o:p></span></p> <p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom: 6.0pt;margin-left:35.4pt;text-align:justify'><b style='mso-bidi-font-weight: normal'><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt; font-family:"Arial","sans-serif";color:white;mso-ansi-language:EN-GB'>E</span></b><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt;font-family: "Arial","sans-serif";color:#0070C0;mso-ansi-language:EN-GB'> </span><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt; mso-bidi-font-size:12.0pt;font-family:"Arial","sans-serif";color:white; mso-ansi-language:EN-GB'> </span></b><span lang=EN-GB style='font-size: 11.0pt;mso-bidi-font-size:12.0pt;font-family:"Arial","sans-serif"; color:#0070C0;mso-ansi-language:EN-GB'> is the </span><b style='mso-bidi-font-weight: normal'><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt; font-family:"Arial","sans-serif";color:white;mso-ansi-language:EN-GB'>planet</span></b><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt;font-family: "Arial","sans-serif";color:#0070C0;mso-ansi-language:EN-GB'><o:p></o:p></span></p> <p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom: 6.0pt;margin-left:35.4pt;text-align:justify'><b style='mso-bidi-font-weight: normal'><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt; font-family:"Arial","sans-serif";color:white;mso-ansi-language:EN-GB'>D</span></b><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt;font-family: "Arial","sans-serif";color:#0070C0;mso-ansi-language:EN-GB'> </span><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt; mso-bidi-font-size:12.0pt;font-family:"Arial","sans-serif";color:white; mso-ansi-language:EN-GB'> </span></b><span lang=EN-GB style='font-size: 11.0pt;mso-bidi-font-size:12.0pt;font-family:"Arial","sans-serif"; color:#0070C0;mso-ansi-language:EN-GB'> is the </span><b style='mso-bidi-font-weight: normal'><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt; font-family:"Arial","sans-serif";color:white;mso-ansi-language:EN-GB'>aphelion</span></b><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt;font-family: "Arial","sans-serif";color:#0070C0;mso-ansi-language:EN-GB'><o:p></o:p></span></p> <p class=MsoNormal style='margin-top:0cm;margin-right:0cm;margin-bottom: 6.0pt;margin-left:35.4pt;text-align:justify'><b style='mso-bidi-font-weight: normal'><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt; font-family:"Arial","sans-serif";color:white;mso-ansi-language:EN-GB'>F</span></b><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt;font-family: "Arial","sans-serif";color:#0070C0;mso-ansi-language:EN-GB'> </span><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt; mso-bidi-font-size:12.0pt;font-family:"Arial","sans-serif";color:white; mso-ansi-language:EN-GB'> </span></b><span lang=EN-GB style='font-size: 11.0pt;mso-bidi-font-size:12.0pt;font-family:"Arial","sans-serif"; color:#0070C0;mso-ansi-language:EN-GB'> is the </span><b style='mso-bidi-font-weight: normal'><span lang=EN-GB style='font-size:11.0pt;mso-bidi-font-size:12.0pt; font-family:"Arial","sans-serif";color:white;mso-ansi-language:EN-GB'>perihelion</span></b><span lang=EN-US style='font-size:11.0pt;mso-bidi-font-size:12.0pt;font-family: "Arial","sans-serif";color:#0070C0;mso-ansi-language:EN-US'><o:p></o:p></span></p> </td> </tr> </table> </td> </tr> <tr style='mso-yfti-irow:5'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal style='margin-bottom:6.0pt'><b style='mso-bidi-font-weight: normal'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:#FFC000;mso-ansi-language:EN-US'>Kepler dimensions the planetary model of Tycho for the case of Mars<o:p></o:p></span></b></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:white; mso-themecolor:background1;mso-ansi-language:EN-US'>The problem consists in varying the position of the center of the orbit until the longitudes correspond to the observed</span><span lang=EN-US style='font-size:11.0pt; font-family:"Arial","sans-serif";color:gray;mso-ansi-language:EN-US'>. The model gives longitudes with a precision of 1' (prime) if the center of the orbit is such that AB = 0,6</span><span dir=RTL></span><span lang=AR-SA dir=RTL style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray'><span dir=RTL></span>` </span><span lang=EN-US style='font-size:11.0pt;font-family: "Arial","sans-serif";color:gray;mso-ansi-language:EN-US'>AC. The scheme, for which the distances correspond to the observations, requires, however, AB = 0,5</span><span dir=RTL></span><span lang=AR-SA dir=RTL style='font-size: 11.0pt;font-family:"Arial","sans-serif";color:gray'><span dir=RTL></span>`</span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'>AC, here the error in longitude reaches 8' (primes), a result acceptable to Ptolemy, who declared a measurement accuracy of 10', not for Kepler, who has <span class=SpellE>Tycho's</span> precise measurements with the accuracy of 1' (p. Chapter 19. 286).<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>Kepler evaluates the accuracy of distances knowing the acronychal latitudes of Mars (Chapter 19 p. 283).<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:#FFC000; mso-ansi-language:EN-US'>This model, applied to Mars, returns or correct longitude or correct distances, but not both. It will be referred to as </span><span lang=EN-US style='font-size:14.0pt;font-family:"Arial","sans-serif"; color:white;mso-themecolor:background1;mso-ansi-language:EN-US'>«</span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:#FFC000;mso-ansi-language:EN-US'> </span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:#00B0F0; mso-ansi-language:EN-US'>vicarious hypothesis </span><span lang=EN-US style='font-size:14.0pt;font-family:"Arial","sans-serif";color:white; mso-themecolor:background1;mso-ansi-language:EN-US'>»</span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'><o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:6'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-size:18.0pt; font-family:"Arial","sans-serif";color:#FFC000;mso-ansi-language:EN-GB'>The model Earth-Sun is assumed </span></i><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-size:18.0pt;font-family:"Arial","sans-serif"; color:#00B0F0;mso-ansi-language:EN-GB'>identical to the planetary model</span></i><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:#FFC000;mso-ansi-language:EN-US'> </span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>( <span class=SpellE>capitolo</span> 22 <span class=SpellE>pagina</span> 306 )<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>Kepler attests a letter from Tycho, where the teacher assumes that the Earth-Sun system has an <span class=SpellE>equant</span> like all the other planets ( it is no longer an eccentric model only). This leads to reconsider the method of reduction the measures from <span class=SpellE>Tycho's</span> geocentric reference to the Sun ( both medium, both observed ).<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>How to find the correct position of the center of the Earth so that it is not only a model, but also a real orbit?<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>Kepler knows that </span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:#FFC000; mso-ansi-language:EN-US'>Mars returns to the same sidereal place every 687 days</span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'>, but the Earth will be in different positions because it always fails to complete two orbits. He performs the triangulations and he discovers that the center is different than that suggested by the ancients.<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>(Chapter 32 page 372): </span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:white; mso-themecolor:background1;mso-ansi-language:EN-US'>&quot;speed is inversely proportional to the distance.&quot;</span><span lang=EN-US style='font-size: 11.0pt;font-family:"Arial","sans-serif";color:gray;mso-ansi-language:EN-US'> In the event of a bisected eccentricity of the law of the distance matches that of the areas.<o:p></o:p></span></p> <div align=center> <table class=MsoNormalTable border=0 cellpadding=0 width=950 style='width:712.5pt;mso-cellspacing:1.5pt;mso-yfti-tbllook:1184;mso-padding-alt: 0cm 5.4pt 0cm 5.4pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><span style='mso-no-proof:yes'><img border=0 width=282 height=281 id="_x0000_i1030" src=aree.jpg alt="Descrizione: Descrizione: D:\backup disco E\03_II_SESTANTE_SITO\en\ASTRONOMIA\i_grandi_astronomi\Keplero\tre_leggi_keplero\aree.jpg"></span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> <td style='padding:.75pt .75pt .75pt .75pt'> <p align=center style='text-align:center'><span style='mso-no-proof:yes'><img border=0 width=570 height=71 id="_x0000_i1029" src=formule.jpg alt="Descrizione: Descrizione: D:\backup disco E\03_II_SESTANTE_SITO\en\ASTRONOMIA\i_grandi_astronomi\Keplero\tre_leggi_keplero\formule.jpg"></span><span style='mso-no-proof:yes'><o:p></o:p></span></p> <p align=center style='text-align:center'><span class=msonormal0><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:11.0pt; font-family:"Arial","sans-serif";color:white;mso-themecolor:background1; mso-ansi-language:EN-US;mso-no-proof:yes'>« </span></b></span><span class=msonormal0><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif";color:red; mso-ansi-language:EN-GB'>equal areas are swept in equal times</span></b></span><span class=msonormal0><b style='mso-bidi-font-weight:normal'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:white; mso-themecolor:background1;mso-ansi-language:EN-US;mso-no-proof:yes'> »</span></b></span><span lang=EN-US style='mso-ansi-language:EN-US;mso-no-proof:yes'><o:p></o:p></span></p> </td> </tr> </table> </div> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'>This &quot;cosmological law&quot; is well adapted to the reality of a </span><span lang=EN-US style='font-size:11.0pt; font-family:"Arial","sans-serif";color:#00B0F0;mso-ansi-language:EN-US'>Sun, rotating magnet, that draws the planets with an intensity that decreases with distance</span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'>.<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:7'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal><span lang=EN-US style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <h2><span lang=EN-US style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US'>&nbsp;</span><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-family:"Arial","sans-serif";color:#FFC000;mso-ansi-language: EN-GB;font-weight:normal;mso-bidi-font-weight:bold'>The model Earth-Sun was assumed </span></i><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-family:"Arial","sans-serif";color:#00B0F0;mso-ansi-language:EN-GB; font-weight:normal;mso-bidi-font-weight:bold'>identical to the planetary model</span></i><span lang=EN-US style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US'><o:p></o:p></span></h2> <p align=center style='text-align:center'><span lang=EN-US style='mso-fareast-font-family: "Times New Roman";mso-ansi-language:EN-US'> <applet code="CabriJava.class" width="1100" height="500" align="bottom" ARCHIVE="CabriJava.jar"> <PARAM NAME=file VALUE="tycho_2.fig"> <PARAM NAME=lang VALUE="en"> <PARAM NAME=bgcolor VALUE="#000000"> <PARAM NAME=autocontrol VALUE="true"> <PARAM NAME=spring VALUE="point 18 size -5,0 "> </applet> </span></p> </td> </tr> <tr style='mso-yfti-irow:8'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=msonormal1><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span class=msonormal11><i style='mso-bidi-font-style: normal'><span lang=EN-GB style='font-size:18.0pt;color:#FFC000;mso-ansi-language: EN-GB'>Equal areas</span></i></span><span class=msonormal0><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif";color:#FFC000; mso-ansi-language:EN-GB'> </span></span><span class=msonormal11><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-size:18.0pt; color:#00B0F0;mso-ansi-language:EN-GB'>are swept</span></i></span><span class=msonormal11><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-size:18.0pt;color:#FFC000;mso-ansi-language:EN-GB'> in equal times</span></i></span><span lang=EN-US style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US'><o:p></o:p></span></p> <p class=msonormal1><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <table class=MsoNormalTable border=0 cellpadding=0 width=1150 style='width:862.5pt;mso-cellspacing:1.5pt;mso-yfti-tbllook:1184;mso-padding-alt: 0cm 5.4pt 0cm 5.4pt'> <tr style='mso-yfti-irow:0;mso-yfti-firstrow:yes;mso-yfti-lastrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal align=center style='text-align:center'><span style='font-size:10.0pt;mso-fareast-font-family:"Times New Roman"'> <applet code="CabriJava.class" width="1100" height="500" align="bottom" ARCHIVE="CabriJava.jar"> <PARAM NAME=file VALUE="tycho_3.fig"> <PARAM NAME=lang VALUE="en"> <PARAM NAME=bgcolor VALUE="#000000"> <PARAM NAME=autocontrol VALUE="true"> <PARAM NAME=spring VALUE="point 18 size -5,0 "> </applet> </span><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> </tr> </table> <p class=msonormal1><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <p class=msonormal1><span style='mso-fareast-font-family:"Times New Roman"'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal3 style='margin-bottom:6.0pt;text-align:justify'><span class=hps><i style='mso-bidi-font-style:normal'><span lang=EN style='font-size:18.0pt;font-family:"Arial","sans-serif";color:#00B0F0; mso-ansi-language:EN'>The</span></i></span><i style='mso-bidi-font-style: normal'><span lang=EN style='font-size:18.0pt;font-family:"Arial","sans-serif"; color:#00B0F0;mso-ansi-language:EN'> <span class=hps>Earth-Sun</span> <span class=hps>model</span>, <span class=hps>now also</span> <span class=hps>the </span></span></i><span class=hps><i style='mso-bidi-font-style:normal'><span lang=EN style='font-size:18.0pt;font-family:"Arial","sans-serif";color:#FFC000; mso-ansi-language:EN'>&quot;</span></i></span><span class=hps><i style='mso-bidi-font-style:normal'><span lang=EN style='font-size:18.0pt; font-family:"Arial","sans-serif";color:red;mso-ansi-language:EN'>physical path</span></i></span><i style='mso-bidi-font-style:normal'><span lang=EN style='font-size:18.0pt;font-family:"Arial","sans-serif";color:#FFC000; mso-ansi-language:EN'>&quot;</span></i><i style='mso-bidi-font-style:normal'><span lang=EN style='font-size:18.0pt;font-family:"Arial","sans-serif";color:#00B0F0; mso-ansi-language:EN'>,</span></i><i style='mso-bidi-font-style:normal'><span lang=EN style='font-size:18.0pt;font-family:"Arial","sans-serif";color:#FFC000; mso-ansi-language:EN'> <span class=hps>leads to</span> a <span class=hps>non-circular</span> <span class=hps>orbit</span> for<span class=hps> Mars</span></span></i><i style='mso-bidi-font-style:normal'><span lang=EN-US style='font-size:18.0pt; font-family:"Arial","sans-serif";color:#00B0F0;mso-ansi-language:EN-US'><o:p></o:p></span></i></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:white; mso-themecolor:background1;mso-ansi-language:EN-US'>How to find an orbit of Mars, which is valid for both longitudes and the distances?<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>Kepler has only two tools:<o:p></o:p></span></p> <p class=MsoListParagraphCxSpFirst style='margin-top:0cm;margin-right:0cm; margin-bottom:6.0pt;margin-left:54.0pt;mso-add-space:auto;text-indent:-18.0pt; mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";mso-fareast-font-family: Arial;color:white;mso-themecolor:background1;mso-ansi-language:EN-US'><span style='mso-list:Ignore'>" <span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Arial","sans-serif";color:#00B0F0;mso-ansi-language:EN-US'>The vicarious hypothesis</span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:white;mso-themecolor:background1;mso-ansi-language:EN-US'> for the longitudes of Earth and Mars<o:p></o:p></span></p> <p class=MsoListParagraphCxSpLast style='margin-top:0cm;margin-right:0cm; margin-bottom:6.0pt;margin-left:54.0pt;mso-add-space:auto;text-indent:-18.0pt; mso-list:l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";mso-fareast-font-family: Arial;color:white;mso-themecolor:background1;mso-ansi-language:EN-US'><span style='mso-list:Ignore'>" <span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Arial","sans-serif";color:#00B0F0;mso-ansi-language:EN-US'>The law of distances</span><span lang=EN-US style='font-size:11.0pt;font-family: "Arial","sans-serif";color:white;mso-themecolor:background1;mso-ansi-language: EN-US'>, satisfactory to the Earth, not enough for Mars, because with an error of 8' in longitude<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>he adds a third: <o:p></o:p></span></p> <p class=MsoListParagraph style='margin-top:0cm;margin-right:0cm;margin-bottom: 6.0pt;margin-left:54.0pt;mso-add-space:auto;text-indent:-18.0pt;mso-list: l0 level1 lfo2'><![if !supportLists]><span lang=EN-US style='font-size:11.0pt; font-family:"Arial","sans-serif";mso-fareast-font-family:Arial;color:white; mso-themecolor:background1;mso-ansi-language:EN-US'><span style='mso-list: Ignore'>" <span style='font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></span></span><![endif]><span lang=EN-US style='font-size:11.0pt; font-family:"Arial","sans-serif";color:#00B0F0;mso-ansi-language:EN-US'>The &quot;physic&quot; orbit of the Earth</span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:white; mso-themecolor:background1;mso-ansi-language:EN-US'>, obtained by means of triangulation ( </span><i style='mso-bidi-font-style:normal'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:red;mso-ansi-language:EN-US'>all, however, must be compliant with the measures of Tycho</span></i><span lang=EN-US style='font-size:11.0pt; font-family:"Arial","sans-serif";color:white;mso-themecolor:background1; mso-ansi-language:EN-US'> )<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>To meet the first two together, Kepler adds an epicycle to the orbit of Mars, but immediately he regrets it because that would not be worth with the Sun as the central engine. Then he obtains the path by means of triangulations with the Earth orbit. The result, though qualitative, is astonishing: </span><span lang=EN-US style='font-size:11.0pt; font-family:"Arial","sans-serif";color:#FFC000;mso-ansi-language:EN-US'>the Mars orbit is not circular</span><span lang=EN-US style='font-size:11.0pt; font-family:"Arial","sans-serif";color:gray;mso-ansi-language:EN-US'> (</span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:black;mso-themecolor:text1;mso-ansi-language:EN-US'>.</span><i style='mso-bidi-font-style:normal'><span lang=EN-US style='font-size:11.0pt; font-family:"Arial","sans-serif";color:#0070C0;mso-ansi-language:EN-US'>longitudes will be the key test</span></i><span lang=EN-US style='font-size:11.0pt; font-family:"Arial","sans-serif";color:black;mso-themecolor:text1;mso-ansi-language: EN-US'>.</span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'>). Kepler tries again to simulate the path with an epicycle, the shape is an ovoid, with the more rounded side in the area near the Sun. Again, having the form, applying the law of distances, he finds deviations in longitude 8' to the octants, as it also happened to the ancient circular orbit, but of opposite sign. <o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:gray; mso-ansi-language:EN-US'>The search for the final solution follows intricate paths, with impossible computations, until </span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:white; mso-themecolor:background1;mso-ansi-language:EN-US'>he tries to put an ellipse to approximate the oval</span><span lang=EN-US style='font-size:11.0pt; font-family:"Arial","sans-serif";color:gray;mso-ansi-language:EN-US'>. </span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:#FFC000;mso-ansi-language:EN-US'>It satisfies the observations</span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'>, </span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif";color:#00B0F0; mso-ansi-language:EN-US'>the Sun can be the central engine</span><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'>. The Pythagorean <span class=SpellE>Kepler's</span> mind is now certain that no other orbit is possible. He is a scientist, so he will address the latter point with Apollonius.<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=MsoNormal style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> <p class=MsoNormal><span lang=EN-US style='mso-fareast-font-family:"Times New Roman"; mso-ansi-language:EN-US'><o:p>&nbsp;</o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:9'> <td style='padding:.75pt .75pt .75pt .75pt'></td> </tr> <tr style='mso-yfti-irow:10'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=msonormal2 style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-US style='mso-ansi-language:EN-US'>&nbsp;<o:p></o:p></span></p> <p class=msonormal2 style='margin-bottom:6.0pt;text-align:justify'><i style='mso-bidi-font-style:normal'><span lang=EN-GB style='font-size:18.0pt; color:#FFC000;mso-ansi-language:EN-GB'>If the orbit of Mars met some limits, as those described by Apollonius, </span></i><i style='mso-bidi-font-style: normal'><span lang=EN-GB style='font-size:18.0pt;color:#00B0F0;mso-ansi-language: EN-GB'>it became an ellipse</span></i><span lang=EN-GB style='font-size:11.0pt; font-family:"Arial","sans-serif";color:#FFC000;mso-ansi-language:EN-GB'> </span><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-GB'>(chapter 59 - page 591) <o:p></o:p></span></p> <p class=msonormal2 style='margin-bottom:6.0pt;text-align:justify'><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-GB'>Kepler warned: the logic of events is obscure. True.  Conics must be thoroughly mastered. Kepler formulated his first law: </span><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif";color:white; mso-ansi-language:EN-GB'>« </span></b><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:red;mso-ansi-language:EN-GB'>the orbits of the planets are ellipses </span></b><b style='mso-bidi-font-weight:normal'><span lang=EN-GB style='font-size:11.0pt; font-family:"Arial","sans-serif";color:white;mso-ansi-language:EN-GB'>»</span></b><span lang=EN-GB style='font-size:11.0pt;font-family:"Arial","sans-serif"; color:gray;mso-ansi-language:EN-GB'>.</span><span lang=EN-US style='mso-ansi-language:EN-US'><o:p></o:p></span></p> </td> </tr> <tr style='mso-yfti-irow:11;mso-yfti-lastrow:yes'> <td style='padding:.75pt .75pt .75pt .75pt'> <p class=MsoNormal align=center style='text-align:center'><span style='font-size:10.0pt;mso-fareast-font-family:"Times New Roman"'> <applet code="CabriJava.class" width="1100" height="500" align="bottom" ARCHIVE="CabriJava.jar"> <PARAM NAME=file VALUE="keplero_1.fig"> <PARAM NAME=lang VALUE="en"> <PARAM NAME=bgcolor VALUE="#000000"> <PARAM NAME=autocontrol VALUE="true"> <PARAM NAME=spring VALUE="point 15 size -5,0 "> </applet> </span><br style='mso-special-character:line-break'> <![if !supportLineBreakNewLine]><br style='mso-special-character:line-break'> <![endif]><span style='mso-fareast-font-family:"Times New Roman"'><o:p></o:p></span></p> </td> </tr> </table> </div> <p align=center style='text-align:center'><o:p>&nbsp;</o:p></p> </div> </body> </html>