NEWDIA "SS000015.SIT",""CALLOUT -1.343380e-02,-3.475532e-03,-1.343380e-02,-3.475532e-03,ff0000,0,40ff0000,ffffffc0,0,0,0,2bc,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,The Transit of Venusand the size of the WorldWAITKEYDELCALLOUT The Transit of Venusand the size of the WorldPAUSE 0.3 sCALLOUT -1.106748e-02,-6.975714e-03,-1.106748e-02,-6.975714e-03,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,The first step in measuring ouruniverse is surely the size ofour planet...PAUSE 3 sCALLOUT -1.124002e-02,3.130444e-03,-1.124002e-02,3.130444e-03,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,... a measurementthat should not befound in myths orlegends, but derived fromtangible and repeatable procedures...PAUSE 2 sCALLOUT 1.283587e-02,7.644631e-03,1.283587e-02,7.644631e-03,ff0000,0,40ff0000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT PgDnDELCALLOUT The first step in measuring our universe is surely the size of our planet...DELCALLOUT ... a measurementthat should not befound in myths orlegends, but derived fromtangible and repeatable procedures...PAUSE 0.3 sCALLOUT -1.064844e-02,-7.197557e-03,-1.064844e-02,-7.197557e-03,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,The first "scientific" measurement of the Earth radiuswas made in the third century B.C.byCALLOUT -9.810368e-03,-5.891151e-03,-9.810368e-03,-5.891151e-03,ff0000,0,40ff0000,fffffff0,0,0,0,2bc,1,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,ERATOSTHENESCALLOUT -1.069774e-02,-5.053079e-03,-1.069774e-02,-5.053079e-03,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,librarian at AlexandriaSHOWJPG 6.577938e-03,-7.537962e-03,6.577938e-03,-7.537962e-03,40000000,eratostene.jpgPAUSE 1 sCALLOUT -1.848687e-03,-1.725442e-04,-1.848687e-03,-1.725442e-04,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,AlexandriaCALLOUT 7.466849e-04,-6.755720e-04,7.466849e-04,-6.755720e-04,ff0000,0,40ff0000,ffffffe0,0,0,0,2bc,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,.PAUSE 1 sCALLOUT 1.134250e-02,6.684607e-03,1.134250e-02,6.684607e-03,ff0000,0,40ff0000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT C:\BC4\ASTRO95\NBRANCH\SCRIPT\eratostene.jpgINTERPOLATE 5 s,DELETECALLOUTS,LINEARNEWDIA "SS000011.SIT",""CALLOUT 5.241213e-03,-4.118096e-03,5.241213e-03,-4.118096e-03,ff0000,0,40ff0000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,.CALLOUT 1.483030e-03,-3.892953e-03,1.483030e-03,-3.892953e-03,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,AlexandriaPAUSE 1 sCALLOUT -1.612795e-02,-1.001045e-02,-1.612795e-02,-1.001045e-02,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Eratosthenes knew that at Syene (now Aswan),on the summer solstice, the bottom of thedeep wells was lit by the Sun...CALLOUT 5.615585e-03,-3.422833e-03,5.615585e-03,-3.422833e-03,ff0000,0,40ff0000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,.CALLOUT 3.373893e-03,-2.521151e-03,3.373893e-03,-2.521151e-03,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,SyenePAUSE 3 sCALLOUT -1.835249e-02,-1.297651e-03,-1.835249e-02,-1.297651e-03,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,...this meant that the Sun's light reachesthe ground perpendicularly...CALLOUT 1.716765e-02,1.021502e-02,1.716765e-02,1.021502e-02,ff0000,0,40ff0000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT .DELCALLOUT AlexandriaDELCALLOUT Eratosthenes knew that at Syene (now Aswan), on the summer solstice, the bottom of the deep wells was lit by the Sun...DELCALLOUT .DELCALLOUT SyeneDELCALLOUT ...this meant that the Sun's light reaches the ground perpendicularly...INTERPOLATE 0 s,DELETECALLOUTS,LINEARNEWDIA "SS000021.SIT",""INTERPOLATE 5 s,DELETECALLOUTS,LINEARNEWDIA "SS000016.SIT",""CALLOUT -4.491423e-04,-5.200595e-04,-4.491423e-04,-5.200595e-04,ff0000,0,40ff0000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,.CALLOUT -2.294260e-03,-3.277514e-04,-2.294260e-03,-3.277514e-04,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,AlexandriaCALLOUT -4.727814e-05,7.091721e-05,-4.727814e-05,7.091721e-05,ff0000,0,40ff0000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,.CALLOUT -1.048804e-03,5.571774e-04,-1.048804e-03,5.571774e-04,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,SyenePAUSE 3 sCALLOUT 7.091721e-05,6.146158e-04,9.408350e-03,-4.113198e-03,ffff00,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 4.727814e-05,6.146158e-04,-6.098880e-03,3.734973e-03,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 0.000000e+00,4.727814e-04,9.455628e-03,-4.373228e-03,ffff00,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 1.418344e-04,7.328112e-04,9.361072e-03,-3.876807e-03,ffff00,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -4.727814e-05,3.309470e-04,9.384711e-03,-4.538701e-03,ffff00,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -1.418344e-04,1.654735e-04,9.455628e-03,-4.775092e-03,ffff00,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -3.545860e-04,2.363907e-05,9.455628e-03,-5.058761e-03,ffff00,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 6.423928e-03,-4.654070e-03,6.423928e-03,-4.654070e-03,ffff00,0,40ffff00,ffffffeb,0,0,0,2bc,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Sun's lightPAUSE 1.5 sCALLOUT -6.309215e-03,-5.112922e-03,-6.309215e-03,-5.112922e-03,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,At Alexandria, on the same day, a high poleprojected a shadow corresponding to anangle of 712'PAUSE 5 sCALLOUT -3.782251e-04,2.363907e-05,7.942728e-03,-5.389708e-03,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -3.545860e-04,2.363907e-05,-7.729976e-03,4.940566e-03,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 2.529380e-03,-1.938404e-03,2.529380e-03,-1.938404e-03,ffff00,0,40ff0000,fffffff0,0,0,0,190,0,22010203,61697241,6172006c,32346870,54422031,0,0,0,0,)CALLOUT 2.694854e-03,-2.269351e-03,2.694854e-03,-2.269351e-03,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,712'PAUSE 1.5 sCALLOUT 1.311006e-03,3.769141e-04,1.311006e-03,3.769141e-04,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Assuming that the Earth is spherical,and that the Sun's rays are parallel,this angle represents the difference inlatitude between Alexandria and Syene.PAUSE 3 sPAUSE 2 sCALLOUT -2.576659e-03,1.465622e-03,-2.576659e-03,1.465622e-03,0,0,40ffff00,ffffffeb,0,0,0,2bc,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,712'CALLOUT -2.789410e-03,1.512900e-03,-2.789410e-03,1.512900e-03,0,0,40ffff00,ffffffeb,0,0,0,190,0,22010203,61697241,6172006c,32346870,54422031,0,0,0,0,)CALLOUT 8.202757e-03,4.656897e-03,8.202757e-03,4.656897e-03,ff0000,0,40ffff00,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT At Alexandria, on the same day, a high pole projected a shadow corresponding to an angle of 712'DELCALLOUT Assuming that the Earth is spherical, and that the Sun's rays are parallel, this angle represents the difference in latitude between Alexandria and Syene.DELCALLOUT PgDnDELCALLOUT Sun's lightPAUSE 0.5 sCALLOUT -6.538640e-03,-4.981821e-03,-6.538640e-03,-4.981821e-03,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,712' is the 50th part of the round angle,corresponding to 1/50 of the Earth circumference...PAUSE 2 sCALLOUT 1.376556e-03,1.638757e-04,1.540432e-03,1.245455e-03,ff0000,0,ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,The distance between the two towns had beenmeasured in about 5000 stadia. So theEarth circumference was calculated inCALLOUT -3.545860e-04,2.363907e-05,4.727814e-05,6.146158e-04,ff0000,0,40000000,ffffffe5,0,0,0,190,0,22010203,61697241,614e206c,776f7272,54422000,0,0,0,0,CALLOUT -3.309470e-04,7.091721e-05,2.363907e-05,5.909767e-04,ff0000,0,40000000,ffffffe5,0,0,0,190,0,22010203,61697241,614e206c,776f7272,54422000,0,0,0,0,CALLOUT -3.545860e-04,4.727814e-05,2.363907e-05,6.146158e-04,ff0000,0,40000000,ffffffe5,0,0,0,190,0,22010203,61697241,614e206c,776f7272,54422000,0,0,0,0,CALLOUT -3.545860e-04,7.091721e-05,2.363907e-05,6.382549e-04,ff0000,0,40000000,ffffffe5,0,0,0,190,0,22010203,61697241,614e206c,776f7272,54422000,0,0,0,0,CALLOUT -7.866034e-04,2.785887e-04,-7.866034e-04,2.785887e-04,ffffff,0,40000000,fffffff5,0,0,0,2bc,b2000000,22010203,61697241,6172006c,32346870,54422031,0,0,0,0,5.000CALLOUT 1.655145e-03,2.294260e-03,1.655145e-03,2.294260e-03,ff0000,0,40ffff00,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,5.000 x 50 = 250.000 stadiaCALLOUT 7.753615e-03,4.680536e-03,7.753615e-03,4.680536e-03,ff0000,0,40ffff00,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT 712' is the 50th part of the round angle, corresponding to 1/50 of the Earth circumference...DELCALLOUT The distance between the two towns had beenmeasured in about 5000 stadia. So theEarth circumference was calculated inDELCALLOUT 5.000 x 50 = 250.000 stadiaDELCALLOUT PgDnPAUSE 0.3 sCALLOUT -7.800483e-03,-5.276798e-03,-7.800483e-03,-5.276798e-03,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,A "stadium" is an antique egyptian measure, which variedin length, depending on the location and the historicalperiod, between 154 and 215 metres...PAUSE 2 sCALLOUT 1.802633e-03,8.193785e-05,1.802633e-03,8.193785e-05,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Having gathered data from many sources,we now think that Eratosthenes used astadium of 157 metres, so his value forthe Earth radius would beCALLOUT 3.876807e-03,1.914765e-03,3.876807e-03,1.914765e-03,ff0000,0,40000000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,12.629 KmCALLOUT 1.819020e-03,2.900600e-03,1.819020e-03,2.900600e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,a measurement only 113kmsmaller than the modern oneCALLOUT 8.108201e-03,4.727814e-03,8.108201e-03,4.727814e-03,ff0000,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT DELCALLOUT DELCALLOUT DELCALLOUT DELCALLOUT DELCALLOUT DELCALLOUT DELCALLOUT DELCALLOUT DELCALLOUT )DELCALLOUT 712'DELCALLOUT 712'DELCALLOUT )DELCALLOUT DELCALLOUT DELCALLOUT DELCALLOUT DELCALLOUT 5.000DELCALLOUT A "stadium" is an antique egyptian measure, which varied in length, depending on the location and the historical period, between 154 and 215 metres...DELCALLOUT Having gathered data from many sources, we now think that Eratosthenes used a stadium of 157 metres, so his value for the Earth radius would beDELCALLOUT 12.629 KmDELCALLOUT a measurement only 113km smaller than the modern oneDELCALLOUT PgDnPAUSE 0.3 sCALLOUT -1.999284e-03,-4.441032e-03,-1.999284e-03,-4.441032e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,This measurement wasn't believed to be true andit was deemed as overstated. Ptolemy, in hisAlmagest, used a value that was lower by 2.200 km.PAUSE 2 sCALLOUT 3.113638e-04,-1.786245e-03,3.113638e-04,-1.786245e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,This error persisted for centuries: Columbusthought that the Far East countries could bereached by sailing westwards because heunderestimated the size of the Earth.CALLOUT 7.611781e-03,4.184115e-03,7.611781e-03,4.184115e-03,ff0000,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT .DELCALLOUT AlexandriaDELCALLOUT .DELCALLOUT SyeneDELCALLOUT This measurement wasn't believed to be true andit was deemed as overstated. Ptolemy, in hisAlmagest, used a value that was lower by 2.200 km.DELCALLOUT This error persisted for centuries: Columbus thought that the Far East countries could be reached by sailing westwards because he underestimated the size of the Earth.DELCALLOUT PgDnPAUSE 0.3 sCALLOUT -7.177756e-03,-4.457419e-03,-7.177756e-03,-4.457419e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,In the same period, another astronomer went farther away...PAUSE 1.5 sCALLOUT 3.277514e-05,-2.982538e-03,3.277514e-05,-2.982538e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,ARISTARCHUS OF SAMOS(the first astronomer who thought of aheliocentric system)observed a Moon eclipse and foundthe distance of our satellite...SHOWJPG 5.247874e-03,-1.843847e-03,5.247874e-03,-1.843847e-03,40000000,arist.jpgCALLOUT 5.522611e-03,2.933375e-03,5.522611e-03,2.933375e-03,ff0000,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Aristarchus of SamosDomenico Seffi, 1620CALLOUT 7.328112e-03,4.302311e-03,7.328112e-03,4.302311e-03,ff0000,0,40ffff00,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT C:\BC4\ASTRO95\NBRANCH\SCRIPT\arist.jpgDELCALLOUT Aristarchus of Samos Domenico Seffi, 1620DELCALLOUT In the same period, another astronomer went farther away...DELCALLOUT ARISTARCHUS OF SAMOS(the first astronomer who thought of aheliocentric system)observed a Moon eclipse and foundthe distance of our satellite...DELCALLOUT PgDnINTERPOLATE 5 s,DELETECALLOUTS,LINEARNEWDIA "SS000000.SIT",YPAUSE 0.5 sCALLOUT -7.006112e-03,4.203667e-03,3.040653e-01,-1.723504e-01,ff0000,0,40ffff80,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PAUSE 0.5 sCALLOUT -1.398794e-01,-1.583357e-01,-1.398794e-01,-1.583357e-01,ff0000,0,40ffff80,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,30 Earth diameters.... ... about 370.000 kmPAUSE 0.5 sCALLOUT 4.413851e-01,2.578249e-01,4.413851e-01,2.578249e-01,ff0000,0,40ffff80,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT 30 Earth diameters.... ... about 370.000 kmDELCALLOUT PgDnDELCALLOUT PAUSE 0.5 sCALLOUT -3.778686e-01,-2.409034e-01,-3.720403e-01,-2.311896e-01,ff0000,0,ffff80,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Aristarchus tried to go even farther...PAUSE 1.5 sCALLOUT -3.827256e-01,-1.855345e-01,-3.827256e-01,-1.855345e-01,ff0000,0,40ffff80,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,...observing the Moon phases he calculated the Earth-Sun distancePAUSE 0.5 sCALLOUT -1.729065e-01,-9.713847e-02,-1.738779e-01,-9.616709e-02,ff0000,0,40ffff80,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,The result was plainly wrong...CALLOUT -2.205043e-01,8.256770e-02,-2.205043e-01,8.256770e-02,ff0000,0,40ffff80,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,7 million km instead of 150 millionCALLOUT 4.539961e-01,2.690347e-01,4.539961e-01,2.690347e-01,ff0000,0,40ffff80,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT Aristarchus tried to go even farther...DELCALLOUT ...observing the Moon phases he calculated the Earth-Sun distanceDELCALLOUT The result was plainly wrong...DELCALLOUT 7 million km instead of 150 millionDELCALLOUT PgDnPAUSE 0.3 sCALLOUT -3.720403e-01,-2.603311e-01,-3.720403e-01,-2.603311e-01,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,In the year 189 B.C. a revolution happened...CALLOUT 4.259716e-01,2.382078e-01,4.259716e-01,2.382078e-01,ff0000,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT In the year 189 B.C. a revolution happened...PAUSE 0.5 sINTERPOLATE 3 s,DELETECALLOUTS,LINEARNEWDIA "SS000001.SIT",""PAUSE 0.5 sCALLOUT -1.127139e-02,-7.146841e-03,-1.123583e-02,-7.146841e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Il grande astronomo IPPARCO DI NICEA ricalcol la distanza della Lunacon un metodo che sarebbe poi stato usato per molti secoli ...PAUSE 1.5 sCALLOUT -5.013456e-03,-1.386700e-03,-5.013456e-03,-1.386700e-03,ff0000,0,40000000,ffffffe3,0,0,0,2bc,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,LA PARALLASSECALLOUT 1.059581e-02,6.293487e-03,1.059581e-02,6.293487e-03,ff0000,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT Il grande astronomo IPPARCO DI NICEA ricalcol la distanza della Lunacon un metodo che sarebbe poi stato usato per molti secoli ...DELCALLOUT LA PARALLASSEDELCALLOUT PgDnPAUSE 0.5 sCALLOUT -1.216030e-02,-6.862390e-03,-1.216030e-02,-6.862390e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,I nostri occhi sono distanti l'uno dall'altrocirca 10 centimetri e questo ci permette di valutare le distanze (fino a qualche centinaio di metri) ...PAUSE 3 sCALLOUT -1.130694e-02,5.013456e-03,-1.130694e-02,5.013456e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,... per valutare distanze maggioriavremmo bisogno di occhi ben pi distanti, anche molte migliaia di chilometriCALLOUT 1.134250e-02,6.720164e-03,1.134250e-02,6.720164e-03,ff0000,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT I nostri occhi sono distanti l'uno dall'altro circa 10 centimetri e questo ci permette di valutare le distanze (fino a qualche centinaio di metri) ...DELCALLOUT ... per valutare distanze maggioriavremmo bisogno di occhi ben pi distanti, anche molte migliaia di chilometriDELCALLOUT PgDnPAUSE 0.5 sCALLOUT -1.041803e-02,-7.786856e-03,-1.041803e-02,-7.786856e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Su questo principio Ipparco misur la parallasse della Luna ...CALLOUT -7.786856e-03,6.293487e-03,-7.786856e-03,6.293487e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,misur cio gli angoli formati rispetto a due punti a distanza nota.SHOWJPG 6.364600e-03,-1.066693e-03,6.364600e-03,-1.066693e-03,40000000,1_02.jpgCALLOUT 1.180473e-02,6.329043e-03,1.180473e-02,6.329043e-03,ff0000,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT Su questo principio Ipparco misur la parallasse della Luna ...DELCALLOUT misur cio gli angoli formati rispetto a due punti a distanza nota.DELCALLOUT PgDnPAUSE 0.5 sCALLOUT -1.148472e-02,-7.075728e-03,-1.148472e-02,-7.075728e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Ipparco osserv la Luna da Alessandria edin Ellesponto (Stretto dei Dardanelli)distante pi di 1000 chilometriPAUSE 0.5 sCALLOUT 1.884490e-03,-5.333463e-04,1.884490e-03,-5.333463e-04,ff0000,0,40000000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,.CALLOUT -7.111284e-05,1.066693e-04,-7.111284e-05,1.066693e-04,ff0000,0,40000000,fffffff4,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,AlessandriaCALLOUT 1.386700e-03,-1.528926e-03,1.386700e-03,-1.528926e-03,ff0000,0,40000000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,.CALLOUT -3.555642e-04,-1.244475e-03,-3.555642e-04,-1.244475e-03,ff0000,0,40000000,fffffff4,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,EllespontoCALLOUT 1.162695e-02,6.897946e-03,1.162695e-02,6.897946e-03,ff0000,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT Ipparco osserv la Luna da Alessandria edin Ellesponto (Stretto dei Dardanelli)distante pi di 1000 chilometriDELCALLOUT .DELCALLOUT AlessandriaDELCALLOUT .DELCALLOUT EllespontoDELCALLOUT PgDnPAUSE 0.3 sINTERPOLATE 0 s,DELETECALLOUTS,LINEARNEWDIA "SS000023.SIT",""INTERPOLATE 5 s,DELETECALLOUTS,LINEARNEWDIA "SS000005.SIT",""PAUSE 0.5 sCALLOUT -1.424491e-01,7.865665e-02,1.845644e-01,-1.275848e-01,ff0000,0,40ffff00,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -1.424491e-01,7.679862e-02,1.746549e-01,-1.220107e-01,ff0000,0,40ffff00,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PAUSE 0.5 sCALLOUT -1.845644e-01,-1.133399e-01,-1.845644e-01,-1.133399e-01,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Come possiamo vedere la difficolt nel misurare questi angoli notevole e, per spingersi oltre, dovremmo osservare da punti ancora pi lontani ...PAUSE 2 sCALLOUT -1.114819e-02,2.787047e-02,-1.114819e-02,2.787047e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Una seconda difficolt, inoltre, sincronizzareperfettamente le osservazioni........ l'orologio un'invenzione "moderna" e i pendolinon gradiscono le traversate atlantiche ....CALLOUT 1.988093e-01,1.077658e-01,1.988093e-01,1.077658e-01,ff0000,0,40ffff00,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT DELCALLOUT DELCALLOUT Come possiamo vedere la difficolt nel misurare questi angoli notevole e, per spingersi oltre, dovremmo osservare da punti ancora pi lontani ...DELCALLOUT Una seconda difficolt, inoltre, sincronizzareperfettamente le osservazioni........ l'orologio un'invenzione "moderna" e i pendolinon gradiscono le traversate atlantiche ....DELCALLOUT PgDnPAUSE 0.5 sCALLOUT -2.142929e-01,-1.282042e-01,-2.142929e-01,-1.282042e-01,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Nel 1672 Giandomenico Cassini prov a misurare la parallasse di Marteanalizzando osservazioni fatte da Bologna ed in Cayenna(nell'attuale Guyana Francese in Sud America) ...PAUSE 2 sCALLOUT 2.539309e-02,6.255372e-02,2.539309e-02,6.255372e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Il problema del sincronismo delle osservazionifu brillantemente risolto utilizzando la posizionedei satelliti di Giove...PAUSE 7 sCALLOUT -1.151979e-01,-5.016684e-02,-7.617928e-02,-3.158653e-02,ff0000,0,ffff00,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Dalle misure di Cassini si pot dedurreuna distanza della Terra dal Sole di 140 milioni di chilometriCALLOUT 1.895192e-01,1.139592e-01,1.895192e-01,1.139592e-01,ff0000,0,40ffff00,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYNEWDIA "SS000006.SIT",""CALLOUT -1.139592e-01,-5.264422e-02,-1.139592e-01,-5.264422e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Una grossa rivoluzione nella ricerca dell'unit astronomicaci fu quando un grandissimo matematico scozzese, JAMES GREGORYpropose di usare i transiti dei pianeti interni (Mercurioe Venere) per trovare questa importantissima misura ...CALLOUT 1.969513e-01,1.139592e-01,1.969513e-01,1.139592e-01,ff0000,0,40ffff00,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT Una grossa rivoluzione nella ricerca dell'unit astronomicaci fu quando un grandissimo matematico scozzese, JAMES GREGORYpropose di usare i transiti dei pianeti interni (Mercurioe Venere) per trovare questa importantissima misura ...DELCALLOUT PgDnPAUSE 0.5 sCALLOUT -1.765130e-01,-1.182947e-01,-1.765130e-01,-1.182947e-01,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,L'interesse fondamentale per questa misuraderiva dal fatto che era possibile risalirealle distanze degli altri pianeti...PAUSE 3 sCALLOUT -9.847565e-02,-4.768947e-02,-9.847565e-02,-4.768947e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,... era possibile misurare l'universo con le misure dell'uomo, era possibile rapportarsicon tutto quello che ci circonda ...CALLOUT 1.907579e-01,1.102432e-01,1.907579e-01,1.096238e-01,ff0000,0,40ffff00,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT L'interesse fondamentale per questa misuraderiva dal fatto che era possibile risalirealle distanze degli altri pianeti...DELCALLOUT ... era possibile misurare l'universo con le misure dell'uomo, era possibile rapportarsicon tutto quello che ci circonda ...DELCALLOUT PgDnPAUSE 0.5 sCALLOUT -1.560746e-01,-7.555993e-02,-1.560746e-01,-7.555993e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Vediamo ora molto velocemente come potertrovare l'unit astronomica osservando il transito di Venere ...PAUSE 1.5 sCALLOUT -9.290156e-03,4.645078e-02,-9.290156e-03,4.645078e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,.. useremo una trattazzione molto semplificata che per ci aiuta a capire senza perdersi in lunghissimi e noiosiconti matematici ....CALLOUT 1.907579e-01,1.220107e-01,1.907579e-01,1.220107e-01,ff0000,0,40ffff00,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT Vediamo ora molto velocemente come potertrovare l'unit astronomica osservando il transito di Venere ...DELCALLOUT .. useremo una trattazzione molto semplificata che per ci aiuta a capire senza perdersi in lunghissimi e noiosiconti matematici ....DELCALLOUT PgDnPAUSE 0.3 sCALLOUT -9.971434e-02,-1.734162e-02,-9.971434e-02,-1.734162e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Innanzitutto premettiamo alcune "propriet" dei TRIANGOLI SIMILIPAUSE 3 sDELCALLOUT Innanzitutto premettiamo alcune "propriet" dei TRIANGOLI SIMILIPAUSE 0.5 sCALLOUT -7.927600e-02,-1.232494e-01,-7.927600e-02,-1.232494e-01,ff0000,0,40ffff00,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,TRIANGOLI SIMILICALLOUT -1.319202e-01,-9.599828e-02,-1.313009e-01,-9.599828e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Due triangoli si dicono simili quando i loro angoli sono ugualiCALLOUT -1.170560e-01,4.397340e-02,-1.170560e-01,4.397340e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Nei triangoli simili la lunghezza dei lati proporzionale ...SHOWJPG -1.455458e-01,-7.246322e-02,-1.455458e-01,-7.246322e-02,40000000,1_triangoli.jpgCALLOUT 2.012867e-01,1.207720e-01,2.012867e-01,1.207720e-01,ff0000,0,40ffff00,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT Due triangoli si dicono simili quando i loro angoli sono ugualiDELCALLOUT C:\astronomia\Perseus\SCRIPT\triangoli.jpgDELCALLOUT Nei triangoli simili la lunghezza dei lati proporzionale ...DELCALLOUT PgDnCALLOUT -1.251074e-01,-9.785631e-02,-1.251074e-01,-9.785631e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Una particolare categoria di triangoli simili quella dei TRIANGOLI RETTANGOLI SIMILI in cui, cio, un angolo retto (90)CALLOUT -1.294428e-01,6.317306e-02,1.201527e-01,-3.901865e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -1.294428e-01,6.379240e-02,1.201527e-01,6.379240e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 1.201527e-01,-3.839931e-02,1.201527e-01,6.379240e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -1.374943e-01,5.574094e-02,-1.362556e-01,5.883765e-02,ff0000,0,ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,oCALLOUT 1.672228e-02,3.716062e-03,1.672228e-02,6.379240e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 1.176753e-02,-1.052884e-02,1.176753e-02,-1.052884e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,aCALLOUT 1.176753e-01,-5.202487e-02,1.195333e-01,-4.583144e-02,ff0000,0,ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,bCALLOUT 1.424491e-02,6.255372e-02,1.486425e-02,6.998584e-02,ff0000,0,ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,cCALLOUT 1.189140e-01,6.255372e-02,1.189140e-01,6.255372e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,dCALLOUT -1.003337e-01,4.892815e-02,-9.909500e-02,5.078619e-02,ff0000,0,ffff00,ffffffeb,0,0,0,190,0,22010203,61697241,6172006c,32346870,54422031,0,0,0,0,)CALLOUT -9.290156e-02,4.459275e-02,-9.290156e-02,4.459275e-02,ff0000,0,40ffff00,ffffffeb,0,0,0,190,2000000,12010203,626d7953,61006c6f,32346870,54422031,0,0,0,0,aCALLOUT 1.963320e-01,1.139592e-01,1.963320e-01,1.139592e-01,ff0000,0,40ffff00,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT PgDnDELCALLOUT Una particolare categoria di triangoli simili quella dei TRIANGOLI RETTANGOLI SIMILI in cui, cio, un angolo retto (90)PAUSE 0.3 sCALLOUT -2.310152e-01,-1.034304e-01,-2.310152e-01,-1.034304e-01,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Nei triangoli rettangoli valgono le seguenti propriet:PAUSE 0.7 sCALLOUT -1.517392e-01,-8.485009e-02,-1.517392e-01,-8.485009e-02,ff0000,0,40ffff00,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,ac bdoc odCALLOUT -1.511199e-01,-6.626978e-02,-1.399717e-01,-6.626978e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -1.300622e-01,-6.688912e-02,-1.176753e-01,-6.688912e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -1.412104e-01,-7.617928e-02,-1.399717e-01,-7.617928e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,=CALLOUT -1.158173e-01,-7.617928e-02,-1.158173e-01,-7.617928e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,=CALLOUT -1.021917e-01,-7.679862e-02,-1.021917e-01,-7.679862e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Tan ( )CALLOUT -7.308256e-02,-7.803731e-02,-7.308256e-02,-7.803731e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,2bc,2000000,12010203,626d7953,61006c6f,32346870,54422031,0,0,0,0,aCALLOUT -1.919966e-01,-7.803731e-02,-1.919966e-01,-7.803731e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,2bc,2000000,12010203,626d7953,61006c6f,32346870,54422031,0,0,0,0,1 )CALLOUT -1.932352e-01,-2.663178e-02,-1.932352e-01,-2.663178e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,2bc,2000000,12010203,626d7953,61006c6f,32346870,54422031,0,0,0,0,2 )CALLOUT -1.542166e-01,-3.592194e-02,-1.542166e-01,-3.592194e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,ac bdoa obCALLOUT -1.535972e-01,-1.796097e-02,-1.418297e-01,-1.796097e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -1.319202e-01,-1.858031e-02,-1.201527e-01,-1.858031e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -1.430684e-01,-2.787047e-02,-1.424491e-01,-2.787047e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,=CALLOUT -1.170560e-01,-2.787047e-02,-1.170560e-01,-2.787047e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,=CALLOUT -1.021917e-01,-2.972850e-02,-1.021917e-01,-2.972850e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,sin( )CALLOUT -8.175337e-02,-3.096719e-02,-8.175337e-02,-3.096719e-02,ff0000,0,40ff0000,ffffffeb,0,0,0,2bc,2000000,12010203,626d7953,61006c6f,32346870,54422031,0,0,0,0,aCALLOUT 1.833257e-01,1.096238e-01,1.833257e-01,1.096238e-01,ff0000,0,40ff0000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYINTERPOLATE 0 s,DELETECALLOUTS,LINEARNEWDIA "SS000030.SIT",YINTERPOLATE 5 s,DELETECALLOUTS,LINEARNEWDIA "SS000007.SIT",YPAUSE 0.5 sCALLOUT -1.055666e+00,-6.942670e-01,-1.055666e+00,-6.942670e-01,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Quando Venere si trova alla Massima Elongazioneda Terra possiamo misurare un angolo (tra Venere ed il Sole)di 46,054 .... =46,o54CALLOUT -6.879267e-01,-4.469938e-01,-6.879267e-01,-4.469938e-01,ff0000,0,40ff0000,ffffffed,0,0,0,190,2000000,12010203,626d7953,61006c6f,32346870,54422031,0,0,0,0,aCALLOUT -6.498847e-01,9.510507e-03,-6.055023e-01,5.167376e-01,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -6.055023e-01,5.167376e-01,-6.340338e-03,0.000000e+00,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -6.498847e-01,9.510507e-03,0.000000e+00,0.000000e+00,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -6.435443e-01,7.291389e-02,-5.833111e-01,7.291389e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -5.864813e-01,7.291389e-02,-5.864813e-01,9.510507e-03,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -5.991620e-01,3.835905e-01,-5.991620e-01,3.835905e-01,ff0000,0,40ffff00,ffffffeb,0,0,0,2bc,2000000,12010203,626d7953,61006c6f,32346870,54422031,0,0,0,0,aCALLOUT -5.769708e-01,3.170169e-03,-5.642901e-01,9.510507e-03,ff0000,0,ffff00,ffffffed,0,0,0,190,2000000,12010203,626d7953,61006c6f,32346870,54422031,0,0,0,0,90PAUSE 3 sCALLOUT 1.585085e-02,-2.726345e-01,1.585085e-02,-2.726345e-01,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Ponendo la distanza Terra-Sole uguale a 1 (1 u.a.),usando le "leggi" dei triangoli simili troviamo che :CALLOUT -1.711891e-01,1.870400e-01,-1.711891e-01,1.870400e-01,ff0000,0,40000000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,dist. Venere-Sole dist. Venere-Soledist. Terra-Sole 1 (u.a.)CALLOUT 3.518888e-01,2.345925e-01,3.518888e-01,2.345925e-01,ff0000,0,40000000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,=CALLOUT -1.870400e-01,2.758047e-01,3.423783e-01,2.758047e-01,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 4.533342e-01,2.789749e-01,9.383700e-01,2.789749e-01,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 9.573911e-01,2.314223e-01,9.573911e-01,2.314223e-01,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,=CALLOUT 1.017624e+00,2.250820e-01,1.017624e+00,2.250820e-01,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,sin( )CALLOUT 1.119070e+00,2.219118e-01,1.119070e+00,2.219118e-01,ff0000,0,40ff0000,ffffffeb,0,0,0,190,2000000,12010203,626d7953,61006c6f,32346870,54422031,0,0,0,0,aPAUSE 4 sCALLOUT 2.345925e-01,3.772501e-01,2.314223e-01,3.772501e-01,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,da cui troviamo che CALLOUT -9.510507e-03,4.977165e-01,-9.510507e-03,4.977165e-01,ff0000,0,40ff0000,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,dist. Venere-Sole = 0,72 u.adist. Terre-Venere=1-0,72=0,28 u.aCALLOUT 1.090538e+00,6.245233e-01,1.090538e+00,6.245233e-01,ff0000,0,40ff0000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYNEWDIA "SS000002.SIT",YPAUSE 0.3 sCALLOUT -1.112729e+00,-4.216325e-01,-1.112729e+00,-4.216325e-01,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Ora ci serve "solo" sapere a quanti chilometri corrispondel'unit astronomica ed ora che entra in gioco il transitoCALLOUT 1.049326e+00,5.959918e-01,1.049326e+00,5.959918e-01,ff0000,0,40ff0000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYINTERPOLATE 0 s,DELETECALLOUTS,LINEARNEWDIA "SS000032.SIT",""INTERPOLATE 3 s,DELETECALLOUTS,LINEARNEWDIA "SS000008.SIT",YPAUSE 0.3 sCALLOUT -8.135459e-01,-4.489256e-01,-8.135459e-01,-4.489256e-01,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Due osservatori sulla Terra, molto distanti uno dall'altro,osserverano il transito di Venere in due zone diverse deldisco solare ( per effetto della Parallasse) e quindi i transiti avranno diversa durata ...PAUSE 1 sCALLOUT -6.913032e-01,-1.180274e-01,-6.913032e-01,-1.180274e-01,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Prendiamo due osservatori (A e B) posti 2000 km uno dall'altro ...CALLOUT 7.482093e-01,4.173111e-01,7.482093e-01,4.173111e-01,ff0000,0,40ff0000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT Due osservatori sulla Terra, molto distanti uno dall'altro,osserverano il transito di Venere in due zone diverse deldisco solare ( per effetto della Parallasse) e quindi i transiti avranno diversa durata ...DELCALLOUT Prendiamo due osservatori (A e B) posti 2000 km uno dall'altro ...DELCALLOUT PgDnPAUSE 0.2 sSHOWJPG -3.793737e-02,-4.531408e-01,-3.793737e-02,-4.531408e-01,40000000,sole.jpgSHOWJPG 4.742172e-01,3.077142e-01,4.742172e-01,3.077142e-01,40000000,terra.jpgPAUSE 0.3 sCALLOUT 5.016164e-01,3.393287e-01,5.016164e-01,3.393287e-01,ff0000,0,40ff0000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,.CALLOUT 4.784324e-01,3.920195e-01,4.784324e-01,3.920195e-01,ff0000,0,40ff0000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,ACALLOUT 5.458766e-01,2.908532e-01,5.458766e-01,2.908532e-01,ff0000,0,40ff0000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,.CALLOUT 5.753835e-01,2.803150e-01,5.753835e-01,2.803150e-01,ff0000,0,40ff0000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,BCALLOUT 5.079393e-01,3.856966e-01,5.543072e-01,3.393287e-01,ff0000,0,40000000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 5.079393e-01,3.856966e-01,5.521995e-01,3.414364e-01,ff0000,0,40000000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 5.100469e-01,3.878043e-01,5.521995e-01,3.435440e-01,ff0000,0,40000000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 5.100469e-01,3.856966e-01,5.543072e-01,3.414364e-01,ff0000,0,40000000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 5.121545e-01,3.856966e-01,5.500919e-01,3.393287e-01,ff0000,0,40000000,ffffffe8,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 5.521995e-01,3.414364e-01,5.100469e-01,3.899119e-01,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 5.332309e-01,3.667279e-01,5.332309e-01,3.667279e-01,4a0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,S oss = 2000 kmCALLOUT 5.079393e-01,3.856966e-01,3.098219e-01,-1.643953e-01,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 2.866379e-01,-2.971761e-01,2.866379e-01,-2.950685e-01,ff0000,0,40ffff00,ffffffc0,0,0,0,2bc,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,.CALLOUT 3.245753e-01,-2.023327e-01,3.245753e-01,-2.023327e-01,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Transito visto da ACALLOUT 5.521995e-01,3.372211e-01,1.475342e-01,-7.587475e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 1.264579e-01,-2.086556e-01,1.243503e-01,-2.086556e-01,ff,0,40ffff00,ffffffc0,0,0,0,2bc,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,.CALLOUT -1.369961e-01,-7.376711e-02,-1.369961e-01,-7.376711e-02,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Transito visto da BCALLOUT 1.475342e-01,-8.219764e-02,3.077142e-01,-1.728258e-01,4a0000,0,40800000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 1.433190e-01,-1.833640e-01,1.433190e-01,-1.833640e-01,4a0000,0,40800000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,S tranCALLOUT 3.098219e-01,-1.665029e-01,1.264579e-01,-4.362798e-01,ff0000,0,40000000,ffffffed,0,0,0,2bc,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 1.454266e-01,-8.219764e-02,-2.107632e-02,-3.393287e-01,ff0000,0,40000000,ffffffed,0,0,0,2bc,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PAUSE 1 sCALLOUT -7.608551e-01,-2.971761e-01,-7.608551e-01,-2.971761e-01,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,In questa trattazione useremo un metodopuramente geometrico e non considereremo,come detto in precedenza, la diversa duratadel transito visto dai due osservatori ...CALLOUT 7.482093e-01,4.468180e-01,7.482093e-01,4.468180e-01,ff0000,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYDELCALLOUT PgDnDELCALLOUT In questa trattazione useremo un metodo puramente geometrico e non considereremo, come detto in precedenza, la diversa durata del transito visto dai due osservatori ...PAUSE 0.2 sCALLOUT 2.234090e-01,-1.243503e-01,5.332309e-01,3.625127e-01,ffff00,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PAUSE 1.5 sCALLOUT -7.524246e-01,-3.013914e-01,-7.524246e-01,-3.013914e-01,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,- l'altezza del triangolo maggiore la diatanza Venere-Sole = 0,72 u.a.CALLOUT 2.381624e-01,-4.215264e-02,2.381624e-01,-4.215264e-02,ffff00,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,0,72 u.a.PAUSE 1.5 sCALLOUT -7.545322e-01,-1.601800e-01,-7.545322e-01,-1.601800e-01,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,- l'altezza del triangolo minore e la distanza Venere-Terra = 0,28 u.a.CALLOUT 4.278493e-01,3.056066e-01,4.278493e-01,3.056066e-01,ffff00,0,4080ff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,0,28 u.a.PAUSE 1.5 sCALLOUT -5.922445e-01,-1.264579e-02,-5.922445e-01,-1.475342e-02,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Applicando le leggi dei triangolisimili possiamo ricavare quanto segue:PAUSE 2 sCALLOUT -7.756085e-01,1.454266e-01,-7.756085e-01,1.454266e-01,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,dist. Osservatori dist. Transito sul disco S oss S tranCALLOUT -6.660117e-01,2.002250e-01,-6.660117e-01,2.002250e-01,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,0,28 0,72 0,28 0,72CALLOUT -7.692856e-01,2.023327e-01,-5.395538e-01,2.023327e-01,ff0000,0,c0ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -4.657866e-01,1.981174e-01,-1.517495e-01,1.981174e-01,ff0000,0,c0ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -1.011663e-01,1.981174e-01,-2.529158e-02,1.981174e-01,ff0000,0,c0ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT 2.318395e-02,2.002250e-01,1.201350e-01,2.002250e-01,ff0000,0,c0ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -5.226927e-01,1.770411e-01,-5.226927e-01,1.770411e-01,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,=CALLOUT -1.412113e-01,1.749334e-01,-1.412113e-01,1.749334e-01,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,=CALLOUT -1.053816e-02,1.770411e-01,-1.053816e-02,1.770411e-01,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,=PAUSE 5 sCALLOUT -3.604050e-01,2.676692e-01,-3.604050e-01,2.676692e-01,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,e quindiCALLOUT -7.861467e-01,3.351135e-01,-7.861467e-01,3.351135e-01,ff0000,0,40ff0000,ffffffed,0,0,0,2bc,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,dist. Transito (sul disco solare) =S tran = 5142,86 KmCALLOUT 9.273580e-02,-2.170861e-01,9.273580e-02,-2.170861e-01,800000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,S tran = 5142,86 KmDELCALLOUT S tranCALLOUT 6.533659e-01,4.404951e-01,6.512582e-01,4.404951e-01,ff0000,0,40ff0000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYNEWDIA "SS000003.SIT",YPAUSE 0.5 sCALLOUT -7.123796e-01,-2.381624e-01,-7.123796e-01,-2.381624e-01,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Suppponiamo ora di osservare il transito (dalle due posizioni)e di poter disegnare con estrema precisione la traiettoria delpianeta su un disco solare del diametro di 16 centimetri (questa semplificazione per evitare i calcoli sui tempi del transito)CALLOUT 6.870880e-01,4.088806e-01,6.870880e-01,4.088806e-01,ff0000,0,40ff0000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYINTERPOLATE 10 s,PRESERVECALLOUTS,LINEARNEWDIA "SS000027.SIT",""NEWDIA "SS000013.SIT",""CALLOUT 7.469946e-03,4.893287e-03,7.375390e-03,4.846009e-03,ff0000,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,PgDnWAITKEYDELCALLOUT PgDnCALLOUT -6.428277e-01,-1.960098e-01,-6.428277e-01,-1.960098e-01,ff0000,0,40ff0000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,77d35400,1010057,12f5ac,0,Suppponiamo ora di osservare il transito (dalle due posizioni)e di poter disegnare con estrema precisione la traiettoria deltransito su un disco solare del diametro di 16 centimetri (questo semplificazione per evitare i calcoli sui tempi dei transiti)DELCALLOUT Suppponiamo ora di osservare il transito (dalle due posizioni)e di poter disegnare con estrema precisione la traiettoria deltransito su un disco solare del diametro di 16 centimetri (questo semplificazione per evitare i calcoli sui tempi dei transiti)PAUSE 0.5 sMOVIE CONT,45 min,1 s,7.8 s,SIMTIME,PRESERVECALLOUTS,SINGLECALLOUT -3.829529e-03,2.529380e-03,2.907606e-03,3.522221e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,CALLOUT -1.536540e-03,1.772930e-03,-1.536540e-03,1.772930e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,Traiettoria disegnata dall'osservatore ACALLOUT 7.020804e-03,4.846009e-03,7.020804e-03,4.846009e-03,ff0000,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,0,0,0,PgDnWAITKEYINTERPOLATE 0.2 s,PRESERVECALLOUTS,LINEARNEWDIA "SS000017.SIT",YCALLOUT -3.829529e-03,2.529380e-03,2.907606e-03,3.522221e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,CALLOUT -1.536540e-03,1.772930e-03,-1.536540e-03,1.772930e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,Traiettoria disegnata dall'osservatore APAUSE 0.5 sMOVIE CONT,45 min,1 s,7.8s,SIMTIME,PRESERVECALLOUTS,SINGLECALLOUT -3.782251e-03,2.623937e-03,2.954884e-03,3.593139e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,PAUSE 0.3 sCALLOUT -1.347427e-03,3.451304e-03,-1.347427e-03,3.451304e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,Traiettoria disegnatadall'osservatore BPAUSE 0.3 sCALLOUT -9.171959e-03,-5.224234e-03,-9.171959e-03,-5.224234e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,Paragonando i due disegni potremo vedere chegli osservatori avranno disegnato due tracce leggermete differenti e separate di appena 0,0592 cm (mezzo millimetro circa) ...CALLOUT -4.775092e-03,2.292990e-03,-4.775092e-03,2.292990e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,0,0592CALLOUT -8.651900e-03,-1.371066e-03,-8.651900e-03,-1.371066e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,.... Facendo le debite proporzioni ....PAUSE 5 sCALLOUT 4.964205e-04,-5.366069e-03,4.964205e-04,-5.366069e-03,ff0000,0,40000000,ffffffed,0,0,0,2bc,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,Se in un disco di 16 cm la separazione di 0,0592 cm vuol dire che la separazione di 5142,86 km corrisponde ad un disco del diametro di ...CALLOUT 9.455628e-04,-2.434824e-03,9.455628e-04,-2.434824e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,(16 cm / 0.0592 cm) = (diam. vero Sole / 5142,86)CALLOUT 3.853168e-03,-1.938404e-03,3.853168e-03,-1.938404e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,da cuiCALLOUT 1.087397e-03,-1.276510e-03,1.087397e-03,-1.276510e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,diametro vero Sole = (16 / 0,0592) x 5142,86 =CALLOUT 3.096718e-03,-7.091721e-05,3.096718e-03,-7.091721e-05,ff0000,0,40000000,ffffffe8,0,0,0,2bc,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,1.390.000 KmCALLOUT 7.517224e-03,4.538701e-03,7.517224e-03,4.538701e-03,ff0000,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,PgDnWAITKEYDELCALLOUT DELCALLOUT Traiettoria disegnata dall'osservatore ADELCALLOUT DELCALLOUT Traiettoria disegnatadall'osservatore BDELCALLOUT Paragonando i due disegni potremo vedere chegli osservatori avranno disegnato due tracce leggermete differenti e separate di appena 0,0592 cm (mezzo millimetro circa) ...DELCALLOUT 0,0592DELCALLOUT .... Facendo le debite proporzioni ....DELCALLOUT Se in un disco di 16 cm la separazione di 0,0592 cm vuol dire che la separazione di 5142,86 km corrisponde ad un disco del diametro di ...DELCALLOUT (16 cm / 0.0592 cm) = (diam. vero Sole / 5142,86)DELCALLOUT da cuiDELCALLOUT diametro vero Sole = (16 / 0,0592) x 5142,86 =DELCALLOUT 1.390.000 KmDELCALLOUT PgDnINTERPOLATE 3 s,DELETECALLOUTS,LINEARNEWDIA "SS000019.SIT",""INTERPOLATE 3 s,DELETECALLOUTS,LINEARNEWDIA "SS000010.SIT",""PAUSE 0.5 sSHOWJPG -6.351761e-02,-3.639978e-04,-6.351761e-02,-3.639978e-04,40000000,terra_small.jpgPAUSE 0.5 sCALLOUT -6.752159e-02,-3.803777e-02,-6.752159e-02,-3.803777e-02,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,misuriamo ora il diametro apparente del Sole visto da terra ....PAUSE 1 sCALLOUT -5.969564e-02,1.819989e-03,3.621778e-02,-4.731971e-03,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,CALLOUT -5.969564e-02,1.819989e-03,3.567178e-02,4.367973e-03,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,CALLOUT -3.166781e-02,-7.279956e-04,-3.166781e-02,-7.279956e-04,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,22010203,61697241,6172006c,32346870,54422031,0,10,202,0,)CALLOUT -3.021182e-02,-7.279956e-04,-3.021182e-02,-7.279956e-04,ff0000,0,40ffff00,fffffff0,0,0,0,190,2000000,12010203,626d7953,61006c6f,32346870,54422031,0,10,202,0,dCALLOUT -4.859370e-02,-3.366979e-02,-4.859370e-02,-3.366979e-02,ff0000,0,40ffff00,ffffffeb,0,0,0,190,2000000,12010203,626d7953,61006c6f,32346870,54422031,0,10,202,0,dCALLOUT -4.568172e-02,-3.348780e-02,-4.568172e-02,-3.348780e-02,ff0000,0,40ffff00,ffffffeb,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,= 0,534PAUSE 1 sCALLOUT -6.733959e-02,-2.693584e-02,-6.733959e-02,-2.693584e-02,ff0000,0,40ffff00,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,il diametro vero abbiamo visto essere di 1.390.000 kmCALLOUT 3.585378e-02,-4.731971e-03,3.585378e-02,4.549972e-03,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,CALLOUT 3.639978e-02,-2.911982e-03,3.639978e-02,-2.911982e-03,0,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,diam.veroCALLOUT -6.733959e-02,-2.183987e-02,-6.733959e-02,-2.183987e-02,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,da cui: - raggio vero =695.000 km - raggio apparente=0,267PAUSE 1 sCALLOUT -6.661159e-02,1.037394e-02,-6.661159e-02,1.037394e-02,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,e quindi, per le leggi dei triangoli rettangoli ...CALLOUT -5.878564e-02,1.601590e-02,-5.878564e-02,1.601590e-02,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,Tan (0,267) = 695.000 / 1 u.a.CALLOUT -5.933164e-02,1.819989e-03,3.585378e-02,1.819989e-04,ff0000,0,40ffffff,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,CALLOUT -2.729983e-03,-2.547984e-03,-2.729983e-03,-2.547984e-03,ffffff,0,40ffffff,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,1 u.a.CALLOUT -5.641966e-02,2.074787e-02,-5.641966e-02,2.074787e-02,ff0000,0,40ffffff,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0, da cui ... 1 u.a. =695.000 / tan (0,267) CALLOUT -5.969564e-02,1.819989e-03,3.603578e-02,-4.731971e-03,ff0000,0,40ffffff,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,DELCALLOUT DELCALLOUT DELCALLOUT )DELCALLOUT dCALLOUT -1.037394e-02,-2.365986e-03,-1.037394e-02,-2.365986e-03,ff0000,0,40ffffff,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,)CALLOUT -1.019194e-02,5.459967e-04,-1.019194e-02,5.459967e-04,ff0000,0,40ffffff,fffffff0,0,0,0,190,2000000,12010203,626d7953,61006c6f,32346870,54422031,0,10,202,0,d/2DELCALLOUT diam.veroCALLOUT 3.639978e-02,-4.913970e-03,3.639978e-02,-4.913970e-03,0,0,40ffffff,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,raggioveroDELCALLOUT CALLOUT 3.585378e-02,-4.731971e-03,3.585378e-02,1.819989e-04,0,0,40000000,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,CALLOUT -2.147587e-02,2.456985e-02,-2.092987e-02,2.638984e-02,ff0000,0,0,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,=CALLOUT -1.710790e-02,2.256786e-02,-1.710790e-02,2.256786e-02,ff0000,0,40000000,ffffffe3,0,0,0,2bc,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,149.140.000 kmCALLOUT 6.224362e-02,3.639978e-02,6.224362e-02,3.639978e-02,ff0000,0,40ffffff,fffffff5,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,PgDnWAITKEYNEWDIA "SS000033.SIT",YPAUSE 0.3 sCALLOUT -6.333561e-02,-3.767377e-02,-6.333561e-02,-3.767377e-02,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,Il risultato ottenuto molto vicinoalla realt e le differenze sono dovutealle molte approssimazioni usatePAUSE 1 sCALLOUT -6.752159e-02,-2.202187e-02,-6.752159e-02,-2.202187e-02,ff0000,0,40000000,fffffff0,0,0,0,190,0,42010203,6c6c6143,61726769,32346870,54422031,0,10,202,0,Ora, grazie alla TERZA LEGGE DI KEPLEROpossiamo trovare le distanze del sistema solare ...SS000015.SIT@SITUFILE06 !yw "2 !yP\BAҜ탙@ߓ` ?xDefinito dall'utentesVP?7@YUAá󫅁A@{P=+¶0V%@d/X)kr> uͿu;:?:(?h"ῡu?x3n⿧bcy????"I+;?W#BO?mĆ>+;?('-4BOw7??dt ?G?f3t90D1%G?sikqE?D)?!ΦѢ>k7ZC?B3DxI10 min0.5 sa@?@E5 ?8eratostene.jpgsJFIFC  !"$"$Cmm" }!1AQa"q2#BR$3br %&'()*456789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz w!1AQaq"2B #3Rbr $4%&'()*56789:CDEFGHIJSTUVWXYZcdefghijstuvwxyz ?ʊ( [h M^&EdUmɄP@PXzO,t<=$%."ʾ 0(5bcH#QQ*P4 >+YKI-A~iϗϵ0p 7iQ +4PR 9bܓp0 w ɨ<`}C]hT)j  G ?SSVGm^x]sb@떱*Ѭ5 DK:'\3 ;qOwR%%"uIfT9+,x.KVIu ֓So^V;ltl.]L5vcƙ2I]}֚6k" &јX\+Y~<-kJ4MJ]3Yo4vp42 Fdr5NC"x;/-jiH){n8S˜.F[; V- UX# وˆ7rZ8J(}-2;▦m]Ifu-6vp B. 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