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حساب حركة الأجرام السماوية

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Muhannad Aulama
Muhannad Aulama

شرائح محاضرة حساب حركة الأجرام السماوية

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‫ﺣﺴﺎﺏ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﻣﺒﺎﺩﺉ ﺍﻟﻬﻨﺪﺳﺔ ﺍﻟﻔﺮﺍﻏﻴﺔ ﻟﺤﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻭ ﺣﺴﺎﺏ ﺍﻟﻈﻮﺍﻫﺮ ﺍﻟﻔﻠﻜﻴﺔ ﻓﻲ ﺍﻟﺴﻤﺎء ﻟﻠﺮﺍﺻﺪ ﺍﻟﻔﻠﻜﻲ ﺍﻟﻬﺎﻭﻱ‬ ‫ﻭ ﺍﻟﻤﺤﺘﺮﻑ‬
‫ﺃﺳﻠﻮﺏ ﺍﻟﻌﺮﺽ‬ ‫ﻫﺪﻑ ﺍﻟﻤﺤﺎﺿﺮﺓ‬ ‫ﺍﻟﻤﺤﺎﺿﺮ‬ ‫ﻣﺒﺘﺪﺉ‬ ‫ﻣﺘﻮﺳﻂ‬ ‫ﻣﺘﻘﺪﻡ‬ ‫ ‬ ‫ ﻣﻬﻨﺪﺱ ﺍﺗﺼﺎﻻﺕ ﻭ ﺣﺎﺳﻮﺏ‬ ‫ﺧﺒﻴﺮ‬ ‫ﻫﺎﻭﻱ ﻓﻠﻚ‬ ‫ﺍﻟﻤﻌﻠﻮﻣﺎﺕ ﺍﻟﺴﺎﺑﻘﺔ‬ ‫ﻣﺪﺓ ﺍﻟﻌﺮﺽ‬ ‫۰٦‬ ‫ﻓﻴﺰﻳﺎء‬ ‫ﺩﻕﻱﻕﺓ‬ ‫ﺭﻳﺎﺿﻴﺎﺕ‬ ‫ﻓﻠﻚ‬ ‫ﺩﻗﻴﻘﺔ ﻧﻘﺎﺵ۰۲‬ ‫ﺑﻌﺪ ﺍﻟﻤﺤﺎﺿﺮﺓ‬
‫ﺃﺟﻨﺪﺓ ﺍﻟﻌﺮﺽ‬ ‫ﺟﺪﻭﻝ ﺍﻟﻤﺤﺎﺿﺮﺓ‬ ‫ ﺍﻟﻨﻤﻮﺫﺝ ﺍﻟﺮﻳﺎﺿﻲ‬ ‫ ﺍﻟﻔﻀﺎء ﺍﻻﻗﻠﻴﺪﻱ ﻟﻠﻜﻮﻥ‬ ‫ ﺗﻔﺎﻋﻞ ﺍﻷﺟﺮﺍﻡ‬ ‫ ﺍﻟﺤﺴﺎﺏ ﺍﻟﻔﻠﻜﻲ‬ ‫ ﺍﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ ﺍﻟﺰﻣﻦ ﻭ ﺍﻟﻮﻗﺖ‬ ‫ﻧﻤﺎﺫﺝ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺗﻄﺒﻴﻖ ﻋﻤﻠﻲ: ﺣﺴﺎﺏ ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ‬
‫ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﺗﺎﺭﻳﺨﻴﺎ ً‬ ‫ﺣﺮﻛﺔ ﺍﻟﺴﻤﺎء ﻭ ﺍﻟﻌﻤﻞ ﺍﻟﺴﺎﺑﻖ‬ ‫ ﺍﻟﻠﻐﺰ ﺍﻟﺘﺎﺭﻳﺨﻲ‬ ‫ ﺣﺮﻛﺔ ﺍﻟﺴﻤﺎء ﻭ ﺍﻷﺟﺮﺍﻡ‬ ‫ﻓﻚ ﺷﻴﻔﺮﺓ ﺣﺮﻛﺔ ﺍﻟﺴﻤﺎء ﻛﺎﻧﺖ ﺍﻟﺴﺆﺍﻝ ﺍﻷﺑﺮﺯ ﻭ‬ ‫ﺍﻟﻨﻈﺮ ﺍﻟﻰ ﺃﻋﻠﻰ ﺳﻮﺍء ﻟﻴﻼً ﺃﻭ ﻧﻬﺎﺭﺍً ﻛﻔﻴﻞ‬ ‫ .ﺍﻷﻫﻢ ﻓﻲ ﻣﺴﻴﺮﺓ ﺍﻟﻌﻠﻢ ﻣﻨﺬ ﻓﺠﺮ ﺍﻟﺘﺎﺭﻳﺦ‬ ‫ﺑﺮﺅﻳﺔ ﺍﻟﺸﻤﺲ ﻭ ﺍﻟﻘﻤﺮ ﻭ ﺍﻟﻜﻮﺍﻛﺐ ﻭ ﺍﻟﻨﺠﻮﻡ‬ ‫ﻣﻌﺮﻓﺘﻨﺎ ﺍﻟﺤﺎﻟﻴﺔ ﻫﻲ ﻧﺘﻴﺠﺔ ﺗﺮﺍﻛﻢ ﺃﻋﻤﺎﻝ ﺍﻟﺒﺤﺜﻴﻦ‬ ‫ﻭ ﺃﺟﺮﺍﻡ ﺍﻟﺴﻤﺎء ﺍﻟﺒﻌﻴﺪﺓ ﻓﻲ ﺣﺮﻛﺔ ﻣﺘﻮﺍﺻﻠﺔ‬ ‫.ﺍﻟﺴﺎﺑﻘﻴﻦ‬
‫ﺍﻟﻨﻤﻮﺫﺝ ﺍﻻﻗﻠﻴﺪﻱ ﻷﺑﻌﺎﺩ ﺍﻟﺴﻤﺎء‬ ‫ﺍﻟﻔﻀﺎء ﺭﻗﻤﻴﺎ ً‬ ‫2=‪t‬‬ ‫1=‪t‬‬ ‫*‬ ‫*‬ ‫ ﺍﻟﺰﻣﻦ ﻛﻤﺘﻐﻴﺮ ﻣﺴﺘﻘﻞ‬ ‫ ﺛﻼﺛﺔ ﺃﺑﻌﺎﺩ ﻣﺘﻌﺎﻣﺪﺓ‬ ‫ﻭﺻﻒ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺪﻳﻜﺎﺭﺗﻴﺔ ﻟﻠﺠﺮﻡ ﺍﻟﺴﻤﺎﻭﻱ‬ ‫ ﺍﻟﺤﺎﺟﺔ ﻟﻨﻤﻮﺫﺝ ﺭﻗﻤﻲ ﻟﻮﺻﻒ ﻣﻜﺎﻥ ﺍﻟﺠﺮﻡ‬ ‫ ﺑﺪﻻﻟﺔ ﺍﻟﺰﻣﻦ‬ ‫ﺍﺻﻄﻼﺡ ﺛﻼﺛﺔ ﻣﺘﻐﻴﺮﺍﺕ ﻋﻤﻮﺩﻳﺔ ﻋﻠﻰ ﺑﻌﻀﻬﺎ‬ ‫ﺍﻟﺰﻣﻦ ﻣﺘﻐﻴﺮ ﻣﺴﺘﻘﻞ ﻻ ﻳﺘﺄﺛﺮ ﺑﺘﻐﻴﺮ ﺍﺣﺪﺍﺛﻴﺎﺕ‬ ‫ ))ﻣﺴﺘﻮﻯ ﺩﻳﻜﺎﺭﺗﻲ ﺛﻼﺛﻲ ﺍﻷﺑﻌﺎﺩ‬ ‫ﺍﻷﺟﺮﺍﻡ‬ ‫ ﺍﻟﺘﻐﻴﺮ ﻓﻲ ﻗﻴﻤﺔ ﺑُﻌﺪ ﻣﻨﻔﺼﻞ ﻋﻦ ﺑﺎﻗﻲ ﺍﻷﺑﻌﺎﺩ‬ ‫ﺍﻟﻨﻈﺮﻳﺎﺕ ﺍﻻﻗﻠﻴﺪﻳﺔ ﻣﻨﻄﺒﻘﺔ ﻣﺜﻞ ﻓﻴﺜﺎﻏﻮﺭﺱ‬
‫ا%4#3ذ1 ا0/.-,ي *)("د ا%$#"ء‬ !"#$% ‫ر,5 ا43$21*ات 0/*.' ً ,'+$*ا('ت‬ t=2 t=1 * x2 + y2 = 1 * dx / dt = value dy / dt = value dz / dt = value x, y, z = f (t ) 56"78 – ‫@.? 0>,ا=-"ت ا%;:م‬A#%‫ ا‬B-C%‫ا‬ ?()‫-:ات ا*ر‬DA#%‫: ا‬FG ‫-:ات‬DA#%‫ ا‬ ‫! ا4:*م‬P*Q4 ID'.*4‫ذج ا‬G3J4‫<ح ا‬WX‫ا‬ !"#$% 71+ ‫ا43$21*ات ا4@.?'ر>1! ا4=<;! 4":*م ذات‬ ID'.*4‫ [<ل ا4*,5 ا4:/*ي ا‬L% 7$. ‫3'وي‬N4‫ا‬ ‫ت‬A@B%) CD'E> 71+ ‫د‬G0‫ و‬IJB. '3% ،L%M4‫4! ا‬A@, L%M4‫4! ا‬A@, ‫4"3$21*ات ا4@.?'ر>1! ا4=<;! 4":*م‬ 7$. L%M"4 !/NJ4', !.‫3'و‬N4‫0*ام ا‬O‫! ا‬P*Q4 (!1RQ4 !1('=4‫و4 و ا‬O‫ ا4@ر0! ا‬L% ‫'+$*ا('ت‬P C%'?$4‫ و ا‬CD'E$4', 'SJT *1/B$4‫ا‬
5CA$H :-I :-DA#J KHL%‫ا‬ ∂t / ∂x = value C]$N% *12$3P L%M"4 C]$N34‫ذج ا‬G3J4‫^@ود ا‬ ∂t / ∂y = value ∂t / ∂x = 0 ∂t / ∂z = value ∂t / ∂y = 0 ∂t / ∂z = 0 f (t ) = t + ∂t / ∂x + ∂t / ∂y + ∂t / ∂z f (t ) is independent of x, y, z ?M"N%‫-? ا‬F$4%‫ - ا‬PCA$H Q-% ً "R,M‫ ر‬KHL%‫ ا%4#3ذ1 ا0/.-,ي ا‬ST 5CA$H :-DA#J KHL%‫ ا‬ ً *;_$. ‫*ا`1! 4":*م‬E4‫^@ا;1'ت ا‬A‫ ا‬Ia b.*N4‫@ ا4$21* ا‬JT L% ‫ أي‬Ia *12$4‫/! ا4 ا‬NJ4', L%M4‫+13! >21* ا‬ ً<]$N% ]/. A ‫ و‬L%M4‫ .%$21* ا‬ '3% ،ً‫*ا‬EX ‫'وي‬N> !;<=4‫*ا`1! ا‬E4‫ا43$21*ات ا‬ c$J. !1"$?4‫0*ام ا‬d4 !14'B4‫'ت ا‬T*N4‫ ا‬Ia !X'[ ‫ت‬A'^ Ia *12> ‫ .$_;* ,_ي‬A ‫ و‬C]$N% L%M4‫ أن ا‬IJB. e,'=4‫@ ا‬f'g3"4 !/NJ4', ‫ %?'ن ا4:*م‬Ia *12> 'SJT ‫@ة‬f'g34‫'رات ا‬k‫ ا‬b130 Ia ‫! ا4:*م‬P*^
‫ﺍﻟﻜﺘﻠﺔ ﺍﻟﻜﺒﻴﺮﺓ ﻟﻠﻌﻨﺎﻗﻴﺪ ﺍﻟﻤﺠﺮﻳﺔ‬ ‫ﺍﻟﻨﺴﺒﻴﺔ ﺍﻟﻌﺎﻣﺔ ﻭ ﺗﻐﻴﺮ ﻣﻜﺎﻥ ﺍﻟﺠﺮﻡ ﺍﻟﻤﺮﺻﻮﺩ‬
‫ﺕﻓﺎﻋﻞ ﺍﻷﺟﺮﺍﻡ‬ ‫ﻗﻮﺓ ﺍﻟﺠﺬﺏ‬ ‫%#'درا4$21* ‪GQ% Ia‬ر دوران ‪'WT‬رد‬ ‫%]@ار ا4$21* );'(1! +‪*+ C?4 !1lG‬ن‬ ‫ا4‪m/N‬‬ ‫)0‪I('14G‬‬ ‫96.0± 36.135‬ ‫ا4‪ @g‬ا4:‪ L% I,n‬ا4?‪G‬ا‪mP‬‬ ‫ا‪*[O‬ى‬ ‫4520.0‬ ‫‪@T‬م %='41! ‪*P‬و.! ا4‪p3g‬‬ ‫2‪m1* m‬‬ ‫40.0± 89.24‬ ‫ا4‪ !1/NJ‬ا4‪!%'B‬‬ ‫‪G‬‬ ‫2‬ ‫96.0±46.475‬ ‫ا43:3‪G‬ع‬ ‫‪d‬‬ ‫56.0±01.475‬ ‫ا4‪ cr'$J‬ا4*‪!.@X‬‬ ‫ ﻣﺠﺎﻝ ﺟﺬﺑﻲ ﺃﻡ ﺍﻧﺤﻨﺎء ﻓﻲ ﺍﻟﺰﻣﻜﺎﻥ؟‬ ‫ ﺃﺭﺑﻌﺔ ﻗﻮﻯ ﻓﻲ ﺍﻟﻜﻮﻥ ﺗﺴﺒﺐ ﺣﺮﻛﺔ ﺍﻷﺟﺴﺎﻡ‬ ‫ﺗﻔﺴﻴﺮ ﺍﻟﺠﺎﺫﺑﻴﺔ ﻛﻤﺠﺎﻝ ﺟﺬﺑﻲ ﻳﻌﺘﺒﺮ ﻛﺎﻓﻴﺎ ً ﻓﻲ ﻣﻌﻈﻢ‬ ‫ ﻗﻮﺓ ﺍﻟﺠﺬﺏ ﺍﻷﻭﻟﻰ ﻭ ﻓﻲ ﺃﻏﻠﺐ ﺍﻟﺤﺎﻻﺕ ﺍﻟﻮﺣﻴﺪﺓ ﺍﻟﻤﺴﺒﺒﺔ‬ ‫ ﺣﺴﺎﺑﺎﺕ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ ﻟﺘﻔﺎﻋﻞ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻣﻊ ﺑﻌﻀﻬﺎ ﺍﻟﺒﻌﺾ‬ ‫ﺗﺒﺪﺃ ﺍﻟﺤﺎﺟﺔ ﺍﻟﻰ ﺍﻟﻨﺴﺒﻴﺔ ﺍﻟﻌﺎﻣﺔ ﻓﻲ ﺍﻟﻤﺠﺎﻻﺕ ﺍﻟﺠﺬﺑﻴﺔ‬ ‫ﺗﺘﻨﺎﺳﺐ ﻁﺮﺩﻳﺎ ً ﻣﻊ ﻛﺘﻠﺔ ﺍﻟﺠﺮﻣﻴﻦ ﺍﻟﻤﺘﻔﺎﻋﻠﻴﻦ ﻭ ﻋﻜﺴﻴﺎ ً ﻣﻊ‬ ‫ﺍﻟﻜﻴﺒﺮﺓ ﻛﺤﺎﻟﺔ ﻋﻄﺎﺭﺩ ﻭ ﺣﻮﻝ ﺍﻟﺜﻘﻮﺏ ﺍﻟﺴﻮﺩﺍء‬ ‫ﻣﺮﺑﻊ ﺍﻟﻤﺴﺎﻓﺔ ﺑﻴﻨﻬﻤﺎ‬
‫ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ‬ ‫ﺍﻷﺟﺮﺍﻡ ﺍﻟﺜﻨﺎﺋﻴﺔ ﻭ ﺍﻟﻤﺘﻌﺪﺩﺓ‬ ‫ ﺍﻷﺟﺮﺍﻡ ﺍﻟﻤﺘﻌﺪﺩﺓ ﺗﺤﺘﺎﺝ ﺍﻟﻰ ﻣﺤﺎﻛﺎﺓ ﺣﺎﺳﻮﺑﻴﺔ‬ ‫ ﻗﻮﺓ ﺍﻟﺠﺬﺏ ﺗُﻨﺘﺞ ﺩﻭﺭﺍﻧﺎ ً ﺑﻴﻀﺎﻭﻳﺎ ً‬ ‫ً‬ ‫ﺣﻞ ﻗﻮﺓ ﺍﻟﺠﺬﺏ ﻟﺠﺮﻣﻴﻦ ﻳُﻨﺘﺞ ﺗﻔﺎﻋﻞ ﺍﻟﺠﺮﻣﻴﻦ ﺑﺎﻟﺪﻭﺭﺍﻥ ﺍﻟﺪﺍﺋﺮﻱ .ﺗﺘﻔﺎﻋﻞ ﺟﻤﻴﻊ ﺍﻷﺟﺮﺍﻡ ﻣﻊ ﺑﻌﻀﻬﺎ ﺟﺬﺑﻴﺎ‬ ‫ﻳﺘﻢ ﺣﺴﺎﺏ ﺍﻟﺤﺮﻛﺔ ﺍﻟﻨﻬﺎﺋﻴﺔ ﻟﻸﺟﺮﺍﻡ ﻣﻦ ﺧﻼﻝ‬ ‫ .ﺣﻮﻝ ﻣﺮﻛﺰﺍﻟﻜﺘﻠﺔ ﻷﻥ ﺍﻟﻘﻮﺓ ﺗﻨﺘﺞ ﺗﺴﺎﺭﻉ ﺩﻭﺭﺍﻥ‬ ‫ﺍﻟﻤﺤﺎﻛﺎﺓ ﺍﻟﺤﺎﺳﻮﺑﻴﺔ ﻟﻜﺘﻞ ﺟﻤﻴﻊ ﺍﻷﺟﺮﺍﻡ‬ ‫ﺍﻟﺠﺮﻡ ﺫﻭ ﺍﻟﻜﺘﻠﺔ ﺍﻟﺼﻐﻴﺮﺓ ﻳﺪﻭﺭ ﺑﺸﻜﻞ ﺑﻴﻀﻮﻱ ﺣﻮﻝ ﺍﻟﺠﺮﻡ ﺫﻭ‬ ‫.ﺑﺎﻻﺿﺎﻓﺔ ﺍﻟﻰ ﺍﻟﺤﺎﻟﺔ ﺍﻻﺑﺘﺪﺍﺋﻴﺔ ﻟﻠﻨﻈﺎﻡ‬ ‫ .ﺍﻟﻜﺘﻠﺔ ﺍﻟﻜﺒﻴﺮﺓ ﻭ ﺍﻟﺬﻱ ﻳﻜﻮﻥ ﻓﻲ ﺍﺣﺪﻯ ﺑﺆﺭﺗﻲ ﺍﻟﻘﻄﻊ ﺍﻟﻨﺎﻗﺺ‬ ‫ .ﺍﻟﺤﺎﻟﺔ ﺍﻻﺑﺘﺪﺍﺋﻴﺔ ﻟﻠﻨﻈﺎﻡ ﻭ ﺍﻟﻤﺆﺛﺮﺍﺕ ﺍﻟﺨﺎﺭﺟﻴﺔ ﺗﺤﺪﺩ ﺷﻜﻞ ﺍﻟﺘﻔﺎﻋﻞ‬
‫ﻧﺘﻴﺠﺔ ﺗﻔﺎﻋﻞ ﻗﻮﺓ ﺍﻟﺠﺬﺏ ﺑﻴﻨﻬﺎ‬ ‫ﺩﻭﺭﺍﻥ ﻣﻠﻴﺎﺭﺍﺕ ﺍﻟﻨﺠﻮﻡ ﻓﻲ ﺍﻟﻤﺠﺮﺓ‬
‫ﺍﻟﻤﺴﺎﻓﺎﺕ ﻭ ﺍﻷﺣﺠﺎﻡ ﻟﻸﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻓﻲ ﺍﻟﻜﻮﻥ‬ ‫ﻣﺴﺎﻓﺎﺕ ﻫﺎﺋﻠﺔ ﺗﺠﻌﻞ ﺍﻷﺣﺠﺎﻡ ﺻﻐﻴﺮﺓ‬ ‫ ﺍﻟﻨﻤﻮﺫﺝ ﺍﻟﻨﻘﻄﻲ ﻟﺤﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ ﺃﺣﺠﺎﻡ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺣﺴﺎﺏ ﻣﺪﺍﺭﺍﺕ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻳﺘﻢ ﻋﻠﻰ ﺍﻓﺘﺮﺍﺽ‬ ‫ﻣﻊ ﺃﻥ ﻛﻮﺍﻛﺐ ﺍﻟﻤﺠﻤﻮﻋﺔ ﺍﻟﺸﻤﺴﻴﺔ ﻭ ﺍﻟﻨﺠﻮﻡ ﻣﺜﻼً ﻫﻲ‬ ‫ .ﺃﻧﻬﺎ ﺃﺟﺮﺍﻡ ﻧﻘﻄﻴﺔ ﺗﺘﺮﻛﺰ ﻛﺘﻠﺘﻬﺎ ﻓﻲ ﻧﻘﻄﺔ‬ ‫ﺃﺟﺮﺍﻡ ﻛﺒﻴﺮﺓ ﺍﻟﺤﺠﻢ٬ ﻟﻜﻦ ﺑﺎﻟﻨﺴﺒﺔ ﺍﻟﻰ ﺍﻟﻤﺴﺎﻓﺎﺕ ﻓﻴﻤﺎ‬ ‫ﺑﻌﺪ ﺣﺴﺎﺏ ﻣﻮﻗﻊ ﺍﻟﺠﺮﻡ ﻳﺘﻢ ﺍﺭﺟﺎﻉ ﺣﺠﻤﻪ ﺍﻟﻄﺒﻴﻌﻲ‬ ‫ﺑﻴﻨﻬﺎ ﻓﻬﻲ ﻓﻌﻠﻴﺎ ً ﺻﻐﻴﺮﺓ ﺟﺪﺍً‬ ‫ ﻟﻴﻐﻄﻲ ﺍﻟﻤﺴﺎﺣﺔ ﺍﻟﻄﺒﻴﻌﻴﺔ ﺍﻟﺘﻲ ﻳﻐﻄﻴﻬﺎ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ ‬
‫ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻔﻀﺎﺋﻴﺔ ﻭ ﺍﻻﺳﻘﺎﻁ ﺍﻷﺭﺿﻲ‬ ‫ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻔﻴﺰﻳﺎﺋﻴﺔ ﺛﻼﺛﻴﺔ ﺍﻷﺑﻌﺎﺩ ﻭ ﺍﺳﻘﺎﻁ ﺍﻟﻜﺮﺓ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫0 = ‪x = 4, y = 2, z‬‬ ‫ ﺍﺳﻘﺎﻁ ﺍﻟﻔﻀﺎء ﺍﻻﻗﻠﻴﺪﻱ ﻟﻠﻜﻮﻥ ﻛﻜﺮﺓ ﺳﻤﺎﻭﻳﺔ‬ ‫ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺪﻳﻜﺎﺭﺗﻴﺔ ﺛﻼﺛﻴﺔ ﺍﻷﺑﻌﺎﺩ‬ ‫ﺍﺳﻘﺎﻁ ﻛﺎﻣﻞ ﺍﻟﻔﻀﺎء ﺍﻻﻗﻠﻴﺪﻱ ﻟﻠﻜﻮﻥ ﻛﻤﺎ ﻳﺮﻯ ﻣﻦ‬ ‫ﻣﻤﺘﺎﺯﺓ ﻟﻠﻤﺴﺎﺋﻞ ﺍﻟﻔﻴﺰﻳﺎﺋﻴﺔ ﻷﻧﻬﺎ ﺗﻌﺒﺮﻋﻦ ﻣﻜﺎﻥ ﺍﻷﺟﺮﺍﻡ‬ ‫ .ﺍﻷﺭﺽ ﻛﻜﺮﺓ ﺳﻤﺎﻭﻳﺔ ﺑﺒﻌﺪﻳﻦ ﺑﺪﻻً ﻣﻦ ﺛﻼﺛﺔ‬ ‫ﻓﻲ ﺍﻟﻔﻀﺎء ﺍﻻﻗﻠﻴﺪﻱ ﺑﺎﺣﺪﺍﺛﻴﺎﺕ ﻣﺘﻌﺎﻣﺪﺓ ﻣﻤﺎ ﻳﺴﻬﻞ‬ ‫ﺍﻟﺒﻌﺪ ﺍﻟﺜﺎﻟﺚ )ﺍﻟﻌﻤﻖ( ﻳﺘﻢ ﺍﻟﺘﻌﺒﻴﺮ ﻋﻨﻪ ﺑﺒﻌﺪ ﺍﻟﺠﺮﻡ ﻋﻦ‬ ‫ ﺍﻟﻌﻤﻠﻴﺎﺕ ﺍﻟﻔﻴﺰﻳﺎﺋﻴﺔ ﻛﺎﻟﻀﺮﺏ ﺍﻟﻤﺘﺠﻬﻲ ﻭ ﺍﻟﻘﻴﺎﺳﻲ‬ ‫ .ﺍﻷﺭﺽ ﺑﺎﻟﻮﺣﺪﺓ ﺍﻟﻔﻠﻜﻴﺔ ﺃﻭ ﺍﻟﺴﻨﻮﺍﺕ ﺍﻟﻀﻮﺋﻴﺔ‬ ‫ﻟﻜﻨﻬﺎ ﻻ ﺗﻌﺒﺮ ﺑﺸﻜﻞ ﻭﺍﺿﺢ ﻋﻦ ﻣﻜﺎﻥ ﺍﻟﺠﺮﻡ ﻛﻢ ﻳﺮﻯ‬ ‫ﺍﻷﻧﺴﺐ ﻭ ﺍﻷﺳﻬﻞ ﻟﻠﻤﺴﺎﺋﻞ ﺍﻟﺮﺻﺪﻳﺔ ﻟﻜﻨﻪ ﻏﻴﺮ ﻣﻨﺎﺳﺐ‬ ‫ﻣﻦ ﺍﻷﺭﺽ ﻟﺬﻟﻚ ﺗﻌﺘﺒﺮ ﺳﻴﺌﺔ ﻛﺎﺣﺪﺍﺛﻴﺎﺕ ﺭﺻﺪﻳﺔ‬ ‫ ﻟﻠﺤﺴﺎﺏ ﺍﻟﻔﻴﺰﻳﺎﺋﻲ ﻷﻥ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﻏﻴﺮ ﻣﺘﻌﺎﻣﺪﺓ‬
‫ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻔﻀﺎﺋﻴﺔ ﺍﻟﺮﺻﺪﻳﺔ‬ ‫ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺴﻤﺘﻴﺔ ﻭ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻻﺳﺘﻮﺍﺋﻴﺔ‬ ‫ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻻﺳﺘﻮﺍﺋﻴﺔ‬ ‫ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺴﻤﺘﻴﺔ‬ ‫ﻣﺮﺟﻌﻴﺘﻪ ﻣﺤﻮﺭ ﺩﻭﺭﺍﻥ ﺍﻟﻜﺮﺓ ﺍﻷﺭﺿﻴﺔ ﺣﻴﺚ ﻳﺘﻢ ﺗﻘﺴﻴﻢ‬ ‫ﻣﺮﺟﻌﻴﺘﻪ ﻣﻮﻗﻊ ﺍﻟﺮﺍﺻﺪ ﺣﻴﺚ ﻳﺘﻢ ﺗﻘﺴﻴﻢ ﺳﻤﺎء‬ ‫ ﺍﻟﺴﻤﺎء ﺍﻟﻰ ﺧﻄﻮﻁ ﻣﻴﻞ ﺍﺳﺘﻮﺍﺋﻲ ﻭ ﻁﺎﻟﻊ ﻣﺴﺘﻘﻴﻢ‬ ‫ﺍﻟﺮﺍﺻﺪ ﺍﻟﻰ ﺧﻄﻮﻁ ﻁﻮﻝ ﻭ ﺧﻄﻮﻁ ﻋﺮﺽ‬ ‫ ﺍﻷﻛﺜﺮ ﺍﺳﺘﺨﺪﺍﻣﺎ ً ﻟﺘﺤﺪﻳﺪ ﻣﻮﻗﻊ ﺍﻟﺠﺮﻡ ﺍﻟﻌﺎﻟﻤﻲ‬ ‫ .ﺑﺎﻟﺪﺭﺟﺎﺕ‬ ‫ ﻧﻔﺲ ﺍﺣﺪﺍﺛﻴﺎﺕ ﺍﻷﺟﺮﺍﻡ ﻷﻱ ﻣﻮﻗﻊ ﺭﺻﺪﻱ ﺃﺭﺿﻲ‬ ‫ .ﺍﻷﺳﻬﻞ ﻭ ﺍﻷﺳﺮﻉ ﻟﺘﺤﺪﻳﺪ ﺍﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺠﺮﻡ ﺭﺻﺪﻳﺎ ً‬ ‫ ﺧﻄﻮﻁ ﺍﻟﻌﺮﺽ ﺑﺎﻟﺪﺭﺟﺎﺕ ﺃﻣﺎ ﺍﻟﻌﺮﺽ ﺑﺎﻟﺴﺎﻋﺔ‬ ‫.ﻣﺘﻐﻴﺮ ﻣﻦ ﻣﻜﺎﻥ ﺭﺻﺪﻱ ﻵﺧﺮ‬ ‫ ‬
‫ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻔﻀﺎﺋﻴﺔ ﺍﻟﺮﺻﺪﻳﺔ‬ ‫ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺸﻤﺴﻴﺔ ﻭ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻤﺠﺮﻳﺔ‬ ‫ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻤﺠﺮﻳﺔ‬ ‫ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺸﻤﺴﻴﺔ‬ ‫ .ﻣﺮﺟﻌﻴﺘﻪ ﺳﻄﺢ ﺍﻟﻤﺠﺮﺓ‬ ‫ .ﻣﺮﺟﻌﻴﺘﻪ ﺳﻄﺢ ﺩﻭﺭﺍﻥ ﺍﻷﺭﺽ ﺣﻮﻝ ﺍﻟﺸﻤﺲ‬ ‫ﺍﻟﻤﺤﻮﺭ ﺍﻷﻭﻝ:ﺍﻻﺯﺍﺣﺔ ﺍﻷﻓﻘﻴﺔ ﻋﻠﻰ ﺳﻄﺢ ﺍﻟﻤﺠﺮﺓ ﻋﻦ‬ ‫ﺍﻟﻤﺤﻮﺭ ﺍﻷﻭﻝ: ﺍﻻﻧﺰﻳﺎﺡ ﺍﻷﻓﻘﻲ ﻋﻦ ﻧﻘﻄﺔ ﺍﻻﻋﺘﺪﺍﻝ‬ ‫ .ﺍﻟﺨﻂ ﺍﻟﻮﺍﺻﻞ ﺑﻴﻦ ﺍﻟﺸﻤﺲ ﻭ ﻣﺮﻛﺰ ﺍﻟﻤﺠﺮﺓ‬ ‫ .ﺍﻟﺮﺑﻴﻌﻲ ﻋﻠﻰ ﺳﻄﺢ ﺩﻭﺭﺍﻥ ﺍﻷﺭﺽ ﺣﻮﻝ ﺍﻟﺸﻤﺲ‬ ‫ﺍﻟﻤﺤﻮﺭ ﺍﻟﺜﺎﻧﻲ: ﺍﻻﻧﺰﻳﺎﺡ ﺍﻟﻌﻤﻮﺩﻱ ﻋﻦ ﺳﻄﺢ ﺩﻭﺭﺍﻥ ﺍﻟﻤﺤﻮﺭ ﺍﻟﺜﺎﻧﻲ: ﺍﻻﺯﺍﺣﺔ ﺍﻟﻌﻤﻮﺩﻳﺔ ﺧﺎﺭﺝ ﺳﻄﺢ ﺍﻟﻤﺠﺮﺓ‬ ‫ .ﺍﻟﺸﻤﺲ ﻓﻲ ﻧﻘﻄﺔ ﺍﻟﺼﻔﺮ ﻟﺘﻘﺎﻁﻊ ﺍﻟﻤﺤﻮﺭﻳﻦ‬ ‫.ﺍﻷﺭﺽ ﺣﻮﻝ ﺍﻟﺸﻤﺲ‬ ‫ ‬
‫‪Qui‬‬ ‫‪zz‬‬ ‫ّ‬ ‫
ﻗﺪﺭ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ‬ ‫ﻟﻸﺟﺮﺍﻡ ﻓﻲ ﺍﻟﺼﻮﺭﺓ‬
‫ﺍﻟﺰﻣﻦ‬ ‫ﺗﻌﺮﻳﻒ ﺍﻟﺰﻣﻦ‬ ‫ﺍﻟﺘﺎﺭﻳﺦ ﺍﻟﺠﻮﻟﻴﺎﻧﻲ‬ ‫ ﻟﻤﻨﺘﺼﻒ ﻟﻴﻠﺔ ﺍﻟﻴﻮﻡ‬ ‫ 5.2906542‬ ‫ ‬ ‫ﺍﻟﺘﺎﺭﻳﺦ ﺍﻟﺠﻮﻟﻴﺎﻧﻲ‬ ‫ﻟﻠﺴﺎﻋﺔ ﺍﻟﺴﺎﺩﺳﺔ ﻣﺴﺎءﺍً‬ ‫ ﺍﻟﻴﻮﻡ‬ ‫52.3906542‬ ‫ ﺍﻟﺰﻣﻦ ﻛﻤﺘﻐﻴﺮ ﺭﻳﺎﺿﻲ‬ ‫ ﺍﻟﻤﺘﻐﻴﺮ ﺍﻟﻤﺴﺘﻘﻞ ﻓﻲ ﺍﻟﻔﻀﺎء ﺍﻻﻗﻠﻴﺪﻱ‬ ‫ﺍﻟﺸﺎﺋﻊ ﻓﻲ ﺣﺴﺎﺏ ﺍﻟﺰﻣﻦ ﻣﻦ ﺧﻼﻝ ﺍﻟﺴﻨﺔ٬ ﺍﻟﺸﻬﺮ٬ ﺍﻟﻴﻮﻡ٬ .ﺍﻟﻄﺮﻳﻘﺔ ﺍﻟﺸﺎﺋﻌﺔ ﻟﻜﺘﺎﺑﺔ ﺍﻟﺰﻣﻦ ﻏﻴﺮ ﻣﻨﺎﺳﺒﺔ ﻟﻠﺤﺴﺎﺏ‬ ‫ . ﺍﻟﺤﻞ ﻫﻮ ﺍﺻﻄﻼﺡ ﺍﻟﻴﻮﻡ ﺍﻟﺠﻮﻟﻴﺎﻧﻲ ﻛﺮﻗﻢ ﻋﺸﺮﻱ‬ ‫ﺍﻟﺴﺎﻋﺔ٬ ﺍﻟﺪﻗﻴﻘﺔ٬ ﻭ ﺍﻟﺜﺎﻧﻴﺔ. ﻣﺮﺟﻌﻴﺔ ﻫﺬﻩ ﺍﻟﻄﺮﻳﻘﺔ ﻓﻲ‬ ‫ .ﺍﻟﻴﻮﻡ ﺍﻟﺠﻮﻟﻴﺎﻧﻲ ﻫﻮ 42 ﺳﺎﻋﺔ ﻛﺎﻟﻴﻮﻡ ﺍﻟﻌﺎﺩﻱ‬ ‫ﻛﺘﺎﺑﺔ ﺍﻟﺰﻣﻦ ﻫﻲ ﺍﻟﻔﺘﺮﺓ ﺍﻟﻼﺯﻣﺔ ﻟﻌﻮﺩﺓ ﺍﻟﺸﻤﺲ ﺍﻟﻰ‬ ‫ﻳﺒﺪﺃ ﺍﻟﻌﺪ ﻣﻦ ﻅﻬﻴﺮﺓ 1 ﻳﻨﺎﻳﺮ 3174 ﻗﺒﻞ ﺍﻟﻤﻴﻼﺩ ﻓﻲ‬ ‫.ﻣﻮﻗﻌﻬﺎ ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﻨﺠﻮﻡ ﺧﻼﻝ ﺳﻨﺔ‬ ‫ ﺍﻟﺘﻮﻗﻴﺖ ﺍﻟﻌﺎﻟﻤﻲ‬ ‫ ‬
‫ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ﺩﻭﺭﺍﻥ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻓﻲ ﻳﻮﻡ‬ ‫ ﺍﻟﺤﺮﻛﺔ ﺍﻟﺤﻘﻴﻘﻴﺔ ﻟﻸﺟﺮﺍﻡ‬ ‫ )ﺣﺮﻛﺔ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻛﻜﻞ )ﺍﻟﻴﻮﻡ ﺍﻟﻨﺠﻤﻲ‬ ‫.1 ﺣﺮﻛﺔ ﺍﻟﺠﺮﻡ ﺍﻟﺤﻘﻴﻘﻴﺔ ﻫﻲ ﺣﺮﻛﺘﻪ ﻓﻲ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ ﺑﻌﺪ‬ ‫ﺩﻭﺭﺍﻥ ﻛﺎﻣﻞ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻓﻲ 32 ﺳﺎﻋﺔ ﻭ‬ ‫ .ﺇﻫﻤﺎﻝ ﺩﻭﺍﺭﻥ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ ﺍﻟﻴﻮﻣﻲ‬ ‫ 65 ﺩﻗﻴﻘﺔ ﺑﺴﺒﺐ ﺩﻭﺭﺍﻥ ﺍﻷﺭﺽ ﺣﻮﻝ ﻧﻔﺴﻬﺎ‬ ‫ﺗﻌﻮﺩ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﺍﻟﺜﺎﺑﺘﺔ ﺍﻟﻰ ﻧﻔﺲ ﻣﻮﻗﻌﻬﺎ .2 ﺍﻷﺳﻬﻞ ﻫﻮ ﺗﺘﺒﻊ ﺣﺮﻛﺔ ﺍﻟﺠﺮﻡ ﺑﺎﻟﻨﺴﺒﺔ ﺍﻟﻰ ﺍﻷﺟﺮﺍﻡ‬ ‫ )ﺍﻟﺜﺎﺑﺘﺔ ﻓﻲ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ )ﻣﺜﻞ ﺍﻟﻨﺠﻮﻡ ﺍﻟﺒﻌﻴﺪﺓ‬ ‫ﻓﻲ ﺍﻟﺴﻤﺎء ﻓﻲ ﻳﻮﻡ ﻧﺠﻤﻲ ﻭﺍﺣﺪ‬ ‫ ‬ ‫ ‬
‫ﻧﻤﺎﺫﺝ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺣﺮﻛﺔ ﺍﻟﺸﻤﺲ‬ ‫ ﺣﺮﻛﺔ ﺍﻟﺸﻤﺲ ﻛﻤﺎ ﺗﺒﺪﻭ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ ﺳﺒﺐ ﺣﺮﻛﺔ ﺍﻟﺸﻤﺲ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ﺍﻟﺸﻤﺲ ﻋﺎﻟﻴﺔ ﻓﻲ ﺍﻟﺴﻤﺎء ﻓﻲ ﺍﻟﺼﻴﻒ ﻭ ﻣﻨﺨﻔﻀﺔ ﻓﻲ‬ ‫ﺩﻭﺭﺍﻥ ﺍﻷﺭﺽ ﺣﻮﻝ ﺍﻟﺸﻤﺲ ﻓﻲ ﻣﺪﺍﺭ ﺩﺍﺋﺮﻱ ﻗﻠﻴﻞ‬ ‫ .ﺍﻟﺸﺘﺎء‬ ‫ :ﺍﻟﺒﻴﻀﺎﻭﻳﺔ ﻳﻜﺘﻤﻞ ﻓﻲ ﺳﻨﺔ ﻳﻨﺘﺞ ﻋﻨﻪ‬ ‫.1ﺯﻣﻦ ﻣﻜﻮﺙ ﺍﻟﺸﻤﺲ ﻓﻮﻕ ﺍﻷﻓﻖ ﻁﻮﻳﻞ ﻓﻲ ﺍﻟﺼﻴﻒ ﻭ‬ ‫ ﺣﺮﻛﺔ ﻋﻤﻮﺩﻳﺔ ﻷﻋﻠﻰ ﺍﻟﺴﻤﺎء ﺃﻭ ﺃﺳﻔﻠﻬﺎ‬ ‫.2.ﻗﺼﻴﺮ ﻓﻲ ﺍﻟﺸﺘﺎء‬‫ ‬ ‫ﺣﺮﻛﺔ ﺃﻓﻘﻴﺔ: ﺍﻛﺘﻤﺎﻝ ﺩﻭﺭﺓ ﻛﺎﻣﻠﺔ ﻟﻠﺸﻤﺲ ﻓﻲ ﺍﻟﻘﺒﺔ‬ ‫ﺍﻧﺰﻳﺎﺡ ﺍﻟﺸﻤﺲ ﺍﻷﻓﻘﻲ ﻟﻠﻴﺴﺎﺭ ﻓﻲ ﺍﻟﺼﻴﻒ ﻭ ﺍﻟﻴﻤﻴﻦ ﻓﻲ‬ ‫ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ ‬ ‫.3ﺍﻟﺸﺘﺎء‬ ‫ﺗﻐﻴﺮ ﻁﻔﻴﻒ ﻓﻲ ﺣﺠﻢ ﺍﻟﺸﻤﺲ ﻓﻲ ﺍﻟﺴﻤﺎء‬
‫ﻧﻤﺎﺫﺝ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺣﺮﻛﺔ ﺍﻟﻘﻤﺮ‬ ‫ ﺳﺒﺐ ﺣﺮﻛﺔ ﺍﻟﻘﻤﺮ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ ﺣﺮﻛﺔ ﺍﻟﻘﻤﺮ ﻛﻤﺎ ﺗﺒﺪﻭ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ﺩﻭﺭﺍﻥ ﺍﻟﻘﻤﺮ ﺣﻮﻝ ﺍﻷﺭﺽ ﻓﻲ ﻣﺪﺍﺭ ﺩﺍﺋﺮﻱ ﻗﻠﻴﻞ‬ ‫ﻛﻮﻥ ﻣﺪﺍﺭ ﺍﻟﻘﻤﺮ ﻳﻤﻴﻞ ﻓﻘﻂ 5 ﺩﺭﺟﺎﺕ ﻋﻦ ﻣﺪﺍﺭ ﺍﻟﺸﻤﺲ ﻓﺄﻥ‬ ‫ :ﺍﻟﺒﻴﻀﺎﻭﻳﺔ ﻳﻜﺘﻤﻞ ﻓﻲ 3.72 ﻳﻮﻡ‬ ‫.1 ﺍﻟﻘﻤﺮ ﻓﻲ ﺍﻟﺴﻤﺎء ﻗﺮﻳﺐ ﻣﻦ ﻣﺴﺎﺭ ﺍﻟﺸﻤﺲ ﻭ ﻟﺬﻟﻚ ﻳﻜﻮﻥ‬ ‫ﻣﺴﺎﺭ‬ ‫ ﻣﺪﺍﺭ ﺍﻟﻘﻤﺮ ﻳﻤﻴﻞ 5 ﺩﺭﺟﺎﺕ ﻋﻦ ﻣﺪﺍﺭ ﺍﻟﺸﻤﺲ‬ ‫ .ﻋﺎﻟﻲ ﻓﻲ ﺍﻟﺼﻴﻒ ﻭ ﻣﻨﺨﻔﺾ ﻓﻲ ﺍﻟﺸﺘﺎء‬ ‫.2‬ ‫ﺣﺮﻛﺔ ﺍﻟﻘﻤﺮ ﻓﻲ ﺍﻟﻘﺒﺔ ﺍﻟﻔﻠﻜﻴﺔ ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﻨﺠﻮﻡ ﺍﻟﺜﺎﺑﺘﺔ‬ ‫ .ﻳﺘﺤﺮﻙ ﺍﻟﻘﻤﺮ ﻓﻲ ﺍﻟﺴﻤﺎء ﺣﻮﺍﻟﻲ 21 ﺩﺭﺟﺔ ﻓﻲ ﺍﻟﻴﻮﻡ‬ ‫ ﺗﺘﻜﺮﺭ ﺑﻌﺪ 3.72 ﻳﻮﻡ‬ ‫ .ﻣﺼﺪﺭ ﺍﺿﺎءﺓ ﺍﻟﻘﻤﺮ ﻫﻮ ﺍﻟﺸﻤﺲ ﻟﺬﻟﻚ ﻳﻈﻬﺮ ﺍﻟﻘﻤﺮ ﺑﺄﻁﻮﺍﺭ‬ ‫.3‬ ‫ ﺗﻐﻴﺮ ﻁﻔﻴﻒ ﻓﻲ ﺣﺠﻢ ﺍﻟﻘﻤﺮ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ ‬
‫ﻧﻤﺎﺫﺝ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺣﺮﻛﺔ ﺍﻟﻜﻮﺍﻛﺐ‬ ‫ ﺳﺒﺐ ﺣﺮﻛﺔ ﺍﻟﻜﻮﺍﻛﺐ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ ﺣﺮﻛﺔ ﺍﻟﻜﻮﺍﻛﺐ ﻛﻤﺎ ﺗﺒﺪﻭ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ :ﺗﺪﻭﺭ ﺍﻟﻜﻮﺍﻛﺐ ﺣﻮﻝ ﺍﻟﺸﻤﺲ ﻓﻲ ﻣﺪﺍﺭﺍﺕ ﺷﺒﻪ ﺩﺍﺋﺮﻳﺔ‬ ‫ﺣﺮﻛﺔ ﺍﻟﻜﻮﺍﻛﺐ ﻓﻲ ﺍﻟﺴﻤﺎء ﻫﻲ ﻣﺤﺼﻠﺔ ﻟﺤﺮﻛﺔ ﺍﻟﻜﻮﻛﺐ‬ ‫.1‬ ‫ ﺍﻟﻜﻮﺍﻛﺐ ﺍﻟﻘﺮﻳﺒﺔ ﻣﻦ ﺍﻟﺸﻤﺲ ﺗﺪﻭﺭ ﺑﺸﻜﻞ ﺃﺳﺮﻉ‬ ‫ﺣﻮﻝ ﺍﻟﺸﻤﺲ ﻭ ﺣﺮﻛﺔ ﺍﻷﺭﺽ ﺣﻮﻝ ﺍﻟﺸﻤﺲ٬ ﻣﻤﺎ ﻳﺆﺩﻱ‬ ‫.2‬ ‫ ﺍﻟﻤﺪﺍﺭﺍﺕ ﺷﺒﻪ ﺍﻟﺪﺍﺋﺮﻳﺔ ﺳﺒﺒﻬﺎ ﻁﺮﻳﻘﺔ ﺍﻟﺘﺸﻜﻞ ﺍﻻﺑﺘﺪﺍﺋﻴﺔ‬ ‫ .ﺍﻟﻰ ﺗﻐﻴﺮﺍﺕ ﻛﺒﻴﺮﺓ ﻓﻲ ﺳﺮﻋﺔ ﺍﻟﻜﻮﻛﺐ ﻭ ﺣﺮﻛﺘﻪ‬ ‫.3‬ ‫ﺍﻟﻜﻮﺍﻛﺐ ﺍﻟﺪﺍﺧﻠﻴﺔ ﺗﺒﺪﻭ ﺑﺄﻁﻮﺍﺭ ﺑﻌﻜﺲ ﺍﻟﻜﻮﺍﻛﺐ ﺍﻟﺨﺎﺭﺟﻴﺔ‬ ‫ ﻣﺴﺎﺭﺍﺕ ﺍﻟﻜﻮﺍﻛﺐ ﺩﺍﺋﻤﺎ ً ﻗﺮﻳﺒﺔ ﻣﻦ ﻣﺴﺎﺭ ﺍﻟﺸﻤﺲ‬ ‫ .ﺍﻟﺘﻲ ﺗﻜﻮﻥ ﻣﻜﺘﻤﻠﺔ ﺍﻻﺿﺎءﺓ‬ ‫.4‬ ‫ ‬ ‫ﺯﺍﻭﻳﺔ ﺗﺴﻄﺢ ﺟﻤﻴﻊ ﻣﺪﺍﺭﺍﺕ ﺍﻟﻜﻮﺍﻛﺐ ﻗﺮﻳﺒﺔ ﻣﻦ ﺯﺍﻭﻳﺔ‬ ‫ ‬ ‫ .ﺗﺴﻄﺢ ﻣﺪﺍﺭ ﺍﻷﺭﺽ‬
‫ﻣﺪﺍﺭﺍﺕ ﺑﻴﻀﻮﻳﺔ٬ ﻟﻤﺎﺫﺍ؟‬ ‫ﻣﺪﺍﺭﺍﺕ ﺍﻟﻤﺬﻧﺒﺎﺕ ﻭ ﺍﻟﻜﻮﺍﻛﺐ ﺍﻟﺼﻐﻴﺮﺓ‬
‫ﻧﻤﺎﺫﺝ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺣﺮﻛﺔ ﺍﻟﻨﺠﻮﻡ ﻭ ﺃﺟﺮﺍﻡ ﻣﺠﺮﺗﻨﺎ‬ ‫ ﺍﻟﻨﺠﻮﻡ ﺛﺎﺑﺘﺔ ﺃﻡ ﻣﺘﺤﺮﻛﺔ؟‬ ‫ﺑﺴﺒﺐ ﺍﻟﺒﻌﺪ ﺍﻟﻜﺒﻴﺮ ﻟﻠﻨﺠﻮﻡ )ﺃﻗﺮﺏ ﻧﺠﻢ 5 ﺳﻨﻴﻦ ﺿﻮﺋﻴﺔ( ﻓﺎﻥ‬ ‫ ﺣﺮﻛﺘﻬﺎ ﺑﻄﻴﺌﺔ ﺟﺪﺍً ﻭ ﻟﺬﻟﻚ ﻓﻬﻲ ﺗﻌﺘﺒﺮﺷﺒﻪ ﺛﺎﺑﺘﺔ‬ ‫ﺍﻟﻨﺠﻮﻡ ﺍﻟﻘﺮﻳﺒﺔ ﻳﺘﻐﻴﺮ ﻣﻮﻗﻌﻬﺎ ﺑﺸﻜﻞ ﻁﻔﻴﻒ ﺟﺪﺍً ﺃﺛﻨﺎء ﺩﻭﺭﺍﻥ ﺣﺮﻛﺔ ﺍﻟﻨﺠﻮﻡ ﻭ ﺃﺟﺮﺍﻡ ﺍﻟﻤﺠﺮﺓ ﻋﻠﻰ ﺍﻟﻤﻨﻈﻮﺭ ﺍﻟﺒﻌﻴﺪ‬ ‫ﻋﻠﻰ ﺍﻟﻤﺪﺍﺭ ﺍﻟﺒﻌﻴﺪ ﺗﺘﺤﺮﻙ ﻧﺠﻮﻡ ﺍﻟﻤﺠﺮﺓ ﺣﻮﻝ ﻣﺮﻛﺰ‬ ‫ ﺍﻷﺭﺽ ﺣﻮﻝ ﺍﻟﺸﻤﺲ ﺑﺴﺒﺐ ﺗﻐﻴﺮ ﻣﻜﺎﻥ ﺍﻟﺮﺅﻳﺔ‬ ‫ﺍﻟﻤﺠﺮﺓ ﻛﻤﺎ ﻭ ﺗﻌﻤﻞ ﻗﻮﻯ ﺍﻟﺠﺬﺏ ﺑﻴﻦ ﺍﻟﻨﺠﻮﻡ ﻋﻠﻰ ﺗﻐﻴﻴﺮ‬ ‫ﺑﺎﻗﻲ ﺍﻟﻨﺠﻮﻡ ﻭ ﺃﺟﺮﺍﻡ ﻣﺠﺮﺓ ﺩﺭﺏ ﺍﻟﺘﺒﺎﻧﺔ ﻛﺎﻟﺴﺪﻡ ﻭ ﺍﻟﻌﻨﺎﻗﻴﺪ‬ ‫ .ﻣﻮﺍﻗﻌﻬﺎ ﺍﻟﻨﺴﺒﻴﺔ‬ ‫ ﺍﻟﻨﺠﻤﻴﺔ ﺛﺎﺑﺘﺔ ﻟﻌﺸﺮﺍﺕ ﺁﻻﻑ ﺍﻟﺴﻨﻴﻦ ﺍﻟﻘﺎﺩﻣﺔ‬ ‫ ‬ ‫ ‬
‫ﻧﻤﺎﺫﺝ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺣﺮﻛﺔ ﺍﻟﻤﺠﺮﺍﺕ ﻭ ﺍﻟﻜﻮﻥ ﺍﻟﻤﻨﻈﻮﺭ‬ ‫ ﺍﻟﻤﺠﺮﺍﺕ ﺛﺎﺑﺘﺔ ﺃﻡ ﻣﺘﺤﺮﻛﺔ‬ ‫ﺑﺴﺒﺐ ﺍﻟﺒﻌﺪ ﺍﻟﻜﺒﻴﺮ ﻟﻠﻤﺠﺮﺍﺕ )ﺃﻗﺮﺏ ﻣﺠﺮﺓ 5.2 ﻣﻠﻴﻮﻥ‬ ‫ﺳﻨﺔ ﺿﻮﺋﻴﺔ( ﻓﺎﻥ ﺣﺮﻛﺘﻬﺎ ﺑﻄﻴﺌﺔ ﺟﺪﺍً ﻭ ﻟﺬﻟﻚ ﻓﻬﻲ‬ ‫ .ﺗﻌﺘﺒﺮ ﺛﺎﺑﺘﺔ‬ ‫ﺍﻟﻤﺠﺮﺍﺕ ﺍﻟﻘﺮﻳﺒﺔ ﻓﻲ ﻋﻨﻘﻮﺩ ﺍﻟﻤﺠﺮﺍﺕ ﺍﻟﻤﺤﻠﻲ ﺗﺘﺤﺮﻙ‬ ‫ﺑﺤﺴﺐ ﺗﻔﺎﻋﻞ ﻗﻮﻯ ﺍﻟﺠﺬﺏ ﺑﻴﻨﻬﺎ ﺃﻣﺎ ﺍﻟﻤﺠﺮﺍﺕ ﺍﻟﺒﻌﻴﺪﺓ‬ ‫ ﺣﺮﻛﺔ ﺍﻟﻤﺠﺮﺍﺕ ﻓﻲ ﺍﻟﻤﺤﺎﻛﻴﺎﺕ ﺍﻟﺤﺎﺳﻮﺑﻴﺔ ﺍﻟﺮﺻﺪﻳﺔ‬ ‫ ﻓﻬﻲ ﻓﻲ ﺍﺑﺘﻌﺎﺩ ﺩﺍﺋﻢ‬ ‫ ‪ J‬ﻣﻮﺍﻗﻌﻬﺎ ﺛﺎﺑﺘﺔ ﻭ ﻻ ﺗﺘﻐﻴﺮ ﺃﺑﺪﺍً‬ ‫ ‬ ‫ ‬
‫ﻣﺜﺎﻝ ﺣﺴﺎﺑﻲ‬ ‫ﺣﺴﺎﺏ ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ ﺍﻟﻴﻮﻡ‬ ‫ﻧﻈﺎﻡ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺸﻤﺴﻲ ﻟﻠﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺃﻱ ﻧﻈﺎﻡ ﺍﺣﺪﺍﺛﻴﺎﺕ ﻧﺴﺘﻌﻤﻞ ﻟﻠﺤﺴﺎﺏ ؟؟‬ ‫ﻧﻈﺎﻡ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻻﺳﺘﻮﺍﺋﻲ )ﺍﻟﻌﺎﻟﻤﻲ( ﺃﻭ ﺍﻟﺴﻤﺘﻲ‬ ‫ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ ﺍﻟﻨﻬﺎﺋﻲ ﺑﺄﻱ ﺍﺣﺪﺍﺛﻴﺎﺕ ﻳﻔﻀﻞ ﻋﺮﺿﻪ؟‬ ‫))ﻟﻤﻮﻗﻊ ﺭﺻﺪ ﻣﺤﺪﺩ‬ ‫‪ epoch‬ﻣﺎ ﻫﻲ ﻧﻘﻄﺔ ﺍﻟﺒﺪء ﻟﻠﺤﺴﺎﺏ؟‬ ‫ﻧﺨﺘﺎﺭ 1-1-0991 ﺣﻴﺚ ﻛﺎﻧﺖ ﺍﻟﺸﻤﺲ ﻋﻠﻰ 4.972‬ ‫ﺩﺭﺟﺔ ﻋﻦ ﻧﻘﻄﺔ ﺍﻟﺒﺪﺍﻳﺔ ﻟﻼﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺸﻤﺴﻴﺔ )ﻭ ﻫﻲ‬ ‫ﻧﻘﻄﺔ ﺍﻻﻋﺘﺪﺍﻝ ﺍﻟﺮﺑﻴﻌﻲ( ﺃﻣﺎ ﺍﻻﺣﺪﺍﺛﻲ ﺍﻟﺜﺎﻧﻲ ﻓﻬﻮ ﺻﻔﺮ‬ ‫‪ J‬ﻷﻥ ﺍﻟﺸﻤﺲ ﻋﻠﻰ ﺍﻟﺨﻂ ﺍﻟﻜﺴﻮﻓﻲ ﺗﻤﺎﻣﺎ ً‬
‫ﻣﺜﺎﻝ ﺣﺴﺎﺑﻲ‬ ‫ﺣﺴﺎﺏ ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ ﺍﻟﻴﻮﻡ‬ ‫ﻛﻢ ﻋﺪﺩ ﺍﻷﻳﺎﻡ ﻣﻨﺬ 1-1-0991 ﺣﺘﻰ ﺍﻟﻴﻮﻡ ﺍﻟﺴﺎﻋﺔ ﺍﻟﺴﺎﺑﻌﺔ ﻣﺴﺎءﺍً؟‬ ‫ﻋﺪﺩ ﺍﻷﻳﺎﻡ ﻓﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺤﺎﻟﻴﺔ ﻣﻨﺬ 1 ﻛﺎﻧﻮﻥ ﺛﺎﻧﻲ + ﻋﺪﺩ ﺍﻟﺴﻨﻴﻦ ﻣﻨﺬ 0991‬ ‫ * 563 + ﻋﺪﺩ ﺍﻟﺴﻨﻮﺍﺕ ﺍﻟﻜﺒﻴﺴﺔ ﻣﻨﺬ 0991‬ ‫ ‬ ‫ﻳﻮﻡ ﻣﻨﺬ 1-1-0991 ﺣﺘﻰ ﺍﻟﻴﻮﻡ 9918 = 5 + 653 * 22 + 461 =‬ ‫ﻛﻢ ﺩﻭﺭﺓ ﺩﺍﺭﺕ ﺍﻟﺸﻤﺲ ﻣﻨﺬ 1-1-0991 ﺣﺘﻰ ﺍﻟﻴﻮﻡ؟ )ﺗﻜﻤﻞ ﺍﻟﺸﻤﺲ ﺩﻭﺭﺓ ﻛﺎﻣﻠﺔ‬ ‫)063 ﺩﺭﺟﺔ ﻓﻲ 42.563 ﻳﻮﻡ‬ ‫ﻋﺪﺩ ﺍﻷﻳﺎﻡ / 191242.563 = 811844.22 ﺩﻭﺭﺓ. ﺍﻟﺪﻭﺭﺍﺕ ﺍﻟﻜﺎﻣﻠﺔ ﻻ ﺗﻬﻤﻨﺎ ﻷﻧﻬﺎ ﺗﻌﻮﺩ ﺑﺎﻟﺸﻤﺲ ﺍﻟﻰ ﻧﻔﺲ‬ ‫ﺍﻟﻤﻮﻗﻊ٬ ﺃﻣﺎ ﺍﻟﻜﺴﺮ ﺍﻟﻌﺸﺮﻱ 811844.0 ﻓﻬﻮ ﺍﺯﺍﺣﺔ ﺍﻟﺸﻤﺲ ﻋﻦ ﺍﻟﻤﻮﻗﻊ ﺍﻟﺬﻱ ﻛﺎﻧﺖ ﻓﻴﻪ ﺍﻟﺸﻤﺲ ﻓﻲ‬ ‫1-1-0991 ﺣﺘﻰ ﺍﻟﻴﻮﻡ‬ ‫ﺍﺯﺍﺣﺔ ﺍﻟﺸﻤﺲ ﺑﺎﻟﺪﺭﺟﺎﺕ ﺑﺎﻟﻨﺴﺒﺔ ﺍﻟﻰ ﺍﻟﻤﻮﻗﻊ ﺍﻟﻤﺮﺟﻌﻲ = 811844.0 * 063 = 84223.161 ﺩﺭﺟﺔ ﻭ ﻫﻲ‬ ‫ﺍﺯﺍﺣﺔ ﺍﻟﺸﻤﺲ ﺑﺎﻟﺪﺭﺟﺎﺕ ﻋﻦ ﺍﻟﻤﻮﻗﻊ ﺍﻟﻤﺮﺟﻌﻲ‬
‫ﻣﺜﺎﻝ ﺣﺴﺎﺑﻲ‬ ‫ﺣﺴﺎﺏ ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ ﺍﻟﻴﻮﻡ‬ ‫ﻛﻢ ﺍﺯﺍﺣﺔ ﺷﻤﺲ ﺍﻟﻴﻮﻡ ﺑﺎﻟﺪﺭﺟﺎﺕ ﻋﻦ ﻧﻘﻄﺔ ﺍﻻﻋﺘﺪﺍﻝ ﺍﻟﺮﺑﻴﻌﻲ؟ )ﻭ‬ ‫)ﻫﻲ ﻧﻘﻄﺔ ﺍﻟﺒﺪﺍﻳﺔ ﻓﻲ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺸﻤﺴﻴﺔ‬ ‫= 063 - 387527.044 = 84223.161 + 303304.972‬ ‫ﺩﺭﺟﺔ 387527.08‬ ‫ﻟﻜﻨﻨﺎ ﻧﻌﻠﻢ ﺃﻥ ﻣﺪﺍﺭ ﺍﻟﺸﻤﺲ ﻟﻴﺲ ﺩﺍﺋﺮﻱ ﺑﻞ ﺑﻴﻀﻮﻱ٬ ﺃﻱ ﺃﻥ ﺍﻟﺸﻤﺲ ﻻ ﺗﺘﺤﺮﻙ‬ ‫ﻓﻲ ﺍﻟﺴﻤﺎء ﻧﻔﺲ ﺍﻟﻤﺴﺎﻓﺔ ﻟﻜﻞ ﻳﻮﻡ ﺑﻞ ﺗﻜﻮﻥ ﺃﺣﻴﺎﻧﺎ ً ﺃﺳﺮﻉ ﻭ ﺃﺣﻴﺎﻧﺎ ً ﺃﺑﻄﺄ٬ ﻟﺬﻟﻚ‬ ‫:ﻧﻌﻮﺽ ﺍﻟﺨﻠﻞ ﻟﻠﻤﺪﺍﺭ ﺍﻟﺒﻴﻀﻮﻱ ﺑﺎﺳﺘﺨﺪﺍﻡ ﻣﻌﺎﺩﻟﺔ ﺍﻟﺘﺼﺤﻴﺢ ﻟﻠﻤﺪﺍﺭ ﺍﻟﺒﻴﻀﻮﻱ‬ ‫ﺍﻟﻤﻮﻗﻊ ﺍﻟﻤﻄﻠﻮﺏ ﻋﻠﻰ ﺍﻟﻘﻄﻊ ﺍﻟﻨﺎﻗﺺ = ﺍﻟﻤﻮﻗﻊ ﺍﻟﻤﻄﻠﻮﺏ ﻋﻠﻰ ﺍﻟﺪﺍﺋﺮﺓ + )063/ﺑﺎﻱ( × ﻣﻌﺎﻣﻞ ﺍﻟﺒﻴﻀﺎﻭﻳﺔ ﻟﻠﻤﺪﺍﺭ‬ ‫ )× ﺟﻴﺐ)ﺍﻟﻤﻮﻗﻊ ﻋﻠﻰ ﺍﻟﺪﺍﺋﺮﺓ - ﻣﻮﻗﻊ ﺍﻟﺤﻀﻴﺾ ﻋﻠﻰ ﺍﻟﺪﺍﺋﺮﺓ‬ ‫ )ﺑﺎﻱ( × 317610.0 × ﺟﻴﺐ)387527.08 - 224867.282/063( + 387527.08‬ ‫ﺩﺭﺟﺔ 935444.18 = 657817.0 + 387527.08 =‬ ‫ﻻﺣﻆ ﺃﻥ ﻗﻴﻤﺔ ﺍﻟﺘﺼﺤﻴﺢ ﻟﻠﻤﺪﺍﺭ ﺍﻟﺒﻴﻀﺎﻭﻱ ﺑﻠﻐﺖ ﻓﻘﻂ 7.0 ﺩﺭﺟﺔ ﻓﻘﻂ ﻭ ﺫﻟﻚ ﻛﻮﻥ ﻣﺪﺍﺭ ﺍﻷﺭﺽ ﺷﺒﻴﻪ ﺑﺎﻟﺪﺍﺋﺮﺓ‬ ‫)ﻫﻜﺬﺍ ﻧﻜﻮﻥ ﻋﺮﻓﻨﺎ ﺗﻤﺎﻣﺎ ً ﺍﺣﺪﺛﻴﺎﺕ ﺷﻤﺲ ﺍﻟﻴﻮﻡ ﺑﺎﻟﻨﻈﺎﻡ ﺍﻻﺣﺪﺍﺛﻲ ﺍﻟﺸﻤﺴﻲ ﻭ ﻫﻲ: )935444.18٬ 0‬
‫ﻣﺜﺎﻝ ﺣﺴﺎﺑﻲ‬ ‫ﺣﺴﺎﺏ ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ ﺍﻟﻴﻮﻡ‬ ‫:ﻧﺴﺘﻄﻴﻊ ﺍﻷﻥ ﺍﻟﺘﺤﻮﻳﻞ ﻣﻦ ﺍﻻﺣﺪﺍﺛﻲ ﺍﻟﺸﻤﺴﻲ ﺍﻟﻰ ﺃﻱ ﺍﺣﺪﺍﺛﻲ ﻧﺮﻳﺪ‬ ‫ :ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻻﺳﺘﻮﺍﺋﻴﺔ ﻟﺸﻤﺲ ﺍﻟﻴﻮﻡ‬ ‫ ﺍﻟﻄﺎﻟﻊ ﺍﻟﻤﺴﺘﻘﻴﻢ: 11886.08 ﺩﺭﺟﺔ = 702973.5 ﺳﺎﻋﺔ‬ ‫ﺍﻟﻤﻴﻞ ﺍﻻﺳﺘﻮﺍﺋﻲ: 816161.32 ﺩﺭﺟﺔ‬ ‫ :ﺗﺤﻮﻳﻞ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻻﺳﺘﻮﺍﺋﻴﺔ ﺍﻟﻰ ﻁﺮﻳﻘﺔ ﺍﻟﻌﺮﺽ ﺑﺎﻟﺪﻗﺎﺋﻖ ﻭ ﺍﻟﺜﻮﺍﻧﻲ ﺍﻟﻘﻮﺳﻴﺔ‬ ‫ ﺍﻟﻄﺎﻟﻊ ﺍﻟﻤﺴﺘﻘﻴﻢ: 702973.5 ﺳﺎﻋﺔ = 54ﺙ 22ﺩ 5ﺱ‬ ‫ ‪ᵒ‬ﺍﻟﻤﻴﻞ ﺍﻻﺳﺘﻮﺍﺋﻲ: 816161.32 ﺩﺭﺟﺔ =9’ 14” 32‬
‫
ﻣﺎ ﺳﺒﺐ ﺍﻻﺧﺘﻼﻑ ﺍﻟﻄﻔﻴﻒ ﻓﻲ ﺍﻟﻨﺘﻴﺠﺔ؟‬ ‫ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ ﺍﻟﻴﻮﻡ ﺍﻟﺴﺎﻋﺔ 00:0 ﻓﻲ ﺳﺘﻼﺭﻳﻮﻡ‬ ‫ﻣﺎﺫﺍ ﻧﻀﻴﻒ ﻟﻠﺤﺴﺎﺑﺎﺕ ﺍﺫﺍ ﺃﺭﺩﻧﺎ ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ‬ ‫ﻫﺬﻩ ﺍﻟﻠﺤﻈﺔ؟‬
‫ﺷﻜﺮﺍً ﻟﻜﻢ‬ ‫ﺃﺳﺌﻠﺔ؟‬

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حساب حركة الأجرام السماوية

  • 1. ‫ﺣﺴﺎﺏ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﻣﺒﺎﺩﺉ ﺍﻟﻬﻨﺪﺳﺔ ﺍﻟﻔﺮﺍﻏﻴﺔ ﻟﺤﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻭ ﺣﺴﺎﺏ ﺍﻟﻈﻮﺍﻫﺮ ﺍﻟﻔﻠﻜﻴﺔ ﻓﻲ ﺍﻟﺴﻤﺎء ﻟﻠﺮﺍﺻﺪ ﺍﻟﻔﻠﻜﻲ ﺍﻟﻬﺎﻭﻱ‬ ‫ﻭ ﺍﻟﻤﺤﺘﺮﻑ‬
  • 2. ‫ﺃﺳﻠﻮﺏ ﺍﻟﻌﺮﺽ‬ ‫ﻫﺪﻑ ﺍﻟﻤﺤﺎﺿﺮﺓ‬ ‫ﺍﻟﻤﺤﺎﺿﺮ‬ ‫ﻣﺒﺘﺪﺉ‬ ‫ﻣﺘﻮﺳﻂ‬ ‫ﻣﺘﻘﺪﻡ‬ ‫ ‬ ‫ ﻣﻬﻨﺪﺱ ﺍﺗﺼﺎﻻﺕ ﻭ ﺣﺎﺳﻮﺏ‬ ‫ﺧﺒﻴﺮ‬ ‫ﻫﺎﻭﻱ ﻓﻠﻚ‬ ‫ﺍﻟﻤﻌﻠﻮﻣﺎﺕ ﺍﻟﺴﺎﺑﻘﺔ‬ ‫ﻣﺪﺓ ﺍﻟﻌﺮﺽ‬ ‫۰٦‬ ‫ﻓﻴﺰﻳﺎء‬ ‫ﺩﻕﻱﻕﺓ‬ ‫ﺭﻳﺎﺿﻴﺎﺕ‬ ‫ﻓﻠﻚ‬ ‫ﺩﻗﻴﻘﺔ ﻧﻘﺎﺵ۰۲‬ ‫ﺑﻌﺪ ﺍﻟﻤﺤﺎﺿﺮﺓ‬
  • 3. ‫ﺃﺟﻨﺪﺓ ﺍﻟﻌﺮﺽ‬ ‫ﺟﺪﻭﻝ ﺍﻟﻤﺤﺎﺿﺮﺓ‬ ‫ ﺍﻟﻨﻤﻮﺫﺝ ﺍﻟﺮﻳﺎﺿﻲ‬ ‫ ﺍﻟﻔﻀﺎء ﺍﻻﻗﻠﻴﺪﻱ ﻟﻠﻜﻮﻥ‬ ‫ ﺗﻔﺎﻋﻞ ﺍﻷﺟﺮﺍﻡ‬ ‫ ﺍﻟﺤﺴﺎﺏ ﺍﻟﻔﻠﻜﻲ‬ ‫ ﺍﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ ﺍﻟﺰﻣﻦ ﻭ ﺍﻟﻮﻗﺖ‬ ‫ﻧﻤﺎﺫﺝ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺗﻄﺒﻴﻖ ﻋﻤﻠﻲ: ﺣﺴﺎﺏ ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ‬
  • 4. ‫ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﺗﺎﺭﻳﺨﻴﺎ ً‬ ‫ﺣﺮﻛﺔ ﺍﻟﺴﻤﺎء ﻭ ﺍﻟﻌﻤﻞ ﺍﻟﺴﺎﺑﻖ‬ ‫ ﺍﻟﻠﻐﺰ ﺍﻟﺘﺎﺭﻳﺨﻲ‬ ‫ ﺣﺮﻛﺔ ﺍﻟﺴﻤﺎء ﻭ ﺍﻷﺟﺮﺍﻡ‬ ‫ﻓﻚ ﺷﻴﻔﺮﺓ ﺣﺮﻛﺔ ﺍﻟﺴﻤﺎء ﻛﺎﻧﺖ ﺍﻟﺴﺆﺍﻝ ﺍﻷﺑﺮﺯ ﻭ‬ ‫ﺍﻟﻨﻈﺮ ﺍﻟﻰ ﺃﻋﻠﻰ ﺳﻮﺍء ﻟﻴﻼً ﺃﻭ ﻧﻬﺎﺭﺍً ﻛﻔﻴﻞ‬ ‫ .ﺍﻷﻫﻢ ﻓﻲ ﻣﺴﻴﺮﺓ ﺍﻟﻌﻠﻢ ﻣﻨﺬ ﻓﺠﺮ ﺍﻟﺘﺎﺭﻳﺦ‬ ‫ﺑﺮﺅﻳﺔ ﺍﻟﺸﻤﺲ ﻭ ﺍﻟﻘﻤﺮ ﻭ ﺍﻟﻜﻮﺍﻛﺐ ﻭ ﺍﻟﻨﺠﻮﻡ‬ ‫ﻣﻌﺮﻓﺘﻨﺎ ﺍﻟﺤﺎﻟﻴﺔ ﻫﻲ ﻧﺘﻴﺠﺔ ﺗﺮﺍﻛﻢ ﺃﻋﻤﺎﻝ ﺍﻟﺒﺤﺜﻴﻦ‬ ‫ﻭ ﺃﺟﺮﺍﻡ ﺍﻟﺴﻤﺎء ﺍﻟﺒﻌﻴﺪﺓ ﻓﻲ ﺣﺮﻛﺔ ﻣﺘﻮﺍﺻﻠﺔ‬ ‫.ﺍﻟﺴﺎﺑﻘﻴﻦ‬
  • 5. ‫ﺍﻟﻨﻤﻮﺫﺝ ﺍﻻﻗﻠﻴﺪﻱ ﻷﺑﻌﺎﺩ ﺍﻟﺴﻤﺎء‬ ‫ﺍﻟﻔﻀﺎء ﺭﻗﻤﻴﺎ ً‬ ‫2=‪t‬‬ ‫1=‪t‬‬ ‫*‬ ‫*‬ ‫ ﺍﻟﺰﻣﻦ ﻛﻤﺘﻐﻴﺮ ﻣﺴﺘﻘﻞ‬ ‫ ﺛﻼﺛﺔ ﺃﺑﻌﺎﺩ ﻣﺘﻌﺎﻣﺪﺓ‬ ‫ﻭﺻﻒ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺪﻳﻜﺎﺭﺗﻴﺔ ﻟﻠﺠﺮﻡ ﺍﻟﺴﻤﺎﻭﻱ‬ ‫ ﺍﻟﺤﺎﺟﺔ ﻟﻨﻤﻮﺫﺝ ﺭﻗﻤﻲ ﻟﻮﺻﻒ ﻣﻜﺎﻥ ﺍﻟﺠﺮﻡ‬ ‫ ﺑﺪﻻﻟﺔ ﺍﻟﺰﻣﻦ‬ ‫ﺍﺻﻄﻼﺡ ﺛﻼﺛﺔ ﻣﺘﻐﻴﺮﺍﺕ ﻋﻤﻮﺩﻳﺔ ﻋﻠﻰ ﺑﻌﻀﻬﺎ‬ ‫ﺍﻟﺰﻣﻦ ﻣﺘﻐﻴﺮ ﻣﺴﺘﻘﻞ ﻻ ﻳﺘﺄﺛﺮ ﺑﺘﻐﻴﺮ ﺍﺣﺪﺍﺛﻴﺎﺕ‬ ‫ ))ﻣﺴﺘﻮﻯ ﺩﻳﻜﺎﺭﺗﻲ ﺛﻼﺛﻲ ﺍﻷﺑﻌﺎﺩ‬ ‫ﺍﻷﺟﺮﺍﻡ‬ ‫ ﺍﻟﺘﻐﻴﺮ ﻓﻲ ﻗﻴﻤﺔ ﺑُﻌﺪ ﻣﻨﻔﺼﻞ ﻋﻦ ﺑﺎﻗﻲ ﺍﻷﺑﻌﺎﺩ‬ ‫ﺍﻟﻨﻈﺮﻳﺎﺕ ﺍﻻﻗﻠﻴﺪﻳﺔ ﻣﻨﻄﺒﻘﺔ ﻣﺜﻞ ﻓﻴﺜﺎﻏﻮﺭﺱ‬
  • 6. ‫ا%4#3ذ1 ا0/.-,ي *)("د ا%$#"ء‬ !"#$% ‫ر,5 ا43$21*ات 0/*.' ً ,'+$*ا('ت‬ t=2 t=1 * x2 + y2 = 1 * dx / dt = value dy / dt = value dz / dt = value x, y, z = f (t ) 56"78 – ‫@.? 0>,ا=-"ت ا%;:م‬A#%‫ ا‬B-C%‫ا‬ ?()‫-:ات ا*ر‬DA#%‫: ا‬FG ‫-:ات‬DA#%‫ ا‬ ‫! ا4:*م‬P*Q4 ID'.*4‫ذج ا‬G3J4‫<ح ا‬WX‫ا‬ !"#$% 71+ ‫ا43$21*ات ا4@.?'ر>1! ا4=<;! 4":*م ذات‬ ID'.*4‫ [<ل ا4*,5 ا4:/*ي ا‬L% 7$. ‫3'وي‬N4‫ا‬ ‫ت‬A@B%) CD'E> 71+ ‫د‬G0‫ و‬IJB. '3% ،L%M4‫4! ا‬A@, L%M4‫4! ا‬A@, ‫4"3$21*ات ا4@.?'ر>1! ا4=<;! 4":*م‬ 7$. L%M"4 !/NJ4', !.‫3'و‬N4‫0*ام ا‬O‫! ا‬P*Q4 (!1RQ4 !1('=4‫و4 و ا‬O‫ ا4@ر0! ا‬L% ‫'+$*ا('ت‬P C%'?$4‫ و ا‬CD'E$4', 'SJT *1/B$4‫ا‬
  • 7. 5CA$H :-I :-DA#J KHL%‫ا‬ ∂t / ∂x = value C]$N% *12$3P L%M"4 C]$N34‫ذج ا‬G3J4‫^@ود ا‬ ∂t / ∂y = value ∂t / ∂x = 0 ∂t / ∂z = value ∂t / ∂y = 0 ∂t / ∂z = 0 f (t ) = t + ∂t / ∂x + ∂t / ∂y + ∂t / ∂z f (t ) is independent of x, y, z ?M"N%‫-? ا‬F$4%‫ - ا‬PCA$H Q-% ً "R,M‫ ر‬KHL%‫ ا%4#3ذ1 ا0/.-,ي ا‬ST 5CA$H :-DA#J KHL%‫ ا‬ ً *;_$. ‫*ا`1! 4":*م‬E4‫^@ا;1'ت ا‬A‫ ا‬Ia b.*N4‫@ ا4$21* ا‬JT L% ‫ أي‬Ia *12$4‫/! ا4 ا‬NJ4', L%M4‫+13! >21* ا‬ ً<]$N% ]/. A ‫ و‬L%M4‫ .%$21* ا‬ '3% ،ً‫*ا‬EX ‫'وي‬N> !;<=4‫*ا`1! ا‬E4‫ا43$21*ات ا‬ c$J. !1"$?4‫0*ام ا‬d4 !14'B4‫'ت ا‬T*N4‫ ا‬Ia !X'[ ‫ت‬A'^ Ia *12> ‫ .$_;* ,_ي‬A ‫ و‬C]$N% L%M4‫ أن ا‬IJB. e,'=4‫@ ا‬f'g3"4 !/NJ4', ‫ %?'ن ا4:*م‬Ia *12> 'SJT ‫@ة‬f'g34‫'رات ا‬k‫ ا‬b130 Ia ‫! ا4:*م‬P*^
  • 8. ‫ﺍﻟﻜﺘﻠﺔ ﺍﻟﻜﺒﻴﺮﺓ ﻟﻠﻌﻨﺎﻗﻴﺪ ﺍﻟﻤﺠﺮﻳﺔ‬ ‫ﺍﻟﻨﺴﺒﻴﺔ ﺍﻟﻌﺎﻣﺔ ﻭ ﺗﻐﻴﺮ ﻣﻜﺎﻥ ﺍﻟﺠﺮﻡ ﺍﻟﻤﺮﺻﻮﺩ‬
  • 9. ‫ﺕﻓﺎﻋﻞ ﺍﻷﺟﺮﺍﻡ‬ ‫ﻗﻮﺓ ﺍﻟﺠﺬﺏ‬ ‫%#'درا4$21* ‪GQ% Ia‬ر دوران ‪'WT‬رد‬ ‫%]@ار ا4$21* );'(1! +‪*+ C?4 !1lG‬ن‬ ‫ا4‪m/N‬‬ ‫)0‪I('14G‬‬ ‫96.0± 36.135‬ ‫ا4‪ @g‬ا4:‪ L% I,n‬ا4?‪G‬ا‪mP‬‬ ‫ا‪*[O‬ى‬ ‫4520.0‬ ‫‪@T‬م %='41! ‪*P‬و.! ا4‪p3g‬‬ ‫2‪m1* m‬‬ ‫40.0± 89.24‬ ‫ا4‪ !1/NJ‬ا4‪!%'B‬‬ ‫‪G‬‬ ‫2‬ ‫96.0±46.475‬ ‫ا43:3‪G‬ع‬ ‫‪d‬‬ ‫56.0±01.475‬ ‫ا4‪ cr'$J‬ا4*‪!.@X‬‬ ‫ ﻣﺠﺎﻝ ﺟﺬﺑﻲ ﺃﻡ ﺍﻧﺤﻨﺎء ﻓﻲ ﺍﻟﺰﻣﻜﺎﻥ؟‬ ‫ ﺃﺭﺑﻌﺔ ﻗﻮﻯ ﻓﻲ ﺍﻟﻜﻮﻥ ﺗﺴﺒﺐ ﺣﺮﻛﺔ ﺍﻷﺟﺴﺎﻡ‬ ‫ﺗﻔﺴﻴﺮ ﺍﻟﺠﺎﺫﺑﻴﺔ ﻛﻤﺠﺎﻝ ﺟﺬﺑﻲ ﻳﻌﺘﺒﺮ ﻛﺎﻓﻴﺎ ً ﻓﻲ ﻣﻌﻈﻢ‬ ‫ ﻗﻮﺓ ﺍﻟﺠﺬﺏ ﺍﻷﻭﻟﻰ ﻭ ﻓﻲ ﺃﻏﻠﺐ ﺍﻟﺤﺎﻻﺕ ﺍﻟﻮﺣﻴﺪﺓ ﺍﻟﻤﺴﺒﺒﺔ‬ ‫ ﺣﺴﺎﺑﺎﺕ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ ﻟﺘﻔﺎﻋﻞ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻣﻊ ﺑﻌﻀﻬﺎ ﺍﻟﺒﻌﺾ‬ ‫ﺗﺒﺪﺃ ﺍﻟﺤﺎﺟﺔ ﺍﻟﻰ ﺍﻟﻨﺴﺒﻴﺔ ﺍﻟﻌﺎﻣﺔ ﻓﻲ ﺍﻟﻤﺠﺎﻻﺕ ﺍﻟﺠﺬﺑﻴﺔ‬ ‫ﺗﺘﻨﺎﺳﺐ ﻁﺮﺩﻳﺎ ً ﻣﻊ ﻛﺘﻠﺔ ﺍﻟﺠﺮﻣﻴﻦ ﺍﻟﻤﺘﻔﺎﻋﻠﻴﻦ ﻭ ﻋﻜﺴﻴﺎ ً ﻣﻊ‬ ‫ﺍﻟﻜﻴﺒﺮﺓ ﻛﺤﺎﻟﺔ ﻋﻄﺎﺭﺩ ﻭ ﺣﻮﻝ ﺍﻟﺜﻘﻮﺏ ﺍﻟﺴﻮﺩﺍء‬ ‫ﻣﺮﺑﻊ ﺍﻟﻤﺴﺎﻓﺔ ﺑﻴﻨﻬﻤﺎ‬
  • 10. ‫ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ‬ ‫ﺍﻷﺟﺮﺍﻡ ﺍﻟﺜﻨﺎﺋﻴﺔ ﻭ ﺍﻟﻤﺘﻌﺪﺩﺓ‬ ‫ ﺍﻷﺟﺮﺍﻡ ﺍﻟﻤﺘﻌﺪﺩﺓ ﺗﺤﺘﺎﺝ ﺍﻟﻰ ﻣﺤﺎﻛﺎﺓ ﺣﺎﺳﻮﺑﻴﺔ‬ ‫ ﻗﻮﺓ ﺍﻟﺠﺬﺏ ﺗُﻨﺘﺞ ﺩﻭﺭﺍﻧﺎ ً ﺑﻴﻀﺎﻭﻳﺎ ً‬ ‫ً‬ ‫ﺣﻞ ﻗﻮﺓ ﺍﻟﺠﺬﺏ ﻟﺠﺮﻣﻴﻦ ﻳُﻨﺘﺞ ﺗﻔﺎﻋﻞ ﺍﻟﺠﺮﻣﻴﻦ ﺑﺎﻟﺪﻭﺭﺍﻥ ﺍﻟﺪﺍﺋﺮﻱ .ﺗﺘﻔﺎﻋﻞ ﺟﻤﻴﻊ ﺍﻷﺟﺮﺍﻡ ﻣﻊ ﺑﻌﻀﻬﺎ ﺟﺬﺑﻴﺎ‬ ‫ﻳﺘﻢ ﺣﺴﺎﺏ ﺍﻟﺤﺮﻛﺔ ﺍﻟﻨﻬﺎﺋﻴﺔ ﻟﻸﺟﺮﺍﻡ ﻣﻦ ﺧﻼﻝ‬ ‫ .ﺣﻮﻝ ﻣﺮﻛﺰﺍﻟﻜﺘﻠﺔ ﻷﻥ ﺍﻟﻘﻮﺓ ﺗﻨﺘﺞ ﺗﺴﺎﺭﻉ ﺩﻭﺭﺍﻥ‬ ‫ﺍﻟﻤﺤﺎﻛﺎﺓ ﺍﻟﺤﺎﺳﻮﺑﻴﺔ ﻟﻜﺘﻞ ﺟﻤﻴﻊ ﺍﻷﺟﺮﺍﻡ‬ ‫ﺍﻟﺠﺮﻡ ﺫﻭ ﺍﻟﻜﺘﻠﺔ ﺍﻟﺼﻐﻴﺮﺓ ﻳﺪﻭﺭ ﺑﺸﻜﻞ ﺑﻴﻀﻮﻱ ﺣﻮﻝ ﺍﻟﺠﺮﻡ ﺫﻭ‬ ‫.ﺑﺎﻻﺿﺎﻓﺔ ﺍﻟﻰ ﺍﻟﺤﺎﻟﺔ ﺍﻻﺑﺘﺪﺍﺋﻴﺔ ﻟﻠﻨﻈﺎﻡ‬ ‫ .ﺍﻟﻜﺘﻠﺔ ﺍﻟﻜﺒﻴﺮﺓ ﻭ ﺍﻟﺬﻱ ﻳﻜﻮﻥ ﻓﻲ ﺍﺣﺪﻯ ﺑﺆﺭﺗﻲ ﺍﻟﻘﻄﻊ ﺍﻟﻨﺎﻗﺺ‬ ‫ .ﺍﻟﺤﺎﻟﺔ ﺍﻻﺑﺘﺪﺍﺋﻴﺔ ﻟﻠﻨﻈﺎﻡ ﻭ ﺍﻟﻤﺆﺛﺮﺍﺕ ﺍﻟﺨﺎﺭﺟﻴﺔ ﺗﺤﺪﺩ ﺷﻜﻞ ﺍﻟﺘﻔﺎﻋﻞ‬
  • 11. ‫ﻧﺘﻴﺠﺔ ﺗﻔﺎﻋﻞ ﻗﻮﺓ ﺍﻟﺠﺬﺏ ﺑﻴﻨﻬﺎ‬ ‫ﺩﻭﺭﺍﻥ ﻣﻠﻴﺎﺭﺍﺕ ﺍﻟﻨﺠﻮﻡ ﻓﻲ ﺍﻟﻤﺠﺮﺓ‬
  • 12. ‫ﺍﻟﻤﺴﺎﻓﺎﺕ ﻭ ﺍﻷﺣﺠﺎﻡ ﻟﻸﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻓﻲ ﺍﻟﻜﻮﻥ‬ ‫ﻣﺴﺎﻓﺎﺕ ﻫﺎﺋﻠﺔ ﺗﺠﻌﻞ ﺍﻷﺣﺠﺎﻡ ﺻﻐﻴﺮﺓ‬ ‫ ﺍﻟﻨﻤﻮﺫﺝ ﺍﻟﻨﻘﻄﻲ ﻟﺤﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ ﺃﺣﺠﺎﻡ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺣﺴﺎﺏ ﻣﺪﺍﺭﺍﺕ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻳﺘﻢ ﻋﻠﻰ ﺍﻓﺘﺮﺍﺽ‬ ‫ﻣﻊ ﺃﻥ ﻛﻮﺍﻛﺐ ﺍﻟﻤﺠﻤﻮﻋﺔ ﺍﻟﺸﻤﺴﻴﺔ ﻭ ﺍﻟﻨﺠﻮﻡ ﻣﺜﻼً ﻫﻲ‬ ‫ .ﺃﻧﻬﺎ ﺃﺟﺮﺍﻡ ﻧﻘﻄﻴﺔ ﺗﺘﺮﻛﺰ ﻛﺘﻠﺘﻬﺎ ﻓﻲ ﻧﻘﻄﺔ‬ ‫ﺃﺟﺮﺍﻡ ﻛﺒﻴﺮﺓ ﺍﻟﺤﺠﻢ٬ ﻟﻜﻦ ﺑﺎﻟﻨﺴﺒﺔ ﺍﻟﻰ ﺍﻟﻤﺴﺎﻓﺎﺕ ﻓﻴﻤﺎ‬ ‫ﺑﻌﺪ ﺣﺴﺎﺏ ﻣﻮﻗﻊ ﺍﻟﺠﺮﻡ ﻳﺘﻢ ﺍﺭﺟﺎﻉ ﺣﺠﻤﻪ ﺍﻟﻄﺒﻴﻌﻲ‬ ‫ﺑﻴﻨﻬﺎ ﻓﻬﻲ ﻓﻌﻠﻴﺎ ً ﺻﻐﻴﺮﺓ ﺟﺪﺍً‬ ‫ ﻟﻴﻐﻄﻲ ﺍﻟﻤﺴﺎﺣﺔ ﺍﻟﻄﺒﻴﻌﻴﺔ ﺍﻟﺘﻲ ﻳﻐﻄﻴﻬﺎ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ ‬
  • 13. ‫ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻔﻀﺎﺋﻴﺔ ﻭ ﺍﻻﺳﻘﺎﻁ ﺍﻷﺭﺿﻲ‬ ‫ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻔﻴﺰﻳﺎﺋﻴﺔ ﺛﻼﺛﻴﺔ ﺍﻷﺑﻌﺎﺩ ﻭ ﺍﺳﻘﺎﻁ ﺍﻟﻜﺮﺓ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫0 = ‪x = 4, y = 2, z‬‬ ‫ ﺍﺳﻘﺎﻁ ﺍﻟﻔﻀﺎء ﺍﻻﻗﻠﻴﺪﻱ ﻟﻠﻜﻮﻥ ﻛﻜﺮﺓ ﺳﻤﺎﻭﻳﺔ‬ ‫ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺪﻳﻜﺎﺭﺗﻴﺔ ﺛﻼﺛﻴﺔ ﺍﻷﺑﻌﺎﺩ‬ ‫ﺍﺳﻘﺎﻁ ﻛﺎﻣﻞ ﺍﻟﻔﻀﺎء ﺍﻻﻗﻠﻴﺪﻱ ﻟﻠﻜﻮﻥ ﻛﻤﺎ ﻳﺮﻯ ﻣﻦ‬ ‫ﻣﻤﺘﺎﺯﺓ ﻟﻠﻤﺴﺎﺋﻞ ﺍﻟﻔﻴﺰﻳﺎﺋﻴﺔ ﻷﻧﻬﺎ ﺗﻌﺒﺮﻋﻦ ﻣﻜﺎﻥ ﺍﻷﺟﺮﺍﻡ‬ ‫ .ﺍﻷﺭﺽ ﻛﻜﺮﺓ ﺳﻤﺎﻭﻳﺔ ﺑﺒﻌﺪﻳﻦ ﺑﺪﻻً ﻣﻦ ﺛﻼﺛﺔ‬ ‫ﻓﻲ ﺍﻟﻔﻀﺎء ﺍﻻﻗﻠﻴﺪﻱ ﺑﺎﺣﺪﺍﺛﻴﺎﺕ ﻣﺘﻌﺎﻣﺪﺓ ﻣﻤﺎ ﻳﺴﻬﻞ‬ ‫ﺍﻟﺒﻌﺪ ﺍﻟﺜﺎﻟﺚ )ﺍﻟﻌﻤﻖ( ﻳﺘﻢ ﺍﻟﺘﻌﺒﻴﺮ ﻋﻨﻪ ﺑﺒﻌﺪ ﺍﻟﺠﺮﻡ ﻋﻦ‬ ‫ ﺍﻟﻌﻤﻠﻴﺎﺕ ﺍﻟﻔﻴﺰﻳﺎﺋﻴﺔ ﻛﺎﻟﻀﺮﺏ ﺍﻟﻤﺘﺠﻬﻲ ﻭ ﺍﻟﻘﻴﺎﺳﻲ‬ ‫ .ﺍﻷﺭﺽ ﺑﺎﻟﻮﺣﺪﺓ ﺍﻟﻔﻠﻜﻴﺔ ﺃﻭ ﺍﻟﺴﻨﻮﺍﺕ ﺍﻟﻀﻮﺋﻴﺔ‬ ‫ﻟﻜﻨﻬﺎ ﻻ ﺗﻌﺒﺮ ﺑﺸﻜﻞ ﻭﺍﺿﺢ ﻋﻦ ﻣﻜﺎﻥ ﺍﻟﺠﺮﻡ ﻛﻢ ﻳﺮﻯ‬ ‫ﺍﻷﻧﺴﺐ ﻭ ﺍﻷﺳﻬﻞ ﻟﻠﻤﺴﺎﺋﻞ ﺍﻟﺮﺻﺪﻳﺔ ﻟﻜﻨﻪ ﻏﻴﺮ ﻣﻨﺎﺳﺐ‬ ‫ﻣﻦ ﺍﻷﺭﺽ ﻟﺬﻟﻚ ﺗﻌﺘﺒﺮ ﺳﻴﺌﺔ ﻛﺎﺣﺪﺍﺛﻴﺎﺕ ﺭﺻﺪﻳﺔ‬ ‫ ﻟﻠﺤﺴﺎﺏ ﺍﻟﻔﻴﺰﻳﺎﺋﻲ ﻷﻥ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﻏﻴﺮ ﻣﺘﻌﺎﻣﺪﺓ‬
  • 14. ‫ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻔﻀﺎﺋﻴﺔ ﺍﻟﺮﺻﺪﻳﺔ‬ ‫ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺴﻤﺘﻴﺔ ﻭ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻻﺳﺘﻮﺍﺋﻴﺔ‬ ‫ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻻﺳﺘﻮﺍﺋﻴﺔ‬ ‫ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺴﻤﺘﻴﺔ‬ ‫ﻣﺮﺟﻌﻴﺘﻪ ﻣﺤﻮﺭ ﺩﻭﺭﺍﻥ ﺍﻟﻜﺮﺓ ﺍﻷﺭﺿﻴﺔ ﺣﻴﺚ ﻳﺘﻢ ﺗﻘﺴﻴﻢ‬ ‫ﻣﺮﺟﻌﻴﺘﻪ ﻣﻮﻗﻊ ﺍﻟﺮﺍﺻﺪ ﺣﻴﺚ ﻳﺘﻢ ﺗﻘﺴﻴﻢ ﺳﻤﺎء‬ ‫ ﺍﻟﺴﻤﺎء ﺍﻟﻰ ﺧﻄﻮﻁ ﻣﻴﻞ ﺍﺳﺘﻮﺍﺋﻲ ﻭ ﻁﺎﻟﻊ ﻣﺴﺘﻘﻴﻢ‬ ‫ﺍﻟﺮﺍﺻﺪ ﺍﻟﻰ ﺧﻄﻮﻁ ﻁﻮﻝ ﻭ ﺧﻄﻮﻁ ﻋﺮﺽ‬ ‫ ﺍﻷﻛﺜﺮ ﺍﺳﺘﺨﺪﺍﻣﺎ ً ﻟﺘﺤﺪﻳﺪ ﻣﻮﻗﻊ ﺍﻟﺠﺮﻡ ﺍﻟﻌﺎﻟﻤﻲ‬ ‫ .ﺑﺎﻟﺪﺭﺟﺎﺕ‬ ‫ ﻧﻔﺲ ﺍﺣﺪﺍﺛﻴﺎﺕ ﺍﻷﺟﺮﺍﻡ ﻷﻱ ﻣﻮﻗﻊ ﺭﺻﺪﻱ ﺃﺭﺿﻲ‬ ‫ .ﺍﻷﺳﻬﻞ ﻭ ﺍﻷﺳﺮﻉ ﻟﺘﺤﺪﻳﺪ ﺍﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺠﺮﻡ ﺭﺻﺪﻳﺎ ً‬ ‫ ﺧﻄﻮﻁ ﺍﻟﻌﺮﺽ ﺑﺎﻟﺪﺭﺟﺎﺕ ﺃﻣﺎ ﺍﻟﻌﺮﺽ ﺑﺎﻟﺴﺎﻋﺔ‬ ‫.ﻣﺘﻐﻴﺮ ﻣﻦ ﻣﻜﺎﻥ ﺭﺻﺪﻱ ﻵﺧﺮ‬ ‫ ‬
  • 15. ‫ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻔﻀﺎﺋﻴﺔ ﺍﻟﺮﺻﺪﻳﺔ‬ ‫ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺸﻤﺴﻴﺔ ﻭ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻤﺠﺮﻳﺔ‬ ‫ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﻤﺠﺮﻳﺔ‬ ‫ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺸﻤﺴﻴﺔ‬ ‫ .ﻣﺮﺟﻌﻴﺘﻪ ﺳﻄﺢ ﺍﻟﻤﺠﺮﺓ‬ ‫ .ﻣﺮﺟﻌﻴﺘﻪ ﺳﻄﺢ ﺩﻭﺭﺍﻥ ﺍﻷﺭﺽ ﺣﻮﻝ ﺍﻟﺸﻤﺲ‬ ‫ﺍﻟﻤﺤﻮﺭ ﺍﻷﻭﻝ:ﺍﻻﺯﺍﺣﺔ ﺍﻷﻓﻘﻴﺔ ﻋﻠﻰ ﺳﻄﺢ ﺍﻟﻤﺠﺮﺓ ﻋﻦ‬ ‫ﺍﻟﻤﺤﻮﺭ ﺍﻷﻭﻝ: ﺍﻻﻧﺰﻳﺎﺡ ﺍﻷﻓﻘﻲ ﻋﻦ ﻧﻘﻄﺔ ﺍﻻﻋﺘﺪﺍﻝ‬ ‫ .ﺍﻟﺨﻂ ﺍﻟﻮﺍﺻﻞ ﺑﻴﻦ ﺍﻟﺸﻤﺲ ﻭ ﻣﺮﻛﺰ ﺍﻟﻤﺠﺮﺓ‬ ‫ .ﺍﻟﺮﺑﻴﻌﻲ ﻋﻠﻰ ﺳﻄﺢ ﺩﻭﺭﺍﻥ ﺍﻷﺭﺽ ﺣﻮﻝ ﺍﻟﺸﻤﺲ‬ ‫ﺍﻟﻤﺤﻮﺭ ﺍﻟﺜﺎﻧﻲ: ﺍﻻﻧﺰﻳﺎﺡ ﺍﻟﻌﻤﻮﺩﻱ ﻋﻦ ﺳﻄﺢ ﺩﻭﺭﺍﻥ ﺍﻟﻤﺤﻮﺭ ﺍﻟﺜﺎﻧﻲ: ﺍﻻﺯﺍﺣﺔ ﺍﻟﻌﻤﻮﺩﻳﺔ ﺧﺎﺭﺝ ﺳﻄﺢ ﺍﻟﻤﺠﺮﺓ‬ ‫ .ﺍﻟﺸﻤﺲ ﻓﻲ ﻧﻘﻄﺔ ﺍﻟﺼﻔﺮ ﻟﺘﻘﺎﻁﻊ ﺍﻟﻤﺤﻮﺭﻳﻦ‬ ‫.ﺍﻷﺭﺽ ﺣﻮﻝ ﺍﻟﺸﻤﺲ‬ ‫ ‬
  • 16. ‫‪Qui‬‬ ‫‪zz‬‬ ‫ّ‬ ‫
ﻗﺪﺭ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ‬ ‫ﻟﻸﺟﺮﺍﻡ ﻓﻲ ﺍﻟﺼﻮﺭﺓ‬
  • 17. ‫ﺍﻟﺰﻣﻦ‬ ‫ﺗﻌﺮﻳﻒ ﺍﻟﺰﻣﻦ‬ ‫ﺍﻟﺘﺎﺭﻳﺦ ﺍﻟﺠﻮﻟﻴﺎﻧﻲ‬ ‫ ﻟﻤﻨﺘﺼﻒ ﻟﻴﻠﺔ ﺍﻟﻴﻮﻡ‬ ‫ 5.2906542‬ ‫ ‬ ‫ﺍﻟﺘﺎﺭﻳﺦ ﺍﻟﺠﻮﻟﻴﺎﻧﻲ‬ ‫ﻟﻠﺴﺎﻋﺔ ﺍﻟﺴﺎﺩﺳﺔ ﻣﺴﺎءﺍً‬ ‫ ﺍﻟﻴﻮﻡ‬ ‫52.3906542‬ ‫ ﺍﻟﺰﻣﻦ ﻛﻤﺘﻐﻴﺮ ﺭﻳﺎﺿﻲ‬ ‫ ﺍﻟﻤﺘﻐﻴﺮ ﺍﻟﻤﺴﺘﻘﻞ ﻓﻲ ﺍﻟﻔﻀﺎء ﺍﻻﻗﻠﻴﺪﻱ‬ ‫ﺍﻟﺸﺎﺋﻊ ﻓﻲ ﺣﺴﺎﺏ ﺍﻟﺰﻣﻦ ﻣﻦ ﺧﻼﻝ ﺍﻟﺴﻨﺔ٬ ﺍﻟﺸﻬﺮ٬ ﺍﻟﻴﻮﻡ٬ .ﺍﻟﻄﺮﻳﻘﺔ ﺍﻟﺸﺎﺋﻌﺔ ﻟﻜﺘﺎﺑﺔ ﺍﻟﺰﻣﻦ ﻏﻴﺮ ﻣﻨﺎﺳﺒﺔ ﻟﻠﺤﺴﺎﺏ‬ ‫ . ﺍﻟﺤﻞ ﻫﻮ ﺍﺻﻄﻼﺡ ﺍﻟﻴﻮﻡ ﺍﻟﺠﻮﻟﻴﺎﻧﻲ ﻛﺮﻗﻢ ﻋﺸﺮﻱ‬ ‫ﺍﻟﺴﺎﻋﺔ٬ ﺍﻟﺪﻗﻴﻘﺔ٬ ﻭ ﺍﻟﺜﺎﻧﻴﺔ. ﻣﺮﺟﻌﻴﺔ ﻫﺬﻩ ﺍﻟﻄﺮﻳﻘﺔ ﻓﻲ‬ ‫ .ﺍﻟﻴﻮﻡ ﺍﻟﺠﻮﻟﻴﺎﻧﻲ ﻫﻮ 42 ﺳﺎﻋﺔ ﻛﺎﻟﻴﻮﻡ ﺍﻟﻌﺎﺩﻱ‬ ‫ﻛﺘﺎﺑﺔ ﺍﻟﺰﻣﻦ ﻫﻲ ﺍﻟﻔﺘﺮﺓ ﺍﻟﻼﺯﻣﺔ ﻟﻌﻮﺩﺓ ﺍﻟﺸﻤﺲ ﺍﻟﻰ‬ ‫ﻳﺒﺪﺃ ﺍﻟﻌﺪ ﻣﻦ ﻅﻬﻴﺮﺓ 1 ﻳﻨﺎﻳﺮ 3174 ﻗﺒﻞ ﺍﻟﻤﻴﻼﺩ ﻓﻲ‬ ‫.ﻣﻮﻗﻌﻬﺎ ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﻨﺠﻮﻡ ﺧﻼﻝ ﺳﻨﺔ‬ ‫ ﺍﻟﺘﻮﻗﻴﺖ ﺍﻟﻌﺎﻟﻤﻲ‬ ‫ ‬
  • 18. ‫ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ﺩﻭﺭﺍﻥ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻓﻲ ﻳﻮﻡ‬ ‫ ﺍﻟﺤﺮﻛﺔ ﺍﻟﺤﻘﻴﻘﻴﺔ ﻟﻸﺟﺮﺍﻡ‬ ‫ )ﺣﺮﻛﺔ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻛﻜﻞ )ﺍﻟﻴﻮﻡ ﺍﻟﻨﺠﻤﻲ‬ ‫.1 ﺣﺮﻛﺔ ﺍﻟﺠﺮﻡ ﺍﻟﺤﻘﻴﻘﻴﺔ ﻫﻲ ﺣﺮﻛﺘﻪ ﻓﻲ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ ﺑﻌﺪ‬ ‫ﺩﻭﺭﺍﻥ ﻛﺎﻣﻞ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ ﻓﻲ 32 ﺳﺎﻋﺔ ﻭ‬ ‫ .ﺇﻫﻤﺎﻝ ﺩﻭﺍﺭﻥ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ ﺍﻟﻴﻮﻣﻲ‬ ‫ 65 ﺩﻗﻴﻘﺔ ﺑﺴﺒﺐ ﺩﻭﺭﺍﻥ ﺍﻷﺭﺽ ﺣﻮﻝ ﻧﻔﺴﻬﺎ‬ ‫ﺗﻌﻮﺩ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ ﺍﻟﺜﺎﺑﺘﺔ ﺍﻟﻰ ﻧﻔﺲ ﻣﻮﻗﻌﻬﺎ .2 ﺍﻷﺳﻬﻞ ﻫﻮ ﺗﺘﺒﻊ ﺣﺮﻛﺔ ﺍﻟﺠﺮﻡ ﺑﺎﻟﻨﺴﺒﺔ ﺍﻟﻰ ﺍﻷﺟﺮﺍﻡ‬ ‫ )ﺍﻟﺜﺎﺑﺘﺔ ﻓﻲ ﺍﻟﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ )ﻣﺜﻞ ﺍﻟﻨﺠﻮﻡ ﺍﻟﺒﻌﻴﺪﺓ‬ ‫ﻓﻲ ﺍﻟﺴﻤﺎء ﻓﻲ ﻳﻮﻡ ﻧﺠﻤﻲ ﻭﺍﺣﺪ‬ ‫ ‬ ‫ ‬
  • 19. ‫ﻧﻤﺎﺫﺝ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺣﺮﻛﺔ ﺍﻟﺸﻤﺲ‬ ‫ ﺣﺮﻛﺔ ﺍﻟﺸﻤﺲ ﻛﻤﺎ ﺗﺒﺪﻭ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ ﺳﺒﺐ ﺣﺮﻛﺔ ﺍﻟﺸﻤﺲ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ﺍﻟﺸﻤﺲ ﻋﺎﻟﻴﺔ ﻓﻲ ﺍﻟﺴﻤﺎء ﻓﻲ ﺍﻟﺼﻴﻒ ﻭ ﻣﻨﺨﻔﻀﺔ ﻓﻲ‬ ‫ﺩﻭﺭﺍﻥ ﺍﻷﺭﺽ ﺣﻮﻝ ﺍﻟﺸﻤﺲ ﻓﻲ ﻣﺪﺍﺭ ﺩﺍﺋﺮﻱ ﻗﻠﻴﻞ‬ ‫ .ﺍﻟﺸﺘﺎء‬ ‫ :ﺍﻟﺒﻴﻀﺎﻭﻳﺔ ﻳﻜﺘﻤﻞ ﻓﻲ ﺳﻨﺔ ﻳﻨﺘﺞ ﻋﻨﻪ‬ ‫.1ﺯﻣﻦ ﻣﻜﻮﺙ ﺍﻟﺸﻤﺲ ﻓﻮﻕ ﺍﻷﻓﻖ ﻁﻮﻳﻞ ﻓﻲ ﺍﻟﺼﻴﻒ ﻭ‬ ‫ ﺣﺮﻛﺔ ﻋﻤﻮﺩﻳﺔ ﻷﻋﻠﻰ ﺍﻟﺴﻤﺎء ﺃﻭ ﺃﺳﻔﻠﻬﺎ‬ ‫.2.ﻗﺼﻴﺮ ﻓﻲ ﺍﻟﺸﺘﺎء‬‫ ‬ ‫ﺣﺮﻛﺔ ﺃﻓﻘﻴﺔ: ﺍﻛﺘﻤﺎﻝ ﺩﻭﺭﺓ ﻛﺎﻣﻠﺔ ﻟﻠﺸﻤﺲ ﻓﻲ ﺍﻟﻘﺒﺔ‬ ‫ﺍﻧﺰﻳﺎﺡ ﺍﻟﺸﻤﺲ ﺍﻷﻓﻘﻲ ﻟﻠﻴﺴﺎﺭ ﻓﻲ ﺍﻟﺼﻴﻒ ﻭ ﺍﻟﻴﻤﻴﻦ ﻓﻲ‬ ‫ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ ‬ ‫.3ﺍﻟﺸﺘﺎء‬ ‫ﺗﻐﻴﺮ ﻁﻔﻴﻒ ﻓﻲ ﺣﺠﻢ ﺍﻟﺸﻤﺲ ﻓﻲ ﺍﻟﺴﻤﺎء‬
  • 20. ‫ﻧﻤﺎﺫﺝ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺣﺮﻛﺔ ﺍﻟﻘﻤﺮ‬ ‫ ﺳﺒﺐ ﺣﺮﻛﺔ ﺍﻟﻘﻤﺮ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ ﺣﺮﻛﺔ ﺍﻟﻘﻤﺮ ﻛﻤﺎ ﺗﺒﺪﻭ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ﺩﻭﺭﺍﻥ ﺍﻟﻘﻤﺮ ﺣﻮﻝ ﺍﻷﺭﺽ ﻓﻲ ﻣﺪﺍﺭ ﺩﺍﺋﺮﻱ ﻗﻠﻴﻞ‬ ‫ﻛﻮﻥ ﻣﺪﺍﺭ ﺍﻟﻘﻤﺮ ﻳﻤﻴﻞ ﻓﻘﻂ 5 ﺩﺭﺟﺎﺕ ﻋﻦ ﻣﺪﺍﺭ ﺍﻟﺸﻤﺲ ﻓﺄﻥ‬ ‫ :ﺍﻟﺒﻴﻀﺎﻭﻳﺔ ﻳﻜﺘﻤﻞ ﻓﻲ 3.72 ﻳﻮﻡ‬ ‫.1 ﺍﻟﻘﻤﺮ ﻓﻲ ﺍﻟﺴﻤﺎء ﻗﺮﻳﺐ ﻣﻦ ﻣﺴﺎﺭ ﺍﻟﺸﻤﺲ ﻭ ﻟﺬﻟﻚ ﻳﻜﻮﻥ‬ ‫ﻣﺴﺎﺭ‬ ‫ ﻣﺪﺍﺭ ﺍﻟﻘﻤﺮ ﻳﻤﻴﻞ 5 ﺩﺭﺟﺎﺕ ﻋﻦ ﻣﺪﺍﺭ ﺍﻟﺸﻤﺲ‬ ‫ .ﻋﺎﻟﻲ ﻓﻲ ﺍﻟﺼﻴﻒ ﻭ ﻣﻨﺨﻔﺾ ﻓﻲ ﺍﻟﺸﺘﺎء‬ ‫.2‬ ‫ﺣﺮﻛﺔ ﺍﻟﻘﻤﺮ ﻓﻲ ﺍﻟﻘﺒﺔ ﺍﻟﻔﻠﻜﻴﺔ ﺑﺎﻟﻨﺴﺒﺔ ﻟﻠﻨﺠﻮﻡ ﺍﻟﺜﺎﺑﺘﺔ‬ ‫ .ﻳﺘﺤﺮﻙ ﺍﻟﻘﻤﺮ ﻓﻲ ﺍﻟﺴﻤﺎء ﺣﻮﺍﻟﻲ 21 ﺩﺭﺟﺔ ﻓﻲ ﺍﻟﻴﻮﻡ‬ ‫ ﺗﺘﻜﺮﺭ ﺑﻌﺪ 3.72 ﻳﻮﻡ‬ ‫ .ﻣﺼﺪﺭ ﺍﺿﺎءﺓ ﺍﻟﻘﻤﺮ ﻫﻮ ﺍﻟﺸﻤﺲ ﻟﺬﻟﻚ ﻳﻈﻬﺮ ﺍﻟﻘﻤﺮ ﺑﺄﻁﻮﺍﺭ‬ ‫.3‬ ‫ ﺗﻐﻴﺮ ﻁﻔﻴﻒ ﻓﻲ ﺣﺠﻢ ﺍﻟﻘﻤﺮ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ ‬
  • 21. ‫ﻧﻤﺎﺫﺝ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺣﺮﻛﺔ ﺍﻟﻜﻮﺍﻛﺐ‬ ‫ ﺳﺒﺐ ﺣﺮﻛﺔ ﺍﻟﻜﻮﺍﻛﺐ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ ﺣﺮﻛﺔ ﺍﻟﻜﻮﺍﻛﺐ ﻛﻤﺎ ﺗﺒﺪﻭ ﻓﻲ ﺍﻟﺴﻤﺎء‬ ‫ :ﺗﺪﻭﺭ ﺍﻟﻜﻮﺍﻛﺐ ﺣﻮﻝ ﺍﻟﺸﻤﺲ ﻓﻲ ﻣﺪﺍﺭﺍﺕ ﺷﺒﻪ ﺩﺍﺋﺮﻳﺔ‬ ‫ﺣﺮﻛﺔ ﺍﻟﻜﻮﺍﻛﺐ ﻓﻲ ﺍﻟﺴﻤﺎء ﻫﻲ ﻣﺤﺼﻠﺔ ﻟﺤﺮﻛﺔ ﺍﻟﻜﻮﻛﺐ‬ ‫.1‬ ‫ ﺍﻟﻜﻮﺍﻛﺐ ﺍﻟﻘﺮﻳﺒﺔ ﻣﻦ ﺍﻟﺸﻤﺲ ﺗﺪﻭﺭ ﺑﺸﻜﻞ ﺃﺳﺮﻉ‬ ‫ﺣﻮﻝ ﺍﻟﺸﻤﺲ ﻭ ﺣﺮﻛﺔ ﺍﻷﺭﺽ ﺣﻮﻝ ﺍﻟﺸﻤﺲ٬ ﻣﻤﺎ ﻳﺆﺩﻱ‬ ‫.2‬ ‫ ﺍﻟﻤﺪﺍﺭﺍﺕ ﺷﺒﻪ ﺍﻟﺪﺍﺋﺮﻳﺔ ﺳﺒﺒﻬﺎ ﻁﺮﻳﻘﺔ ﺍﻟﺘﺸﻜﻞ ﺍﻻﺑﺘﺪﺍﺋﻴﺔ‬ ‫ .ﺍﻟﻰ ﺗﻐﻴﺮﺍﺕ ﻛﺒﻴﺮﺓ ﻓﻲ ﺳﺮﻋﺔ ﺍﻟﻜﻮﻛﺐ ﻭ ﺣﺮﻛﺘﻪ‬ ‫.3‬ ‫ﺍﻟﻜﻮﺍﻛﺐ ﺍﻟﺪﺍﺧﻠﻴﺔ ﺗﺒﺪﻭ ﺑﺄﻁﻮﺍﺭ ﺑﻌﻜﺲ ﺍﻟﻜﻮﺍﻛﺐ ﺍﻟﺨﺎﺭﺟﻴﺔ‬ ‫ ﻣﺴﺎﺭﺍﺕ ﺍﻟﻜﻮﺍﻛﺐ ﺩﺍﺋﻤﺎ ً ﻗﺮﻳﺒﺔ ﻣﻦ ﻣﺴﺎﺭ ﺍﻟﺸﻤﺲ‬ ‫ .ﺍﻟﺘﻲ ﺗﻜﻮﻥ ﻣﻜﺘﻤﻠﺔ ﺍﻻﺿﺎءﺓ‬ ‫.4‬ ‫ ‬ ‫ﺯﺍﻭﻳﺔ ﺗﺴﻄﺢ ﺟﻤﻴﻊ ﻣﺪﺍﺭﺍﺕ ﺍﻟﻜﻮﺍﻛﺐ ﻗﺮﻳﺒﺔ ﻣﻦ ﺯﺍﻭﻳﺔ‬ ‫ ‬ ‫ .ﺗﺴﻄﺢ ﻣﺪﺍﺭ ﺍﻷﺭﺽ‬
  • 22. ‫ﻣﺪﺍﺭﺍﺕ ﺑﻴﻀﻮﻳﺔ٬ ﻟﻤﺎﺫﺍ؟‬ ‫ﻣﺪﺍﺭﺍﺕ ﺍﻟﻤﺬﻧﺒﺎﺕ ﻭ ﺍﻟﻜﻮﺍﻛﺐ ﺍﻟﺼﻐﻴﺮﺓ‬
  • 23. ‫ﻧﻤﺎﺫﺝ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺣﺮﻛﺔ ﺍﻟﻨﺠﻮﻡ ﻭ ﺃﺟﺮﺍﻡ ﻣﺠﺮﺗﻨﺎ‬ ‫ ﺍﻟﻨﺠﻮﻡ ﺛﺎﺑﺘﺔ ﺃﻡ ﻣﺘﺤﺮﻛﺔ؟‬ ‫ﺑﺴﺒﺐ ﺍﻟﺒﻌﺪ ﺍﻟﻜﺒﻴﺮ ﻟﻠﻨﺠﻮﻡ )ﺃﻗﺮﺏ ﻧﺠﻢ 5 ﺳﻨﻴﻦ ﺿﻮﺋﻴﺔ( ﻓﺎﻥ‬ ‫ ﺣﺮﻛﺘﻬﺎ ﺑﻄﻴﺌﺔ ﺟﺪﺍً ﻭ ﻟﺬﻟﻚ ﻓﻬﻲ ﺗﻌﺘﺒﺮﺷﺒﻪ ﺛﺎﺑﺘﺔ‬ ‫ﺍﻟﻨﺠﻮﻡ ﺍﻟﻘﺮﻳﺒﺔ ﻳﺘﻐﻴﺮ ﻣﻮﻗﻌﻬﺎ ﺑﺸﻜﻞ ﻁﻔﻴﻒ ﺟﺪﺍً ﺃﺛﻨﺎء ﺩﻭﺭﺍﻥ ﺣﺮﻛﺔ ﺍﻟﻨﺠﻮﻡ ﻭ ﺃﺟﺮﺍﻡ ﺍﻟﻤﺠﺮﺓ ﻋﻠﻰ ﺍﻟﻤﻨﻈﻮﺭ ﺍﻟﺒﻌﻴﺪ‬ ‫ﻋﻠﻰ ﺍﻟﻤﺪﺍﺭ ﺍﻟﺒﻌﻴﺪ ﺗﺘﺤﺮﻙ ﻧﺠﻮﻡ ﺍﻟﻤﺠﺮﺓ ﺣﻮﻝ ﻣﺮﻛﺰ‬ ‫ ﺍﻷﺭﺽ ﺣﻮﻝ ﺍﻟﺸﻤﺲ ﺑﺴﺒﺐ ﺗﻐﻴﺮ ﻣﻜﺎﻥ ﺍﻟﺮﺅﻳﺔ‬ ‫ﺍﻟﻤﺠﺮﺓ ﻛﻤﺎ ﻭ ﺗﻌﻤﻞ ﻗﻮﻯ ﺍﻟﺠﺬﺏ ﺑﻴﻦ ﺍﻟﻨﺠﻮﻡ ﻋﻠﻰ ﺗﻐﻴﻴﺮ‬ ‫ﺑﺎﻗﻲ ﺍﻟﻨﺠﻮﻡ ﻭ ﺃﺟﺮﺍﻡ ﻣﺠﺮﺓ ﺩﺭﺏ ﺍﻟﺘﺒﺎﻧﺔ ﻛﺎﻟﺴﺪﻡ ﻭ ﺍﻟﻌﻨﺎﻗﻴﺪ‬ ‫ .ﻣﻮﺍﻗﻌﻬﺎ ﺍﻟﻨﺴﺒﻴﺔ‬ ‫ ﺍﻟﻨﺠﻤﻴﺔ ﺛﺎﺑﺘﺔ ﻟﻌﺸﺮﺍﺕ ﺁﻻﻑ ﺍﻟﺴﻨﻴﻦ ﺍﻟﻘﺎﺩﻣﺔ‬ ‫ ‬ ‫ ‬
  • 24. ‫ﻧﻤﺎﺫﺝ ﺣﺮﻛﺔ ﺍﻷﺟﺮﺍﻡ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺣﺮﻛﺔ ﺍﻟﻤﺠﺮﺍﺕ ﻭ ﺍﻟﻜﻮﻥ ﺍﻟﻤﻨﻈﻮﺭ‬ ‫ ﺍﻟﻤﺠﺮﺍﺕ ﺛﺎﺑﺘﺔ ﺃﻡ ﻣﺘﺤﺮﻛﺔ‬ ‫ﺑﺴﺒﺐ ﺍﻟﺒﻌﺪ ﺍﻟﻜﺒﻴﺮ ﻟﻠﻤﺠﺮﺍﺕ )ﺃﻗﺮﺏ ﻣﺠﺮﺓ 5.2 ﻣﻠﻴﻮﻥ‬ ‫ﺳﻨﺔ ﺿﻮﺋﻴﺔ( ﻓﺎﻥ ﺣﺮﻛﺘﻬﺎ ﺑﻄﻴﺌﺔ ﺟﺪﺍً ﻭ ﻟﺬﻟﻚ ﻓﻬﻲ‬ ‫ .ﺗﻌﺘﺒﺮ ﺛﺎﺑﺘﺔ‬ ‫ﺍﻟﻤﺠﺮﺍﺕ ﺍﻟﻘﺮﻳﺒﺔ ﻓﻲ ﻋﻨﻘﻮﺩ ﺍﻟﻤﺠﺮﺍﺕ ﺍﻟﻤﺤﻠﻲ ﺗﺘﺤﺮﻙ‬ ‫ﺑﺤﺴﺐ ﺗﻔﺎﻋﻞ ﻗﻮﻯ ﺍﻟﺠﺬﺏ ﺑﻴﻨﻬﺎ ﺃﻣﺎ ﺍﻟﻤﺠﺮﺍﺕ ﺍﻟﺒﻌﻴﺪﺓ‬ ‫ ﺣﺮﻛﺔ ﺍﻟﻤﺠﺮﺍﺕ ﻓﻲ ﺍﻟﻤﺤﺎﻛﻴﺎﺕ ﺍﻟﺤﺎﺳﻮﺑﻴﺔ ﺍﻟﺮﺻﺪﻳﺔ‬ ‫ ﻓﻬﻲ ﻓﻲ ﺍﺑﺘﻌﺎﺩ ﺩﺍﺋﻢ‬ ‫ ‪ J‬ﻣﻮﺍﻗﻌﻬﺎ ﺛﺎﺑﺘﺔ ﻭ ﻻ ﺗﺘﻐﻴﺮ ﺃﺑﺪﺍً‬ ‫ ‬ ‫ ‬
  • 25. ‫ﻣﺜﺎﻝ ﺣﺴﺎﺑﻲ‬ ‫ﺣﺴﺎﺏ ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ ﺍﻟﻴﻮﻡ‬ ‫ﻧﻈﺎﻡ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺸﻤﺴﻲ ﻟﻠﻘﺒﺔ ﺍﻟﺴﻤﺎﻭﻳﺔ‬ ‫ﺃﻱ ﻧﻈﺎﻡ ﺍﺣﺪﺍﺛﻴﺎﺕ ﻧﺴﺘﻌﻤﻞ ﻟﻠﺤﺴﺎﺏ ؟؟‬ ‫ﻧﻈﺎﻡ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻻﺳﺘﻮﺍﺋﻲ )ﺍﻟﻌﺎﻟﻤﻲ( ﺃﻭ ﺍﻟﺴﻤﺘﻲ‬ ‫ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ ﺍﻟﻨﻬﺎﺋﻲ ﺑﺄﻱ ﺍﺣﺪﺍﺛﻴﺎﺕ ﻳﻔﻀﻞ ﻋﺮﺿﻪ؟‬ ‫))ﻟﻤﻮﻗﻊ ﺭﺻﺪ ﻣﺤﺪﺩ‬ ‫‪ epoch‬ﻣﺎ ﻫﻲ ﻧﻘﻄﺔ ﺍﻟﺒﺪء ﻟﻠﺤﺴﺎﺏ؟‬ ‫ﻧﺨﺘﺎﺭ 1-1-0991 ﺣﻴﺚ ﻛﺎﻧﺖ ﺍﻟﺸﻤﺲ ﻋﻠﻰ 4.972‬ ‫ﺩﺭﺟﺔ ﻋﻦ ﻧﻘﻄﺔ ﺍﻟﺒﺪﺍﻳﺔ ﻟﻼﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺸﻤﺴﻴﺔ )ﻭ ﻫﻲ‬ ‫ﻧﻘﻄﺔ ﺍﻻﻋﺘﺪﺍﻝ ﺍﻟﺮﺑﻴﻌﻲ( ﺃﻣﺎ ﺍﻻﺣﺪﺍﺛﻲ ﺍﻟﺜﺎﻧﻲ ﻓﻬﻮ ﺻﻔﺮ‬ ‫‪ J‬ﻷﻥ ﺍﻟﺸﻤﺲ ﻋﻠﻰ ﺍﻟﺨﻂ ﺍﻟﻜﺴﻮﻓﻲ ﺗﻤﺎﻣﺎ ً‬
  • 26. ‫ﻣﺜﺎﻝ ﺣﺴﺎﺑﻲ‬ ‫ﺣﺴﺎﺏ ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ ﺍﻟﻴﻮﻡ‬ ‫ﻛﻢ ﻋﺪﺩ ﺍﻷﻳﺎﻡ ﻣﻨﺬ 1-1-0991 ﺣﺘﻰ ﺍﻟﻴﻮﻡ ﺍﻟﺴﺎﻋﺔ ﺍﻟﺴﺎﺑﻌﺔ ﻣﺴﺎءﺍً؟‬ ‫ﻋﺪﺩ ﺍﻷﻳﺎﻡ ﻓﻲ ﺍﻟﺴﻨﺔ ﺍﻟﺤﺎﻟﻴﺔ ﻣﻨﺬ 1 ﻛﺎﻧﻮﻥ ﺛﺎﻧﻲ + ﻋﺪﺩ ﺍﻟﺴﻨﻴﻦ ﻣﻨﺬ 0991‬ ‫ * 563 + ﻋﺪﺩ ﺍﻟﺴﻨﻮﺍﺕ ﺍﻟﻜﺒﻴﺴﺔ ﻣﻨﺬ 0991‬ ‫ ‬ ‫ﻳﻮﻡ ﻣﻨﺬ 1-1-0991 ﺣﺘﻰ ﺍﻟﻴﻮﻡ 9918 = 5 + 653 * 22 + 461 =‬ ‫ﻛﻢ ﺩﻭﺭﺓ ﺩﺍﺭﺕ ﺍﻟﺸﻤﺲ ﻣﻨﺬ 1-1-0991 ﺣﺘﻰ ﺍﻟﻴﻮﻡ؟ )ﺗﻜﻤﻞ ﺍﻟﺸﻤﺲ ﺩﻭﺭﺓ ﻛﺎﻣﻠﺔ‬ ‫)063 ﺩﺭﺟﺔ ﻓﻲ 42.563 ﻳﻮﻡ‬ ‫ﻋﺪﺩ ﺍﻷﻳﺎﻡ / 191242.563 = 811844.22 ﺩﻭﺭﺓ. ﺍﻟﺪﻭﺭﺍﺕ ﺍﻟﻜﺎﻣﻠﺔ ﻻ ﺗﻬﻤﻨﺎ ﻷﻧﻬﺎ ﺗﻌﻮﺩ ﺑﺎﻟﺸﻤﺲ ﺍﻟﻰ ﻧﻔﺲ‬ ‫ﺍﻟﻤﻮﻗﻊ٬ ﺃﻣﺎ ﺍﻟﻜﺴﺮ ﺍﻟﻌﺸﺮﻱ 811844.0 ﻓﻬﻮ ﺍﺯﺍﺣﺔ ﺍﻟﺸﻤﺲ ﻋﻦ ﺍﻟﻤﻮﻗﻊ ﺍﻟﺬﻱ ﻛﺎﻧﺖ ﻓﻴﻪ ﺍﻟﺸﻤﺲ ﻓﻲ‬ ‫1-1-0991 ﺣﺘﻰ ﺍﻟﻴﻮﻡ‬ ‫ﺍﺯﺍﺣﺔ ﺍﻟﺸﻤﺲ ﺑﺎﻟﺪﺭﺟﺎﺕ ﺑﺎﻟﻨﺴﺒﺔ ﺍﻟﻰ ﺍﻟﻤﻮﻗﻊ ﺍﻟﻤﺮﺟﻌﻲ = 811844.0 * 063 = 84223.161 ﺩﺭﺟﺔ ﻭ ﻫﻲ‬ ‫ﺍﺯﺍﺣﺔ ﺍﻟﺸﻤﺲ ﺑﺎﻟﺪﺭﺟﺎﺕ ﻋﻦ ﺍﻟﻤﻮﻗﻊ ﺍﻟﻤﺮﺟﻌﻲ‬
  • 27. ‫ﻣﺜﺎﻝ ﺣﺴﺎﺑﻲ‬ ‫ﺣﺴﺎﺏ ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ ﺍﻟﻴﻮﻡ‬ ‫ﻛﻢ ﺍﺯﺍﺣﺔ ﺷﻤﺲ ﺍﻟﻴﻮﻡ ﺑﺎﻟﺪﺭﺟﺎﺕ ﻋﻦ ﻧﻘﻄﺔ ﺍﻻﻋﺘﺪﺍﻝ ﺍﻟﺮﺑﻴﻌﻲ؟ )ﻭ‬ ‫)ﻫﻲ ﻧﻘﻄﺔ ﺍﻟﺒﺪﺍﻳﺔ ﻓﻲ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻟﺸﻤﺴﻴﺔ‬ ‫= 063 - 387527.044 = 84223.161 + 303304.972‬ ‫ﺩﺭﺟﺔ 387527.08‬ ‫ﻟﻜﻨﻨﺎ ﻧﻌﻠﻢ ﺃﻥ ﻣﺪﺍﺭ ﺍﻟﺸﻤﺲ ﻟﻴﺲ ﺩﺍﺋﺮﻱ ﺑﻞ ﺑﻴﻀﻮﻱ٬ ﺃﻱ ﺃﻥ ﺍﻟﺸﻤﺲ ﻻ ﺗﺘﺤﺮﻙ‬ ‫ﻓﻲ ﺍﻟﺴﻤﺎء ﻧﻔﺲ ﺍﻟﻤﺴﺎﻓﺔ ﻟﻜﻞ ﻳﻮﻡ ﺑﻞ ﺗﻜﻮﻥ ﺃﺣﻴﺎﻧﺎ ً ﺃﺳﺮﻉ ﻭ ﺃﺣﻴﺎﻧﺎ ً ﺃﺑﻄﺄ٬ ﻟﺬﻟﻚ‬ ‫:ﻧﻌﻮﺽ ﺍﻟﺨﻠﻞ ﻟﻠﻤﺪﺍﺭ ﺍﻟﺒﻴﻀﻮﻱ ﺑﺎﺳﺘﺨﺪﺍﻡ ﻣﻌﺎﺩﻟﺔ ﺍﻟﺘﺼﺤﻴﺢ ﻟﻠﻤﺪﺍﺭ ﺍﻟﺒﻴﻀﻮﻱ‬ ‫ﺍﻟﻤﻮﻗﻊ ﺍﻟﻤﻄﻠﻮﺏ ﻋﻠﻰ ﺍﻟﻘﻄﻊ ﺍﻟﻨﺎﻗﺺ = ﺍﻟﻤﻮﻗﻊ ﺍﻟﻤﻄﻠﻮﺏ ﻋﻠﻰ ﺍﻟﺪﺍﺋﺮﺓ + )063/ﺑﺎﻱ( × ﻣﻌﺎﻣﻞ ﺍﻟﺒﻴﻀﺎﻭﻳﺔ ﻟﻠﻤﺪﺍﺭ‬ ‫ )× ﺟﻴﺐ)ﺍﻟﻤﻮﻗﻊ ﻋﻠﻰ ﺍﻟﺪﺍﺋﺮﺓ - ﻣﻮﻗﻊ ﺍﻟﺤﻀﻴﺾ ﻋﻠﻰ ﺍﻟﺪﺍﺋﺮﺓ‬ ‫ )ﺑﺎﻱ( × 317610.0 × ﺟﻴﺐ)387527.08 - 224867.282/063( + 387527.08‬ ‫ﺩﺭﺟﺔ 935444.18 = 657817.0 + 387527.08 =‬ ‫ﻻﺣﻆ ﺃﻥ ﻗﻴﻤﺔ ﺍﻟﺘﺼﺤﻴﺢ ﻟﻠﻤﺪﺍﺭ ﺍﻟﺒﻴﻀﺎﻭﻱ ﺑﻠﻐﺖ ﻓﻘﻂ 7.0 ﺩﺭﺟﺔ ﻓﻘﻂ ﻭ ﺫﻟﻚ ﻛﻮﻥ ﻣﺪﺍﺭ ﺍﻷﺭﺽ ﺷﺒﻴﻪ ﺑﺎﻟﺪﺍﺋﺮﺓ‬ ‫)ﻫﻜﺬﺍ ﻧﻜﻮﻥ ﻋﺮﻓﻨﺎ ﺗﻤﺎﻣﺎ ً ﺍﺣﺪﺛﻴﺎﺕ ﺷﻤﺲ ﺍﻟﻴﻮﻡ ﺑﺎﻟﻨﻈﺎﻡ ﺍﻻﺣﺪﺍﺛﻲ ﺍﻟﺸﻤﺴﻲ ﻭ ﻫﻲ: )935444.18٬ 0‬
  • 28. ‫ﻣﺜﺎﻝ ﺣﺴﺎﺑﻲ‬ ‫ﺣﺴﺎﺏ ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ ﺍﻟﻴﻮﻡ‬ ‫:ﻧﺴﺘﻄﻴﻊ ﺍﻷﻥ ﺍﻟﺘﺤﻮﻳﻞ ﻣﻦ ﺍﻻﺣﺪﺍﺛﻲ ﺍﻟﺸﻤﺴﻲ ﺍﻟﻰ ﺃﻱ ﺍﺣﺪﺍﺛﻲ ﻧﺮﻳﺪ‬ ‫ :ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻻﺳﺘﻮﺍﺋﻴﺔ ﻟﺸﻤﺲ ﺍﻟﻴﻮﻡ‬ ‫ ﺍﻟﻄﺎﻟﻊ ﺍﻟﻤﺴﺘﻘﻴﻢ: 11886.08 ﺩﺭﺟﺔ = 702973.5 ﺳﺎﻋﺔ‬ ‫ﺍﻟﻤﻴﻞ ﺍﻻﺳﺘﻮﺍﺋﻲ: 816161.32 ﺩﺭﺟﺔ‬ ‫ :ﺗﺤﻮﻳﻞ ﺍﻻﺣﺪﺍﺛﻴﺎﺕ ﺍﻻﺳﺘﻮﺍﺋﻴﺔ ﺍﻟﻰ ﻁﺮﻳﻘﺔ ﺍﻟﻌﺮﺽ ﺑﺎﻟﺪﻗﺎﺋﻖ ﻭ ﺍﻟﺜﻮﺍﻧﻲ ﺍﻟﻘﻮﺳﻴﺔ‬ ‫ ﺍﻟﻄﺎﻟﻊ ﺍﻟﻤﺴﺘﻘﻴﻢ: 702973.5 ﺳﺎﻋﺔ = 54ﺙ 22ﺩ 5ﺱ‬ ‫ ‪ᵒ‬ﺍﻟﻤﻴﻞ ﺍﻻﺳﺘﻮﺍﺋﻲ: 816161.32 ﺩﺭﺟﺔ =9’ 14” 32‬
  • 29. ‫
ﻣﺎ ﺳﺒﺐ ﺍﻻﺧﺘﻼﻑ ﺍﻟﻄﻔﻴﻒ ﻓﻲ ﺍﻟﻨﺘﻴﺠﺔ؟‬ ‫ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ ﺍﻟﻴﻮﻡ ﺍﻟﺴﺎﻋﺔ 00:0 ﻓﻲ ﺳﺘﻼﺭﻳﻮﻡ‬ ‫ﻣﺎﺫﺍ ﻧﻀﻴﻒ ﻟﻠﺤﺴﺎﺑﺎﺕ ﺍﺫﺍ ﺃﺭﺩﻧﺎ ﻣﻮﻗﻊ ﺍﻟﺸﻤﺲ‬ ‫ﻫﺬﻩ ﺍﻟﻠﺤﻈﺔ؟‬