
bhramanapatha modeling

guruthwaakarshanam kaaranam mattoru valia vasthuvin chuttum bhramanapathathil neengumbol oru valia vasthuvinte chalanam anukarikkunnathinayi ganithashaasthra maathrkakal srishtikkunna prakriyayaan bhramanapatha modeling. thritheeya pindangalil ninnulla guruthwaakarshana aakarshanam, vaayu prathirodham, soura marddam allengil propulsion sisttathil ninnulla oorjjam thudangiya mattu sakthikal saadhaaranayaayi dvitheeya falangalaayi maathrkayaakkappedunnu. oru bhramanapathathe nerittu model cheiyunnathu valare valia bhramanapathangalilekku cheria vyathiyanangal maathrkayaakkendathinte aavasyakatha kaaranam yanthra krithyathayude paridhikal thallaan kazhiyum. ekkaaranathaal, mikacha krithyatha nedunnathinaayi bhramanapathathe maathrkayaakkaan palappozhum aswasthatha reethikal upayogikkunnu.
pashchaathalam.
bhramanapatha chalanathekkurichum bhramanapathangalude ganithashaasthra maathrkayekkurichum patanam aarambhichath aakaashathile grahangalude chalanagal pravachikkanulla aadya sramangalodeyaanu, ennirunnaalum purathana kaalath kaaranagal oru nigoodathayaayi thudarnnu. nyoottan, thante chalanatthinteyum guruthwaakarshanathinteyum niyamangal roopappeduthiya samayat, avayude kanakkukoottalinte sankeernamaaya budhimuttukal thiricharinju kondu, aswasthathakalude aadya vishakalanathil avaa prayogichu.
athinusesham niravadhi mahanaaya ganithashaasthranjar ulppettirikkunna vividha prasnangalil shradha cheluthiyittundu; 18,19 noottaandukaliludaneelam chandranteyum grahangaludeyum sthaanam sambandhicha krithyamaaya pattikakal kadalil naavigeshan aavasyangalkkaayi aavashyamaayirunnu.
bhramanapathangalude sankeernamaaya chalanagal takarkkaan kazhiyum. mattoru vasthuvinte guruthwaakarshana phalatthil maathram shareeram pinthudarunna saangalppika chalanam saadhaaranayaayi oru conic vibhagamaanu, jyaamithiyude reethikal upayogichu eluppathil maathrkayaakkaan kazhiyum. ithine rund shareera prashnamo aswasthathayillaatha keplerian bhramanapathamo ennu vilikkunnu. keplerian bhramanapathavum shareerathinte yadhaartha chalanavum thammilulla vyathyaasangal aswasthathakal moolamaanu undaakunnath. praadhamikavum dvitheeyavumaaya body thammilulla guruthwaakarshana prabhavam ozhikeyulla sakthikal moolamaanu eee aswasthathakal undaakunnath, krithyamaaya bhramanapatha simuleshan srishtikkunnathinu ithu maathrkayaakkanam. mikka bhramanapatha modeling rund shareera prashnathe maathrkayaakkukayum thudarnnu eee aswasthappeduthunna shakthikalude modalukal cherkkukayum kaalakramena eee modalukal anukarikkukayum cheiyunnu. praadhamika, sourakkaattu, valichidal, kaanthikakshethrangal, propulsive fozhsu ennivaykku purame mattu vasthukkalil ninnulla guruthwaakarshanavum aswasthappeduthunna shakthikalil ulppedaam.
lalithamaaya rund-body, moonnu-body prashnangalkk vishakalana pariharangal (bhaaviyile eathu samayathum sthaanangalum chalanangalum pravachikkunnathinulla ganitha padaprayogangal) nilavilundu; chila prathyeka kesukal ozhike "enn"-body prashnathinu onnum kandethiyitla. shareerangalilonninte aakruthi kramarahithamaanengil rund shareerangalude prashnam polum layikilla.
thaalpparyamulla mikka prasnangalkkum vishakalana pariharangal kandethunnathile budhimuttu kaaranam, oorbittal chalanam vishakalanam cheyyaan computer modeling simuleshan saadhaaranayaayi upayogikkunnu. bahirakasha pedakatthinte bhramanapathangalum sanjaarapathangalum anukarikkunnathin vaividhyamaarnna softweyarukal labhyamaan.
keplerian bhramanapatha maathruka.
athinte ettavum lalithamaaya roopathil, rund vasthukkal maathrame ulppedunnulloovennum randum golaakrithiyilulla pooyint pindangalayi pravarthikkunnuvennum mattu shakthikalonnum vasthukkalil pravartthikkunnillennum anumaanichukondu oru bhramanapatha maathruka srishtikkaan kazhiyum. eee saahacharyathil model oru keppler bhramanapathathilekku lalithamaakkiyittund.
keplerian bhramanapathangal conic vibhaagangale pinthudarunnu. oru kendra pindove bhramanapathathilulla pindove thammilulla dooram nalkunna bhramanapathatthinte ganithashaasthra maathruka ingane prakadippikkaam
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marimari, samavaakyam ingane prakadippikkaam
ivide soothravaakyam _ 7 neey vakrathinte semi-laattas malaashayamenn vilikkunnu. ardha-pradhana aksham ananthamaaya parabolic sanjaarapathangal kaikaaryam cheyyumbol samavaakyathinte eee roopam prathyekichum upayogapradamaanu.
oru ithara sameepanam thaazhe nirvachichirikkunnathupo aisak nyoottante saarvathrika guruthwaakarshana niyamam upayogikkunnu
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praadhamika vasthuvinte pindam dvitheeya vasthuvinte pindatthekkaal valare valuthaanennu adhikamaayi anumaanikkukayum nyoottante chalana niyamathil pakaram vaykkukayum cheiyunnathu inipparayunna deferential samavaakyathin kaaranamaakunnu.
eee deferential samavaakyam pariharikkunnath oru bhramanapathathil keplerian chalanathinu kaaranamaakunnu.
praayogikamaayi, keplerian bhramanapathangal saadhaaranayaayi phastt-oordar ekadesha kanakkukalkko prathyeka kesukalkko allengil oru aswasthamaaya bhramanapathatthinte adisthaana maathrkayaayo maathrame upayogikkukayulloo.
bhramanapatha simuleshan reethikal.
bhramanapatha maathrkakal saadhaaranayaayi prathyeka aswasthatha reethikal upayogichu samayathum sthalathum pracharippikkunnu. oru keplerian bhramanapathamaayi bhramanapathathe aadyam maathrkayaakkiyaanu ithu nadathunnathu. bhramanapathathe badhikkunna vividha aswasthathakal kanakkileduthu modalil aswasthathakal cherkkunnu.
aswasthappeduthunna sakthikal cheruthaaya kesukalil maathram parimithappedaathathinaal, khagola mechanicsile eathu prashnathinum prathyeka aswasthathakal prayogikkaam. yanthram srishtikkunna ettavum krithyamaaya grahangalude ephimerideukalude adisthaanamaanu prathyeka perterbation reethikal.
udaaharanathinu, jettu propulsion laborattari development ephimeris kaanuka.
kovellinte reethi.
kovellinte reethi oru prathyeka aswasthathappeduthunna reethiyaanu;
ganithashaasthraparamaayi, formula _ 15 parasparabandhithamaya vasthukkalkk, mattu bodikal formula _ 17 ll ninnulla body formula _ 16 leeii neutonian sakthikal lalithamaayi ingane samgrahikkunnu
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ellah vektarukalum sisttathinte baarisentarilekku ruffer cheiyunnu. eee samavaakyam formula _ 31, formula _ 32, formula _ 33 ennivayile gadakangalaayi pariharikkappedunnu, koodaathe simuleshan samayakramathil munnott pookumbool puthiya vegathayum position vektarukalum roopappeduthunnathinaayi iva samkhyaaparamaayi samyojippichirikkunnu. cowell reethiyude prayojanam prayogathinteyum prograaminginteyum eluppamaanu. oru poraayma, aswasthathakal valuthaakkumbol (oru vasthu mattonninodu adutha sameepanam pulartthumbol) reethiyude pishakukalum valuthaakunnu ennathaanu.
mattoru poraayma, sooryaneppolulla oru prabalamaaya kendra pindamulla samvidaanangalil, kendra pindatthinteyum aswasthappeduthunna pindangaludeyum shakthikalile valia vyathyasam kaaranam ganithathil niravadhi pradhana akkangal vahikkendathu aavasyamaanu ennathaanu.
enkeyude reethi.
enkkinte reethi oru referenzaayi ausculating bhramanapathathil aarambikkukayum samayathinte pravartthanamaayi referencil ninnulla vyathiyaanam pariharikkunnathin samkhyaaparamaayi samyojippikkukayum cheiyunnu.
aswasthathakal saadhaaranayaayi cheruthayathinaal samyojanathinu valia ghattangalil munnott pookaan kazhiyum (pishakukal kuravaayirikkum), koodaathe kovellinte reethiyekkaal theevramaaya aswasthathakal eee reethiye valare kurache baadhikkunnulloo ennathaanu ithinte gunangal. athinte poraayma sankeernathayaanu; idaykkide ausculating bhramanapatham update cheyyaathe anischithamaayi upayogikkaan kazhiyilla, avide ninnu thudarnnu, "thiruthal" ennariyappedunna oru prakriya.
formula _ 34 ooksyuletting bhramanapathatthinte radius vector, formula _ 35 perterbed bhramanapathatthinte radius vector, formula _ 36 ooksyuletting bhramanapathathil ninnulla vyathiyaanam,
formula 37 umm formula 38 umm formula 35, formula 34 ennivayude chalanatthinte samavaakyangal maathramaan.
formula _ 41 ennathu kendra bodiyudeyum aswasthamaaya bodiyudeyum pindangalaya formula _ 42 umm formula _ 43 umm ulla guruthwaakarshana paaraameteraanu, formula _ 44 ennathu aswasthathayundaakkunna aaksilareshanaan, formula _ 2 umm formula _ 46 umm formula _ 35, formula _ 34 ennivayude vyaapthiyaan.
(), () ennee samavakyangalil ninnu samavaakyam () aayi maattisthaapikkunnu.
sidhaanthathil, formula _ 36 kandethaan randuthavana samyojippikkaan kazhiyum. rund body reethikalaal ooksyuletting bhramanapatham eluppathil kanakkakkunnathinaal, formula _ 34, formula _ 36 enniva kanakkaakkukayum formula _ 35 pariharikkukayum cheyyaam. praayogikamaayi, brackettukalile alavu, formula _ 53, ekadesham thulyamaaya rund vektarukalude vyathyaasamaan, koodaathe adhika praadhaanyamulla akkangalude aavasyakatha ozhivakkaan kooduthal krithrimathvam aavasyamaanu.
sperling-burdet reethi.
1991ll vijayicha aarr. bond maikkal eph. rund shareera prasnangalulla prashnam pariharikkunnathin kaaryakshamavum valare krithyavumaaya oru reethi friyetta srishtichu. hans sperling uruthirinja chalanatthinte rekheeyavum kramappeduthiyathumaaya deferential samavaakyangalum sii vikasippicha eee samavaakyangale adisthaanamaakkiyulla oru perterbation sidhaanthavum eee reethi upayogikkunnu.eiii. 1864-ll bond hansen 1973-ll, rund shareera oorjjathinu pakaram perterbed sisttathinte motham oorjjathe oru paaraameteraayi upayogichum moolakangalude ennam 13 aayi kurachukondu bond hansen bardettinte deferential samavaakyangalude koottam mechappeduthi. 1989-ll bond gottlieb jacobian integral ulcherthu, ithu neutonian samavaakyangalile pottensial function samayatheyum sthaanatheyum vyakthamaayi aashrayikkumbol sthiramaanu. chalanatthinte deferential samavaakyangalude punarnirmmaanatthil motham oorjjathe maattisthaapikkaan jacobian sthiraangam oru moolakamaayi upayogichu. eee prakriyayil, koneeya chalanatthinte oru gadakathinu aanupaathikamaaya mattoru ghadakam avatharippikkunnu. ithu moolakangalude aake ennam 14 aayi thirike konduvannu. 1991-ll, bond friyettayum laplace vektarinu pakaram mattoru vekttar integralum athupole thanne mattoru scaler integralum upayogichu kooduthal parishkaarangal nadatthi, ithu chila moolakangalude deferential samavakyangalil prathyakshappetta cheria mathethara padangal neekkam cheythu.
spurling-burdet reethi inipparayunna 5 ghatta prakriyayilaanu nadappilaakkunnathu
aswasthamaakkunna shakthikalude maathrkakal.
aswasthamaakkunna sakthikal bhramanapathangal oru thikanja keplerian bhramanapathathil ninnu aswasthamaakkunnu. bhramanapathathil avayude swaadheenam nirnnayikkaan kazhiyunna tharatthil bhramanapatha anukarana samayat eee shakthikalude oronninum maathrkakal srishtikkukayum nadappilaakkukayum cheiyunnu.
golamallatha guruthwaakarshanam.
bhoomi oru thikanja golamalla, bhoomiyil pindam thulyamaayi vitharanam cheythitilla. ithu bhoomiye chuttipattiyulla bhramanapathangalkku, prathyekichu thaazhnna bhouma bhramanapathangalkku pooyint-maas guruthwaakarshana maathruka krithyamallaathathinu kaaranamaakunnu. bhoomiyude uparithalathinu chuttumulla guruthwaakarshana sheshiyile vyathiyanangal kanakkiledukkumbol, bhoomiyude guruthwaakarshana mandalam samavaakyathiloode prakadippikkunna golaakrithiyilulla harmonics upayogichu maathrkayaakkappedunnu
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oru praadhamika pindatthinu chuttumulla oru bhramanapathathile aswasthathakal model cheyyumbol, pooyint-maas guruthwaakarshana model 117 enna soothravaakyathil kanakkakkappedunnathinaal 99 padangalude koottam maathrame aswasthathayil ulppeduthendathulloo.
moonnaam shareera aswasthathakal.
moonnaamathe vasthukkalil ninnulla guruthwaakarshana sakthikal oru bhramanapathathilekku aswasthathakal undaakkum. udaaharanathinu, suryan chandran bhoomiye chutti sanjarikkunna bhramanapathangalil aswasthathakal srishtikkunnu. nerittulla guruthwaakarshana enn-body simuleshanukaliloode praadhamika bodic guruthwaakarshanam maathrkayaakkunna athe reethiyilaan eee sakthikal roopakalppana cheythirikkunnathu. saadhaaranayaayi, eee moonnaamathe bodikalil ninnulla modeling efakttukalkkaayi oru golaakrithiyilulla pooyint-maas guruthwaakarshana model maathrame upayogikkunnulloo.
moonnaam shareera aswasthathakalude chila prathyeka kesukalkku ekadesha vishakalana parihaarangalund. udaaharanathinu, aarohana nodinte valath aarohanathinulla aswasthathakalum vrithaakrithiyilulla bhoomiyude bhramanapathathinaayulla perijiyude vaadavum ivayaanu
sourorjja vikiranam.
soura vikirana marddam bhramanapathangalil aswasthathakal srishtikkunnu. bhoomiyude bhramanapathathil oru bahirakasha pedakatthinu athu nalkunna thwaranathinte vyaapthi chuvadeyulla samavaakyam upayogichu maathrkayaakkunnu
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bhoomiye chuttipattiyulla bhramanapathangalil, soura vikirana marddam 800 kilometer uyarathil valikkunnathinekkaal sakthamaaya shakthiyaayi maarunnu.
propulsion.
vividha tharatthilulla bahirakasha pedaka propulsion undu. rokkatt enchinukal ettavum vyaapakamaayi upayogikkunna onnaanu. oru rokkatt enchininte shakti eee samavakyathaal maathrkayaakkappedunnu
mattoru saadhyamaaya reethi solar paaykkalaanu. aavasyamulla propulsive fozhsu nedunnathinu solar seyilukal radiation marddam upayogikkunnu. sourorjja kaatt moolamundaakunna aswasthathayude maathruka oru sourorjja kappalil ninnulla pranodakashakthiyude maathrkayaayi upayogikkaam.
valichiduka.
thaazhnna bhouma bhramanapathathil upagrahangalil pravartthikkunna praadhamika guruthwaakarshanamallaatha shakti anthareeksha valichedukkalaanu. valichidal vegathayude dishaykku virudhamaayi pravartthikkukayum oru bhramanapathathil ninnu oorjjam neekkam cheyyukayum cheyyum. valichidal moolamundaakunna balam thaazhepparayunna samavakyathaal maathrkayaakkappedunnu
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120 kilometeril thaazheyulla bhramanapathangalkku saadhaaranayaayi valare uyarnna valichedukkal undengil, bhramanapathangal valare vegathil shayikkukayum oru upagrahathin eathoru praayogika dauthyavum poortthiyaakkaan mathiyaya ayuss nalkukayum cheiyunnu. maruvashathu, 600 kilometerinu mukalilulla bhramanapathangalkku thaarathamyena cheria valichedukkal undu, athinaal bhramanapatham mandagathiyilaakukayum upagrahathinte upayogapradamaaya aayussil yadhaartha swaadheenam cheluthaathirikkukayum cheiyunnu. bhoomiye parikramanam cheiyunna thaazhnna upagrahangal vasikkunna thaapamandalatthil vaayuvinte saandrata ganyamaayi vyathyaasappedaam. eee vyathiyaanam praadhamikamaayi sourorjja pravartthanam moolamaanu, athinaal sourorjja pravartthanam oru bahirakasha pedakatthile valichedukkal sakthiye valareyadhikam swaadheenikkukayum deerghakaala bhramanapatha simuleshan sankeernamaakkukayum cheyyum.
kaanthikakshethrangal.
deerghakaala exposure soukaryathil kandathupole bhramanapathathile aswasthathayude uravidamaayi kaanthikakshethrangalkk oru pradhana punk vahikkaan kazhiyum. guruthwaakarshanam pole, bhoomiyude kaanthikakshethram chuvade kaanichirikkunnathupole golaakrithiyilulla harmonixiloode prakadippikkaan kazhiyum
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