
rotational braunian motion (khagolshastra)

khagolshastrat, firnari braunian gatee mhanje dwaiti taayachya kakshiy pratalachya dishene yadruchchik chaal, jee taryanmadhun jaananya gurutvakarshanachya vikshobhanmule prerit hote.
siddhant.
done prachand vastoo (taare, krishna chhidre ii.) asalelya dwaiticha vichar qaraa.) aanee teey mothya sankhyene taare asalelya tarakeey pranalimadhye antarbhut aahe. sootra 1 aanee sootra 2 heey dviaadharichya done ghatakanche vastuman asoo dya, jyanche ekoon vastuman sootra 3 aahe. eka kshetra taara joou prabhav mapdand sootra 4 saha dviaadharikade jaato aanee veg sootra 5 dviaadharipasun antar sootra 6 paar karate, jethe
sootra _ 7
nantarchi abhivyakti yaa maryadet vaidh aahe qee gurutvakarshanachya kendrabindune samna daravar varchasva gajavale aahe. dviaadhari, i shhee jordar sanvad sadhananya tanyanshi honanya bheticha darr.eae. sootra 8 chey samadhan karnare sootra andaje sootra 9 aahe, jethe sootra 10 aanee sootra 11 heey kshetra tanyanchi sankhya ghanata aanee veg prasaran aahe aanee sootra 12 haah dviaadharicha ardh-pramukh aksh aahe.
dwaitijavalun jaat asatana, kshetra taachaa veg kramane badalato 
sootra _ 13, 
jethe sootra _ 14 haah dwaititil done tanyancha sapeksh veg aahe.
binary sootra _ 15 chya sandarbhat kshetra taayachya vishisht koneey gatimadhye jhalela badal nantar δ "l" ± "a" "v" biin aahe. koneey gatiche sanwardhan asey soochit karate qee dviaadharichi koneey gatee δ "l" biin ±-(m/μ12) δ "l" neey badalate jethe "m" heey kshetra taache vastuman aahe aanee "μ12" heey dviaadhari qamee jhalele vastuman aahe. l" binchya parimanatil badal heey "e" = 1-"l" b2/"gm" 12μ12 "a" yaa sambandhadvare binarychya kakshiy utkendratetil badalanshi sambandhit aahet. ell" binchya dishene honare badal heey dviaadharichya dishadarshanatil badalanshi sambandhit asatat, jyamule paribhraman prasar hoto. paribhraman prasar gunank aahe
sootra _ 16
jethe ρ = "mn" hii kshetra tanyanchi vastuman ghanata aahe.
binarycha rotation aksh 't' velevar θ konat sthit asanyachi sambhavyata 'f' (θ, t ') asoo dya. eff' sathee utkrantiche samikaran aahe 
sootra _ 17
jarr <δx2>, "a", ρ aanee σ velenusar sthir asateel, tarr heey hote
sootra _ 18
jethe 't' rile 'yaa vishrantichya velechya ekkanmadhil vel hii' m '=' cos θ 'aanee' τ 'aahe, jethe
sootra _ 19
yaa samikaranacha upay asey sangato qee, velenusar, microche apekshit moolya qamee hote.
sootra _ 20
mhanoon, 'tii' reel haah dwaitichya abhimukhatacha vel sthirank aahe joou kshetra tanyanmadhil tokandware yadruchchik keela jaato.
anuprayog.
aakashgangechya kendranvar dwaiti supermassive black holchya sandarbhat rotational braunian gativar pratham charcha karnyat aalee. taryanmadhun jaat asalelya vikshobhanmule asha dwaitiche kakshiy pratal badaloo shakate, jeey tyaa donhi ekatra aalyavar tayar honanya ekach krishnabinduchya firki akshachi disha badalate.
dviaadhari krishna chhidre asalelya aakashgangechya aine-boddy anukarananmadhye varanvar firatya braunian gatiche nirikshan kele jaate. prachand dwaiti gatishil gharshanadvare aakashgangechya madhyabhagi budate jithe tee pudhe jaananya tanyanshi sanvad sadhate. binarychya dishene yadruchchik chalanyas pravrutt karananya tyach gurutviya vikshobhanmule, gurutvakarshanachya slingshotdware binary dekhil sankuchit hote. heey darshavile jaau shakate qee dviaadharichya dishene aar. emm. ess. badaltat, dviaadhari tayar hoiparyant done krishna chhidre ekmekanshi bhidatat, andaje
sootra _ 21
vastavik aakashganget, gurutvakarshaniy laharinchya utsarjanamule done krishnavivara akheris ekatra yeteel. ektrit chhidracha firki aksh haah aadhipasoon astitvat asalelya dviaadharichya kakshachya koneey gatee akshasah sanrekhit keela jaeel. tyamule, dwaiti krishna chhidranchya kakshanvar parinam karnari ghoornan braunian gatisarkhi yantrana dekhil krishnabindu firanyachya vitarnavar parinam karoo shakate. supermassive black holschya firki aksh tyanchya yazman aakashgangechya sandarbhat yadruchchikpane sanrekhit qaa disatat heey heey kahee pramanat spasht karoo shakate.