First Solutions to Gravitation and Orbital Precession under Vectorial Relativity

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1 niesi Centl e enezel o the SeleteWoks of Joge A no h, 8 ist Soltions to ittion n Obitl Peession ne etoil Reltiity Joge A no, niesi Centl e enezel Ailble t: htts://woksbeesso/joge_fno/6/

2 Jonl of etoil Reltiity JR 8) - ist Soltions to ittion n Obitl Peession ne etoil Reltiity J A no R ASTRACT: In eios wok, it ws estblishe the oet eqtion tht goens gittionl effet of ssie boy, onsiee it with fixe n onstnt ss, on lnet of ss, oing t eloity n oent, bee:, whee the le of the gittionl fiel exete by the ssie boy on t t the lnet s ible ss ws fon to be:, enoting by the onstnt le of the line oent fo the lnet ttte by the ssie boy, t its neest oint ) One of the esons of the sess of Einstein s enel Theoy of Reltiity TR) ws tht it llowe to llte lnet s eession ottion of the ellitil th xis with tie, ie: ey Peession) The ft tht its oene hs been exeientlly obsee is not onte by lssi Kele s o Newton ws bese it is only lible to onstnt sses This wok shows tht lnet s eession is iet onseqene of onsieing ible lnet s ss insie ete hysil lws in o known theeiensionl se Aoing to s, this wok ositiely onfis new efinitions of ss n Enegy obtine ne etoil Reltiity KEYWORDS: niesl ittion, Kele ws, etoil oentz Tnsfotions, Obitl Peession, ey s Peession, STR, TR INDEX I Intotion II Clssi eqtion n soltion of lnet s otion ne the inflene of entl foe III Reltiisti etoil) eqtion fo lnet s otion ) Test on the onsisteny of lnet s sstion b) Ext eqtion fo lnet s otion on ssie boy ) A ey oxite soltion fo lnet s otion ) Plnet s eession ey s Peihelion Ane I Conlsion REERENCES I INTRODCTION This wok is ontintion of eios ones on etoil Reltiity efee to: ss n Enegy [], ittion [] n Peession [] In the esent wok it is eie n ext eqtion of lnet Ineenent Resehe, Cs, enezel, jfno@yhooo h, 8

3 J A no R: Soltions to ittion n Obitl Peession in etoil Reltiity h, 8 otion bot ey ssie boy st o Sn) n ey oxite exession of ngle of eession s n effet of the ition of the lnet s ss, with its eloity In Setion II, in oe to t le the se oee fo hieing sh eition we eet tht efee to the lssi ision ee in [] Setion III issses how the onsietion of ible ss insie etoil Reltiity Theoy llows eiting the effet of eession obsee in lnets otion The eition of the exession fo llting the eihelion ne of ey is esente At the en of this wok e esente soe onlsions II CASSIC EQATION AND SOTION OR PANET S OTION o onstnt sses it ws esente in [] how Kele's ws n be ietly ee fo Newton s niesl w of ittion [], let s ese it hee etting, the following exessions of eloity n eletion n be obtine: n t t t t t t t t t ) y lying the efinition of oe n Newton s niesl ittion w to two ttting boies of onstnt sses n, we n wite tht: ) t Sbstitting the obtine exession ) of eletion in ) we ie t: t t t t t ) This etoil eqtion etes the following two sl eqtions: ) ) t t t t t y eebeing tht ngl eloity is efine s oent Consetion w: ), fist eqtion genetes Angl t t t t t t t t t og og JR 8) - Jonl of etoil Reltiity

4 J A no R: Soltions to ittion n Obitl Peession in etoil Reltiity h, 8 Constnt Constnt, fo, ese t eihelion 5) t Deeloent of the seon sl eqtion llows obtining the following exession: q 6) t K Doing q K 7) t t q Defining, n sbstitting q by its eqilent exession, we obtin: fo h h h y integting both sies of this eqtion we get the finl soltion fo ngle: h h os h 8) eos h os h Eqtion 8) eesents oni with eentiity e, with one fos t oigin Alie to h lnets, fo, is the le of is t eihelion Howee, it is neessy to intoe the following iotnt oent: ese eqtion 8) eesents efet oni, the henoenon of eession ottion of the oni lne xis, eset to the ente of the oni) is bsent in this soltion The non-eition of this henoenon in lssi nlysis, in tho s oinion, is gien by the non-onsietion of the eltiisti eenene of ss on its see n on the see of light III REATIISTIC ECTORIA) EQATION OR PANET S OTION et s ty to follow siil oee fo obtining genel exession of the eqtion fo lnet s otion on ssie boy, siil to tht of [] t t t t JR 8) - Jonl of etoil Reltiity

5 J A no R: Soltions to ittion n Obitl Peession in etoil Reltiity h, 8 JR 8) - Jonl of etoil Reltiity t t t t t t t Sbstitting oely, t t t t t t t t t y eseing the efinition of the gittionl fiel s qotient between oe n ss: t t t t t ; ;, ) o, fo, 9) Whee, enotes the gittionl fiel The seon onition lie to ss oing on nothe one oigintes n eqtion siil to tht of following eqtion: t t t t t t t t An ext exession obtine fo this se is []: K K q ) The sse exession, tht enses onsetion of ngl oent beoes: K q ) Asstion in this se ilies the eqlity of these two tes: K ) Ths, thogh this oess the following exessions wee obtine []:

6 J A no R: Soltions to ittion n Obitl Peession in etoil Reltiity h, 8 JR 8) - Jonl of etoil Reltiity 5 ittionl iel) ) ss) ) oent) 5) enei Ris) 6) K q Ril eloity) 7) Tngentil eloity) 8) A) CONSISTENCY O PREIOS ASSPTION OR PANETS Y CHECKIN OTAINED AE OR INEAR OENT Aitionlly to those ontols one in [] let s hek tht obtine exession fo eets the genel eltionshi: The exession of line oent, n be t s:

7 J A no R: Soltions to ittion n Obitl Peession in etoil Reltiity h, 8 JR 8) - Jonl of etoil Reltiity 6 fo 9) Oeting on this eltionshi: Sbstitting,, n It is obtine effetiely n onsistently tht: ) EXACT EQATION OR PANET S OTION AROND A ASSIE ODY On the othe hn, s we will see the following onesions n be se efetly n eqtely on ible ss fo obtining sitble eqtions of otion [5] [6] [7]: ; ; ; t t ) In effet, in the eqtion, t t t t, by oeting on the fist te, t : K t t t t

8 J A no R: Soltions to ittion n Obitl Peession in etoil Reltiity h, 8 JR 8) - Jonl of etoil Reltiity 7 t y sing this onesion n othes in the eqtion of otion fo lnets: t t t t t t sing eios onesions on the lst te, t t, we get: t t Sbstitting n silifying we he the ext eqtion of otion fo PANETS: t t t t ) C) A ERY APPROXIATE SOTION OR PANET S OTION In oe to obtin the soltion of this ext eqtion we sessflly se ll the eslts n efinitions obtine thogh the noel etoil Theoy of Reltiity []: ) The new efinition of eltiisti ss,, tht oets tht gien by Einstein s in 95,, whee is the est ss The new efinition is lso iet onseqene of oeting eoneos sstions insie oentz Tnsfotions [], b) The New efinition of Reltiisti Kineti Enegy [], K, whih is onseqene of the oete efinition of ss inite in )

9 J A no R: Soltions to ittion n Obitl Peession in etoil Reltiity h, 8 JR 8) - Jonl of etoil Reltiity 8 ) The onsietion of gittion s the effet of entl foe, oe by ssie boy, onsiee fixe, on ying oing sses eening on its eloities n the see of light o hee new efinition of gittionl fiel ws obtine n new efinition of tngentil eloity []: In oe to he this eqtion oe sitble to hnle, let s llte the gittionl foe s eslt of oeting oe the kineti enegy Reebe tht: E E E t t ) An tht []: Ths, E E E E E 6 Peios one is the exession of gittionl foe: Diiing by ss, we obtin gittionl fiel: ) Woking on the genei tngentil eloity:, whee: king the following oxitions gien tht, ): 9 9 Dising lst tes with

10 J A no R: Soltions to ittion n Obitl Peession in etoil Reltiity h, 8 JR 8) - Jonl of etoil Reltiity 9 An going, we he: ) king new oxitions: 5) Tking eities eltie to tie n silifying: Diiing by n silifying,

11 J A no R: Soltions to ittion n Obitl Peession in etoil Reltiity h, 8 JR 8) - Jonl of etoil Reltiity Dising those tes being t lest eight oes of gnite slle thn othes, 6 6 6) Intoing lst eslt into, fo o 6 6 ) f Intoing,, fo, the ss t est, n silifying: ) ) 8 6 ) ) ) ) f f f f f f Sbstitting

12 J A no R: Soltions to ittion n Obitl Peession in etoil Reltiity h, 8 JR 8) - Jonl of etoil Reltiity o 6 n 6 7) This seon oe iffeentil eqtion hs known soltion gien by: os A Whee, by tking twie the eities of : os sin os A An sbstitting in the seon oe eqtion, we he: os 6 os 6 A A 6 os 6 ien tht the tigonoeti fntion os is n ineenent othogonl fntion, we n obtin the les of onstnts A, n, by eqling oeffiients: 6 6 8) 6 6 A A 9) Initil onitions ily: 6 6 os 6, ) The olete eqtion of lnet tjetoy beoes: 6 os 6 6 )

13 J A no R: Soltions to ittion n Obitl Peession in etoil Reltiity h, 8 6 o n 6 ) h' O efining h ' we n obtin sitble exession fo ngle: os, ) 6 h' / h' o fo is: ) os h' D) PANET S PRECESSION o one yle of the fntion the ngle is, then ngle C, gete thn, swet by is eets So, the ositie eession e eoltion is: C C 6 6 5) 6 Obsee tht this oxite le of obitl eession is ey lose to those gien by obsetions n enel Theoy of Reltiity Peession fo lnet ey is the le: I CONCSION Aoing to this wok, obtine eslt fo ey s eession, onfi the liity of: o itiiss to oentz Tnsfotions [], o new efinitions of Reltiisti ss [], Reltiisti Enegy [], ittionl iel [] n onsietion of ittionl oe s Centl oe In this sense it is iotnt to obsee its ossible lition to Qnt ehnis [8] [9] Along ll this wok stte in 996, it hs been shown tht it is ossible to he only one n onsistent theoy fo exlining the hysis of o niese, insie the known thee iensions by now) with the se fnentl onets of hysis ls onsieing ition of ss with eloity n see of light s n niesl onstnt etoil Reltiity) This wok lso les to estblish s fist onlsie ft tht Seil Theoy of Reltiity SRT) is not oet JR 8) - Jonl of etoil Reltiity

14 J A no R: Soltions to ittion n Obitl Peession in etoil Reltiity h, 8 REERENCES [] J A no R Enegy in etoil Reltiity, E Pblishe by JR on Noebe 6th 6 JR 6) -7 [] J Qinteo D n J A no R ittionl oes in etoil Reltiity Pblishe by JR on h 6th 7 JR 7) - [] J Qinteo D n J A no R Peession in etoil Reltiity Pblishe by JR on h 6th 7 JR 7) 5-6 [] J A no R etoil oentz Tnsfotions Pblishe by EJTP on eby 5th 6 EJTP 9 6) 5-6 [5] D wz Obitl Peession withot R //7 [6] Refletions on eltiity Anolos Peession [7] otion ne the Inflene of Centl oe htt://she/books/989fbook/chte5f, [8] J A no R Qnt ehnis in etoil Reltiity Pblishe by JR on Noebe 6th 6 JR 6) -7 [9] J A no R ittionl Wes in etoil Reltiity Pblishe by JR on Jne 6th 7 JR 7) -5 JR 8) - Jonl of etoil Reltiity