New Newton Mechanics Taking Law of Conservation of Energy as Unique Source Law

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1 Science Jonal of hysics ISSN: Atho(s 5. CC Attibtion 3. License. Reseach Aticle blished By Science Jonal blication Intenational Open Access blishe New Newton Mechanics Taking Law of Conseation of Enegy as Uniqe Soce Law Yha CNOOC Reseach Institte Accepted on Mach 7, 5 Abstact: Accoding to the pinciple of the niqeness of tth, this pape pesents the New Newton Mechanics (NNM taking law of conseation of enegy as niqe soce law. Eamples show that in some cases othe laws may be contadicted with the law of conseation of enegy. The oiginal Newton's thee laws and the law of gaity, in pinciple can be deied by the law of conseation of enegy. Thogh the eample of fee falling body, this pape deies the oiginal Newton's second law and the oiginal law of gaity by sing the law of conseation of enegy; and thogh the eample of a small ball olls along the inclined plane (belonging to the poblem cannot be soled by geneal elatiity that a body is foced to moe in flat space, deies impoed Newton's second law and impoed law of gaity by sing law of conseation of enegy. Whethe o not othe conseation laws (sch as the law of conseation of momentm and the law of conseation of angla momentm can be tilized, shold be tested by law of conseation of enegy. When the oiginal Newton's second law is not coect, then the laws of conseation of momentm and angla momentm ae no longe coect; theefoe the geneal foms of impoed law of conseation of momentm and impoed law of conseation of angla momentm ae pesented. In the cases that law of conseation of enegy cannot be sed effectiely, New Newton Mechanics will not eclde that accoding to othe theoies o accate epeiments to deie the laws o fomlas to sole some specific poblems. o eample, with the help of the eslt of geneal elatiity, the impoed Newton's fomla of niesal gaitation can be deied, which can be sed to sole the poblem of adance of planetay peihelion and the poblem of deflection of photon aond the Sn. Again, accoding to accate epeimental eslt, the synthesized gaitational fomla (inclding the effects of othe celestial bodies and snlight pesse fo the poblem of deflection of photon aond the Sn is pesented. Unlike the oiginal Newton Mechanics, in New Newton Mechanics, fo diffeent poblems, may hae diffeent laws of motion, diffeent fomlas of gaity, as well as diffeent epessions of enegy. o eample, fo the poblem of a small ball olls along the inclined plane, and the poblem of adance of planetay peihelion, the two fomlas of gaity ae completely diffeent. Keywods: Uniqeness of tth, law of conseation of enegy, niqe soce law, New Newton Mechanics (NNM Intodction One of the deelopment tends of natal science is sing fewe laws to sole inceasing poblems. In this pocess, some laws will play the inceasingly geat oles; while othes will play the smalle oles, o een disappea fom the anks of laws. Now we discss the law of conseation of enegy. Its main contents ae as follows: In a closed system, the total enegy of this system emains nchanged. Becase the law of conseation of enegy is the most impotant one in natal sciences, it shold play an inceasingly geat ole. o this eason and accoding to the pinciple of the niqeness of tth, this pape pesents the New Newton Mechanics (NNM taking law of conseation of enegy as niqe soce law. In the aea of Newton Mechanics, thee shold be one tth only. Othe so-called tth, eithe it can be deied by the niqe tth, o we can poe that in cetain cases it is not te. As well-known, when Newton fonded the classical mechanics, fo laws wee poposed, they wee Newton's thee laws and the law of gaity. If the law of conseation of enegy is choosing as the niqe soce law, that in pinciple, all the Newton's fo laws can be deied accoding to the law of conseation of enegy; afte stdying caeflly we fond that this may indeed be the eal case. In addition, in the aeas sch as physics, mechanics, engineeing and so on, thee ae thee ey impotant laws: the law of conseation of enegy, the law of conseation of momentm and the law of conseation of angla momentm. How to Cite this Aticle: Yha, "New Newton Mechanics Taking Law of Conseation of Enegy as Uniqe Soce Law", Science Jonal of hysics, Volme 5, Aticle I sjp-3, ages, 5, doi:.737/sjp/3

2 S c i e n c e J o n a l o f h y s i c s ( I S S N : a g e If we beliee that the law of conseation of enegy is the tth, then fo the law of conseation of momentm and the law of conseation of angla momentm, eithe they can be deied by the law of conseation of enegy, o we can poe that in cetain cases they ae not te. We beliee that the te sitation is the latte, namely, the law of conseation of momentm and the law of conseation of angla momentm ae not te in some cases (o thei eslts ae contadicted to the law of conseation of enegy. Of cose, we can also find that in some cases, these two laws still can be sed. Taking the eample that a man walks along the ca located on the hoizontal smooth ail, we can see that at pesent in the aea of Newton mechanics, some people do not notice the case of the contadiction between the law of conseation of enegy and the law of conseation of momentm. Taking Law of Conseation of Enegy as Uniqe Soce Law. eiing Oiginal Newton's Second Law and Oiginal Law of Gaity.. eiing Oiginal Newton's Second Law by Using Law of Conseation of Enegy In this section, only Newton's second law can be deied, bt we hae to apply the law of gaity at the same time, so we pesent the geneal foms of Newton's second law and the law of gaity with ndetemined constants fistly. Assming that fo the law of gaity, the elated eponent is nknown, and we only know the fom of this fomla is as follows whee: is an ndetemined constant, in the net section we will deie that its ale is eqal to. Similaly, assming that fo Newton's second law, the elated eponent is also nknown, and we only know the fom of this fomla is as follows ' ma whee: is an ndetemined constant, in this section we will deie that its ale is eqal to. As shown in ige, spposing that cicle O denotes the Eath, M denotes its mass; m denotes the mass of the small ball (teated as a mass point, A O is a plmb line, and coodinate y is paallel to AO. The length of AC is eqal to H, and O C eqals the adis R of the Eath. We also assme that it does not take into accont the motion of the Eath and only consideing the fee falling of the small ball in the gaitational field of the Eath (fom point A to point C. ige A small ball fee falls in the gaitational field of the Eath o this eample, the ale of which is the sqae of the elocity fo the small ball located at point will be inestigated. To distingish the qantities calclated by diffeent methods, we denote the ale gien by the law of gaity How to Cite this Aticle: Yha, "New Newton Mechanics Taking Law of Conseation of Enegy as Uniqe Soce Law", Science Jonal of hysics, Volme 5, Aticle I sjp-3, ages, 5, doi:.737/sjp/3

3 S c i e n c e J o n a l o f h y s i c s ( I S S N : a g e 3 and Newton s second law as,while ' denotes the ale gien by the law of conseation of enegy. Now we calclate the elated qantities accoding to the law of conseation of enegy. om the law of gaity contained ndetemined constant, the potential enegy of the small ball located at point is as follows V ( O ' Accoding to the law of conseation of enegy, we can get ( A And theefoe GM [ m' ( R H ( ' O ' Now we calclate the elated qantities accoding to the law of gaity and Newton s second law. o the small ball located at any point, we hae We also hae Theefoe d/ dt a dy dt d ady Accoding to the law of gaity contained ndetemined constant, along the plmb diection, the foce acted on the small ball is as follows a om the Newton's second law contained ndetemined constant, it gies a a ( m Then we hae / ' GM d { ( R H y GM ( } / ' dy / ' o the two sides of this epession, we n the integal opeation fom A to, it gies Let / ' ( GM ( GM / / ' ( GM [ ( / ' y p ( R H y / ' dy ' { [( R H y / ' ( / ' ( R H ( / ' ', then we shold hae: / ' ( / ' ' / ', and ; these two eqations all gie:, this means that fo fee falling poblem, by sing the law of conseation of enegy, we stictly deie the oiginal Newton's second law ma. Hee, althogh the oiginal law of gaity cannot be deied (the ale of may be any constant, cetainly inclding the case that =, we aleady poe that the oiginal law of gaity is not contadicted to the law of conseation of enegy, o the oiginal law of gaity is tenable accately... eiing Oiginal Law of Gaity by Using Law of Conseation of Enegy In ode to eally deie the oiginal law of gaity fo the eample of fee falling poblem, we shold conside the case that a small ball fee falls fom point A to point (point is also shown in ige thogh a ey shot distance Z (the two endpoints of the inteal Z ae point A and point. As deiing the oiginal Newton's second law, we aleady each GM [ ( R H Z ( R H ' ' y p } How to Cite this Aticle: Yha, "New Newton Mechanics Taking Law of Conseation of Enegy as Uniqe Soce Law", Science Jonal of hysics, Volme 5, Aticle I sjp-3, ages, 5, doi:.737/sjp/3

4 S c i e n c e J o n a l o f h y s i c s ( I S S N : a g e 4 whee: R H Z ' Z o the eason that the distance of is ey shot, and in this inteal the gaity can be consideed as a linea fnction, theefoe the wok W of gaity in this inteal can be witten as follows Whee, W a a Z R H Z ( Z is the aeage ale of gaity in this Z inteal, namely the ale of gaity fo the midpoint of inteal. Z Omitting the second ode tem of Z ( 4 ( Z, it gies W ( R H Z RH RZ HZ As the small ball fee falls fom point A to point, its kinetic enegy is as follows m' ' ( R H ( R H Z [ ( R H RH RZ HZ / Accoding to the law of conseation of enegy, we hae W m' ' Sbstitting the elated qantities into the aboe epession, it gies ( R H ( R H Z [ ( R H RH RZ HZ ( R H Z RH RZ HZ / To compae the elated tems, we can each the following thee eqations / Z ( R H ( R H Z All of these thee eqations will gie the following eslt Ths, we aleady deie the oiginal law of gaity by sing the law of conseation of enegy.. New Thee Laws of Motion and New Law of Gaity (omla Ceated By Law of Conseation Of Enegy fo New Newton Mechanics The oiginal Newton's thee laws of motion ae as follows. Newton's ist Law of Motion: Eey object in a state of nifom motion (o at est tends to emain in that state of motion (o at est nless an etenal foce is applied to it. o shot: est emains est, and moing emains moing. Newton's Second Law of Motion: The elationship between an object's mass m, its acceleation a, and the applied foce is = ma. The diection of the foce is the same as the diection of the acceleation. Newton's Thid Law of Motion: o eey action thee is an eqal and opposite eaction. The oiginal Newton s law of gaity: The attactie foce between two objects is as follows ( While fo NNM, taking law of conseation of enegy as niqe soce law, then we hae the following NNM s thee laws of motion and law of gaity. NNM's ist Law of Motion: Eey object in a state of nifom motion (o in a state of nifom otation, o at est tends to emain in that state of motion (o in a state of nifom otation, o at est nless an etenal foce is applied to it; othewise the law of conseation of enegy will be destoyed. o shot: est emains est, moing emains moing, and otating emains otating. NNM's Second Law of Motion: The elationship between an object's mass m, its acceleation a, and the applied foce is a fnction that shold be deied by law of conseation of enegy. The diection of the foce is the same as the diection How to Cite this Aticle: Yha, "New Newton Mechanics Taking Law of Conseation of Enegy as Uniqe Soce Law", Science Jonal of hysics, Volme 5, Aticle I sjp-3, ages, 5, doi:.737/sjp/3

5 S c i e n c e J o n a l o f h y s i c s ( I S S N : a g e 5 of the acceleation. In geneal, the fnction can be witten as the fom of aiable dimension factal:, whee: is a constant o a aiable. o diffeent poblems, the foms of second law may be diffeent. ma NNM's Thid Law of Motion: In geneal, fo eey action thee is an eqal and opposite eaction. In special case, the fnction elationship between action and eaction shold be deied by law of conseation of enegy. The impoed fom of the oiginal Newton s thid law ( is as follows: AB BA AB, whee: BA is a constant o a aiable. o diffeent poblems, the foms of thid law may be diffeent. NNM s law (fomla of gaity: The attactie foce between two objects is a fnction that shold be deied by law of conseation of enegy, o epeimental data; o deied with the help of othe theoies. o diffeent poblems, the foms of law (fomla of gaity may be diffeent. The eslts of oiginal Newton s law of gaity ae only accate in the cases that two objects ae elatie static o nning the staight line between one cente and anothe cente, and the like; fo othe cases its eslts ae all appoimate. In geneal, NNM s law (fomla of gaity may be taken as the fom that adding the amending tem to oiginal Newton s law of gaity, o the following fom of aiable dimension factal: ( whee: is a constant o a aiable. Now fo an eample, a NNM s law (fomla of gaity (an impoed Newton s law of gaity and a NNM's second law of motion (an impoed Newton s second law of motion, they ae sitable fo this eample only, ae deied simltaneosly by law of conseation of enegy. istly, the aiational pinciples established by the law of conseation of enegy can be gien with least sqaes method (LSM. Spposing that the initial total enegy of a closed system eqals W (, and fo time the total enegy eqals W (t, then accoding to the law of conseation of enegy: W ( = (t W (3 This can be witten as: t R W W ( t W ( = t,t (4 Accoding to LSM, fo the inteal [,we can wite the following aiational pinciple: t W dt min t Whee: R (5 min fnctional Π denotes the minimm ale of and it shold be eqal to zeo. It shold be noted that, in many cases W(t appoimate, and R W is not identically eqal to zeo, theefoe Eq.(5 can be sed to sole the poblem. Besides the time coodinate, anothe one can also be sed. o eample, fo inteal [, the following aiational pinciple can be, gien accoding to the law of conseation of enegy: R (6 W d min The aboe-mentioned pinciples ae established by sing the law of conseation of enegy diectly. Sometimes, a cetain pinciple shold be established by sing the law of conseation of enegy indiectly. o eample, a special physical qantity Q may be inteested,not only it can be calclated by sing the law of conseation of enegy, bt also can be calclated by sing othe laws (fo this pape they ae the law of gaity, and Newton s second law. o distingishing the ales, let s denote the ale gien by othe laws as Q,while denote the ale gien by the law of conseation of enegy as Q ',then the ale of R W can be edefined as follows: Q R W = Q' (7 Sbstitting Eq.(7into Eqs.(5and(6,as is Q ' is the eslt calclated with the law of conseation of enegy, it gies the aiational pinciple established by sing the law of conseation of enegy indiectly. Othewise, it is clea that the etent of the ale of Q accods with Q '. How to Cite this Aticle: Yha, "New Newton Mechanics Taking Law of Conseation of Enegy as Uniqe Soce Law", Science Jonal of hysics, Volme 5, Aticle I sjp-3, ages, 5, doi:.737/sjp/3

6 S c i e n c e J o n a l o f h y s i c s ( I S S N : a g e 6 Sbstitting the elated qantities into Eq.(5o Eq.(6,the eqations deied by the condition of an etemm can be witten as follows: a i k i (8 Afte soling these eqations, the impoed law of gaity, and Newton s second law can be eached at once. Accoding to the ale of Π, the effect of the soltion can be jdged. The neae the ale of is to zeo, the bette the effect of the soltion. Π It shold be noted that besides of soling eqations, optimm-seeking methods cold also be sed fo finding the minimm and the constants to be detemined. In fact, the optimm seeking method will be sed in this pape. Now we sole an eample. As shown in ig., spposing that the small ball olls along a long incline fom A to B. Its initial elocity is zeo and the fiction and the otational enegy of small ball ae neglected. ige. A small ball olls fom A to B Spposing that cicle denotes the Eath, M denotes its mass; small ball (teated as a mass point, O A is a plmb line, coodinate is othogonal to O A, coodinate y is othogonal to coodinate (paallel to O A, BC is othogonal to O A. The lengths of OA, OB, BC, and AC ae all eqal to H, and O C eqals the adis R of the Eath. In this eample, the ale of m denotes the mass of the which is the sqae of the elocity fo the ball located at point is inestigated. To distingish the qantities, denote the ale gien by the impoed law of gaity and impoed Newton s second law as,while ' denotes the ale gien by the law of conseation of enegy,then Eq.(6can be witten as H ( ' d min (9 Spposing that the impoed law of gaity and impoed Newton s second law can be witten as the following constant dimension factal foms ( ma ( whee: and ae constants. Now we calclate the elated qantities accoding to the law of conseation of enegy. om Eq.(, the potential enegy of the small ball located at point is V ( ( O ' Accoding to the law of conseation of enegy, we can get ( A And theefoe GM [ m' ( R H ( ' (4 O ' (3 Now we calclate the elated qantities accoding to the impoed law of gaity and impoed Newton s second law. How to Cite this Aticle: Yha, "New Newton Mechanics Taking Law of Conseation of Enegy as Uniqe Soce Law", Science Jonal of hysics, Volme 5, Aticle I sjp-3, ages, 5, doi:.737/sjp/3

7 S c i e n c e J o n a l o f h y s i c s ( I S S N : a g e 7 Spposing that the eqation of olling line is y H o the ball located at point, (5 d/ dt a (6 Becase dt ds Theefoe d a d d (7 Accoding to the impoed law of gaity, the foce along to the tangent is a (8 Accoding to the impoed Newton s second law, fo point, the acceleation along to the tangent is a ( m ( GM a (9 / / O ' om Eq.(7, it gies GM / d { } d / [( H ( R H y ( Sbstitting Eq.(5 into Eq.(, and fo the two sides, we n the integal opeation fom A to, it gies B,and deie the impoed law of gaity and the impoed Newton s second law. istly, accoding to the oiginal law of gaity, the oiginal Newton s second law (i.e., let Eq.(, = in Eq.( and the law of conseation of enegy, all the elated qantities can be calclated, then sbstitte them into Eq.(9, it gies =57.45 = in Hee, accoding to the law of conseation of enegy, it gies ' B =.767 7,while accoding to the oiginal law of gaity, and the oiginal Newton s second law, it gies B =.35 7,the diffeence is abot 5.4 %. o Π the eason that the ale of is not eqal to zeo, then the ales of and can be decided by the optimm seeking method. At pesent all the optimm seeking methods can be diided into two types, one type may not depend on the initial ales which pogam may be complicated, and anothe type eqies the bette initial ales which pogam is simple. One method of the second type, namely the seaching method will be sed in this pape. istly, the ale of is fied so let =,then seach the ale of,as =.46, the ale of eaches the minimm ;then the ale of is fied,and seach the ale of,as Π =.99989, the ale of Π eaches the minimm ;then the ale of is fied,and seach the ale of as =.458, the ale of eaches minimm Becase the last two eslts ae highly close, the seaching can be stopped, and the final eslts ae as follows Π H ( { [( H GM ( R / } ( / / Then the ale can be calclated by a method of nmeical integal. The gien data ae assmed to be: fo Eath, GM= m 3 /s ; the adis of the Eath R= m, H=R/, ty to sole the poblem shown in ig., find the soltion fo the ale of d =.99989,ε=.458, =37.33 Hee the ale of Π is only 4% of Π. While accoding to the law of conseation of enegy, it gies ' B =.785 7,accoding to the impoed law of gaity and the impoed Newton s second law, it gies B =.73 7, the diffeence is abot.7 % only. The eslts sitable fo this eample with the constant dimension factal fom ae as follows How to Cite this Aticle: Yha, "New Newton Mechanics Taking Law of Conseation of Enegy as Uniqe Soce Law", Science Jonal of hysics, Volme 5, Aticle I sjp-3, ages, 5, doi:.737/sjp/3

8 S c i e n c e J o n a l o f h y s i c s ( I S S N : a g e 8 The impoed law of gaity eads ( The impoed Newton s second law eads.458 ma (3 The aboe mentioned eslts hae been pblished on efeence [. Accoding to the aboe eslts, it can be said that we cold not ely on any epeimental data, only apply the law of conseation of enegy to deie the impoed law of gaity, and impoed Newton's second law; and demonstate that the oiginal Newton s law of gaity and Newton's second law ae all tenable appoimately fo this eample. o the eample shown in ig. that a small ball olls along the inclined plane, in ode to obtain the bette eslts, we discss the aiable dimension factal soltion with Eq.(4 that is established by the law of conseation of enegy diectly. Spposing that the impoed Newton s second law and the impoed law of gaity with the fom of aiable dimension factal can be witten as follows: ; ma, k /, k ; whee: is the hoizon distance that the small ball olls. H With the simila seaching method, the ales of k, k can be detemined, and the eslts ae as follows ,.7 The eslts of aiable dimension factal ae mch bette than that of constant dimension factal. o Π eample, the final, it is only.9% of Π (3.7. While accoding to the ' B law of conseation of enegy, it gies =.767 7,accoding to the impoed law of gaity and the impoed Newton s second law, it gies B =.777 7, the diffeence is abot.93 % only. The impoed law of gaity eads.7 3 (4 The impoed Newton s second law eads 8.85 (5 ma 8 whee: is the hoizon distance that the small ball olls is. H Thee is anothe poblem shold also be discssed. That is the impoed kinetic enegy fomla. As well-known, the kinetic enegy fomla has been modified in the theoy of elatiity, now we impoe the kinetic enegy fomla with the law of conseation of enegy. Spposing that the impoed kinetic enegy fomla is Ed m, is the hoizon distance that the small ball olls ( H. k 3 ;whee: With the simila seaching method, we can get: 3 k , then the impoed kinetic enegy fomla with aiable dimension factal fom eads E d m Becase the effect of impoement is ey small (the ale of is only impoed fom into , theefoe these eslts shold be fo efeence only. 3 With the Help of Geneal Relatiity and Accate Epeimental ata to eie the Impoed Newton's omla of Uniesal Gaitation Π of. H Ning deied an eqation accoding to geneal elatiity, with the help of H's eqation and Binet s fomla, we get the following impoed Newton's fomla of niesal gaitation [ The eslts sitable fo this eample with the aiable dimension factal fom ae as follows How to Cite this Aticle: Yha, "New Newton Mechanics Taking Law of Conseation of Enegy as Uniqe Soce Law", Science Jonal of hysics, Volme 5, Aticle I sjp-3, ages, 5, doi:.737/sjp/3

9 S c i e n c e J o n a l o f h y s i c s ( I S S N : a g e 9 3G M c 4 mp (6.5 4 (8 whee: G is gaitational constant, M and m ae the masses of the two objects, is the distance between the two objects, c is the speed of light, p is the half nomal chod fo the object m moing aond the object M along with a ce, and the ale of p is gien by: p = a(-e (fo ellipse, p = a (e - (fo hypebola, p = y / (fo paabola. It shold be noted that, this impoed Newton's fomla of niesal gaitation can also be witten as the fom of aiable dimension factal. Sppose 3G M mp 4 c GMp It gies 3 ln( / ln 4 c o the poblem of gaitational defection of a photon obit aond the Sn, M=.99 3 kg, = m, c= m/s, then we hae: The impoed Newton s niesal gaitation fomla (Eq.(6 can gie the same eslts as gien by geneal elatiity fo the poblem of planetay adance of peihelion and the poblem of gaitational defection of a photon obit aond the Sn. o the poblem of planetay adance of peihelion, the impoed Newton s niesal gaitation fomla eads 3G M ma( e 4 c (7 o the poblem of gaitational defection of a photon obit aond the Sn, the impoed Newton s niesal gaitation fomla eads whee: is the shotest distance between the light and the Sn, if the light and the Sn is tangent, it is eqal to the adis of the Sn. The fnny thing is that, fo this poblem, the maimm gaitational foce gien by the impoed Newton s niesal gaitation fomla is.5 times of that gien by the oiginal Newton s law of gaity. Althogh the deflection angles gien by Eq. (6 and Eq. (8 ae all eactly the same as gien by geneal elatiity, they hae still slight deiations with the pecise astonomical obseations. What ae the easons? The answe is that the deflection angle not only is depended on the gaitational effect of the Sn, bt also depended on the gaitational effects of othe celestial bodies, as well as the inflences of snlight pesse and so on. If all factos ae taken into accont, not only geneal elatiity can do nothing fo this poblem, bt also fo a long time it cold not be soled by theoetical method. Theefoe, at pesent the only way to sole this poblem is based on the pecise obseations to deie the synthesized gaitational fomla (inclding the effects of othe celestial bodies and snlight pesse fo the poblem of deflection of photon aond the Sn. As well-known, the deflection angle gien by geneal elatiity o the impoed Newton's fomla of niesal gaitation is as follows =.75 Adding an additional tem to Eq.(8, it gies the synthesized gaitational fomla between the photon and the Sn as follows GMp wg M p ( c c (9 whee: w is a constant to be detemined. How to Cite this Aticle: Yha, "New Newton Mechanics Taking Law of Conseation of Enegy as Uniqe Soce Law", Science Jonal of hysics, Volme 5, Aticle I sjp-3, ages, 5, doi:.737/sjp/3

10 S c i e n c e J o n a l o f h y s i c s ( I S S N : a g e ige 3. eflection of photon aond the Sn Now We etemine The Vale Of W Accoding To Accate Epeimental ata. istly the poblem of deflection of photon aond the Sn as shown in ig.3 will be soled with Eq.(9. The method to be sed is the same as pesented in efeences [ and [3. Spposing that m epesents the mass of photon. Becase the deflection angle is ey small, we can assme that =; ths on point (, y, its coodinate can be witten as (,y, then the foce acted on photon eads ( y (3 / Whee: The ale of is gien by Eq.(9. Becase m Hence dt dy y c dy (3 GM dy 6G M p dy c 3 3 ( y c ( y / 5/ Theefoe GM 4G M p 6wG M p c c 5c Becase tg c 3 3 By sing the half nomal chod gien in efeence [, it gies c p GM Then the deflection angle is as follows 4GM w c 5 Whee: is the adis of Sn. Becase 4 GM c (34 ( wg M p 5 c Becase dy 3 ( y / dy 7 ( y / (3 dy (, 5/ 4 dy 8 ( 7 / y 5 6 y 3, Then, it gies w ( 5 (35 Ths the ale of w can be soled as follows w 5 ( (36 Now we can detemine the ale of w accoding to the epeimental data. How to Cite this Aticle: Yha, "New Newton Mechanics Taking Law of Conseation of Enegy as Uniqe Soce Law", Science Jonal of hysics, Volme 5, Aticle I sjp-3, ages, 5, doi:.737/sjp/3

11 S c i e n c e J o n a l o f h y s i c s ( I S S N : a g e Table shows the epeimental data of adio astonomy fo the deflection angle of photon aond the Sn (taken fom efeence [4. Table. The epeimental data of adio astonomy fo the deflection angle of photon aond the Sn Yea Obsee Obseed ale / 969 G.A.Seielstd et al.77±. 969.O.Mhleman et al I.I.Shapio.8±. 97 R.A.Samak.57±.8 97 J.M.Hill.87± ± ± ±. Now we choose the epeimental data in 975, it gies.76 φ.8 Then, we hae.857 w.4857 Taking the aeage ale, it gies w=.574 Ths, accoding to the epeimental data, the synthesized gaitational fomla can be decided. 4 Contadiction between the Law of Conseation Of Enegy and the Law of Conseation Of Momentm As Well As the Law of Conseation of Angla Momentm As well-known, nlike the law of conseation of enegy, the law of conseation of momentm and the law of conseation of angla momentm ae only coect nde cetain conditions. o eample, consideing fiction foce and the like, these two laws will not be coect. Now we point ot fthe that fo NNM the law of conseation of momentm as well as the law of conseation of angla momentm will be not coect nde cetain conditions (o thei eslts contadict with the law of conseation of enegy. As well-known, in ode to poe the law of conseation of momentm as well as the law of conseation of angla momentm, the oiginal Newton's second law shold be applied. Howee, as we hae made clea, the oiginal Newton's second law will not be coect nde cetain conditions, fo sch cases, these two laws also will not coect. Hee we find anothe poblem, if the oiginal thee conseation laws ae all coect, theefoe fo cetain isses, the law of conseation of enegy and the othe two conseation laws cold be combined to apply. While fo NNM, if the othe two conseation laws cannot be applied, how to complement the new fomlas to eplace these two conseation laws? The soltion is ey simple: accoding to the law of conseation of enegy, fo any time, the deiaties of total enegy W (t shold be all eqal to zeo, then we hae n d W ( t n dt n,,3, (37 In addition, nning the integal opeations to the both sides of Eq.(3, it gies t W ( t = W ( t dt (38 Now we illstate that, becase thee is one tth only, een within the scope of oiginal classical mechanics, the contadiction cold also appea between the law of conseation of enegy and the law of conseation of momentm. As shown in ig.4, a man walks along the ca located on the hoizontal smooth ail, the length of the ca eqals L, the mass of the man is m and the ca is m. At beginning the man and the ca ae all at est, then the man walks fom one end to the othe end of the ca, ty to decide the moing distances of the man and the ca. This eample is taken fom efeences [5. How to Cite this Aticle: Yha, "New Newton Mechanics Taking Law of Conseation of Enegy as Uniqe Soce Law", Science Jonal of hysics, Volme 5, Aticle I sjp-3, ages, 5, doi:.737/sjp/3

12 S c i e n c e J o n a l o f h y s i c s ( I S S N : a g e ige 4 A Man Walks along the Ca Located On the Hoizontal Smooth Rail As soling this poblem by sing the oiginal classical mechanics, the law of conseation of momentm will be sed, it gies m m Howee, at beginning the man and the ca ae all at est, the total enegy of the system is eqal to zeo; while once they ae moing, they will hae speeds, and the total enegy of the system is not eqal to zeo; ths the law of conseation of enegy will be destoyed. o this paado, the oiginal classical mechanics looks withot seeing. In fact, consideing the lost enegy of the man and applying the law of conseation of enegy, the completely diffeent eslt will be eached. As the oiginal law of conseation of momentm and the law of conseation of t ( Const angla momentm ( L t L Const ae not coect, we can popose thei impoed foms of aiable dimension factal. The impoed law of conseation of momentm: t ( is a constant o a aiable, and the impoed law of conseation of angla momentm: ( is a constant o a aiable. Refeences L L t. Yha, eiing Impoed Newton s Second Law and the Law of Gaity at One Time with om of actal omla, Engineeing Science. 3,Vol.5,No.6, Yha, Impoed Newton s fomla of niesal gaitation, Zianzazhi (Nate Jonal, (, C. Kittel et al, Tanslated into Chinese by Chen Bingqian et al, Mechanics, Beijing: Science ess, 979, Li Liao, Geneal elatiity, Beijing: Highe edcation pess, 987, 5. X Heing, Mechanics (eised edition, Shanghai: East China Nomal Uniesity ess, 998, How to Cite this Aticle: Yha, "New Newton Mechanics Taking Law of Conseation of Enegy as Uniqe Soce Law", Science Jonal of hysics, Volme 5, Aticle I sjp-3, ages, 5, doi:.737/sjp/3