1 Dark Cloud Hanging over Twentieth Century Physics

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1 We ae Looking fo Moden Newton by Caol He, Bo He, and Jin He Wuhan FutueSpace Scientific Copoation Limited, Wuhan, Hubei , China Abstact Newton discoveed the dynamic law of univesal gavity, based on his pinciples of kinetic physics and Keple s thee laws of planetay motion in the Sola system. Howeve, astonomes obseved lage mateial systems in the univese that ae galaxies. If Newton s theoy was applicable to galaxies then stas would otate aound the galaxy cente at a speed deceasing with the distance fom the cente. Howeve, astonomical obsevation shows that the speed is constant egadless of the distance. This is called the poblem of constant otational cuves. It is the dak cloud hanging ove twentieth centuy physics. Fotunately, D. Jin He found out that the obsevational galaxy stuctue is ational. This suggests Jin He might be a moden Keple. In this aticle we pesent Cylindical Conjectue on galaxy foce field based on Jin He s obsevational esult. The conjectue simply poves constant otational cuves. We ae looking fo a moden Newton who will develop the conjectue into a systematic theoy on galaxy dynamics, be the conjectue a cosmic tuth. keywods: Spial Galaxy, Rotational Cuve, Rational Stuctue, Cylindical Conjectue, Divegence Theoem PACS: Lj, N 1 Dak Cloud Hanging ove Twentieth Centuy Physics Accoding to Newton s theoy of univesal gavity, the gavitational foce F between two bodies of masses M and m is F = GMm 2 (1) whee G is the gavitational constant and is the distance between the two bodies. If Newton s theoy was applicable to galaxy dynamics then a sta of mass m in a galaxy would suffe a gavity descibed by the above fomula, whee is the distance of the sta fom the galaxy cente and M is the mass of the whole galaxy (note that galaxy stella density deceases exponentially outwads fom the galaxy cente). If we suppose the sta otates in a cicle aound the galaxy cente, then its acceleation is a = v2 (2) 1

2 Accoding to Newton s pinciple of kinetic physics F = ma (3) we have F = GM (4) Hee we see the speed of the sta deceases as its distance fom the galaxy cente inceases. Howeve, astonomical obsevation shows that the speed is appoximately constant. This is the famous poblem of galaxy constant otational cuves. It is the dak cloud hanging ove twentieth centuy physics. 2 Divegence Theoem and the Flux of Foce Why is Newton s univesal gavity invesely popotional to the squaed distance between two bodies (see fomula (1))? In fact, most familia foces in the natue obey the squae law, fo example, Coulomb s foce law and Ampèe s foce law. It is staightfowad to esolve the secet of squae law. Suppose thee is a sphee whose cente is the sun. We calculate the flux of sola gavity though the sphee. The flux is Φ = F S (5) whee S is the suface aea of the sphee and F is the gavitational foce on the sphee. Because S is popotional to the squaed distance fom the sola cente and F is invesely popotional to the squaed distance fom the cente, the flux is constant egadless of the distance Φ = GMm 2 4π 2 = 4πGMm = constant (6) Theefoe, the secet of the squae law is the equiement of constant flux of foce. In fact, the constancy of the flux is esulted fom the famous Divegence Theoem. 3 Spial Galaxies ae Cylindically Stuctued Although spial galaxies ae flat and consideed to be two-dimensional, they still have a cetain thickness (see Figue 1 and the efeence [1]). What is the vetical stuctue? We use z to descibe the vetical diection and to descibe the hoizontal diection as seen on an image of hoizontal edge-on spial galaxy. Astonomical obsevation shows that the stella density distibution on an edge-on spial galaxy image of longe-wavelength can be descibed by a fomula whose vaiables z and can be sepaated ρ(, z) = σ() τ(z). (7) This means that the atio of galaxy light fom two sides of each vetical staight line is constant along the line. This is the futhe evidence of ational galaxy stuctue [2,11]. Rational Evidence: Spial galaxies consideed to be 3-dimensional ae still ational stuctue. 2

3 Figue 1: A longe-wavelength image of edge-on spial galaxy NGC 4565 (Coutesy of [1]) We know that the level cuves of stella density on an edge-on spial galaxy image ae not cylindically stuctued. Howeve, the Rational Evidence suggests that the distibution of density-atios is cylindically stuctued. That is, the vetical popotion cuves (Dawin cuves) ae staight lines pependicula to the galaxy disk. The Rational Evidence must set some constaints to galaxy dynamics. As a ty, we pesent a conjectue on galaxy dynamics: the Cylindical Conjectue. 4 Cylindical Conjectue and Rotational Cuves Cylindical Conjectue: The gavitational foce field of spial galaxies is cylindically stuctued. Although spial galaxies ae disks, they still have a cetain thickness. As the above Rational Evidence suggests, the disk is composed of many simila layes. The Cylindical Conjectue says that the gavitational foce at any point on a spial galaxy has no vetical component. That is, the foce is always paallel to the layes. Howeve, Newtonian theoy suggests that the gavitational foce suffeed by a sta always points to the galaxy cente, and has a vetical component wheneve the sta is positioned outside the middle laye. Fo spial galaxies which ae the lage-scale system of many bodies, we assume the Cylindical Conjectue is tue and Newtonian theoy is wong. Now we show that the Conjectue simply endoses constant otational cuves. We imagine a ight cylinde whose cente is the spial galaxy cente and whose height is h (see Figue 2). The axis of the cylinde is pependicula to the galaxy disk. That is, the adius of the cylinde is paallel to the disk. We want to calculate the flux of gavitational foce though the whole cylindical suface. Because the gavitational foce field of spial galaxies is cylindically stuctued, the flux contibution fom the two bases is zeo, because the bases ae paallel 3

4 Figue 2: Right cylinde whose cente is the spial galaxy cente and whose height is h. The axis of the cylinde is pependicula to the galaxy disk. to the gavitational foce. Now we need to calculate the flux contibution fom the lateal aea of the cylinde. Because the gavitational foce is always pependicula to the lateal aea, we have the flux: Φ = F S = F h 2π (8) whee is the distance of the lateal aea fom the axis of the cylinde, not fom the galaxy cente. Because of the divegence theoem and the fact that stella density deceases exponentially fom the axis, the flux is appoximately constant egadless of the distance. That is: Φ = constant = F h 2π (9) Theefoe, F is invesely popotional to the distance fom the axis of the cylinde: F = constant Now we suppose a sta otates ciculaly at the distance. Its acceleation is the fomula (2). Theefoe: v 2 = constant (11) Finally, we poved the constant otational cuves of spial galaxies: 5 Discussion (10) v = constant (12) We poposed spial galaxy Cylindical Conjectue. That is, gavitational foce inside spial galaxies is always paallel to the disk plane. Howeve, Newtonian theoy assumes that the foce always points to the galaxy cente. Because Newtonian theoy is only 4

5 applicable to two-body system and galaxies ae the esult of many-body inteaction, it is a easonable assumption that Newtonian theoy fails to the explanation of galaxy stuctue and dynamics. Futhemoe, the conjectue is suppoted by the evidence that the distibution of stella density-atios is cylindically stuctued. That is, spial galaxies ae cylindically-stuctued ational stuctue. Howeve, galaxy bulges ae not cylindically-stuctued. Theefoe, the gavitational foce nea the cental bulge tends to pointing to the galaxy cente. If we assume the Conjectue is tue then the constant otational cuves of spial galaxies can be easily explained by the disk and the non-constancy nea galaxy cente can be explained by the cental bulge. We look fowad to astonomes and physicists fo futhe testification of the Conjectue with galaxy obsevational data. If the Conjectue is poved, a moden Newton is expected who will develop the Conjectue into a systematic theoy on galaxy dynamics. Refeences [1] Jaett T., Cheste T., Cuti R., Schneide S. and Hucha J. (2003) Aston. J. 125, 525 [2] He J. (2003) Astophys. Space Sci. 283, 301 [3] He J. (2008) Astophys. Space Sci. 313, 373 [4] He J. (2010) Electonic Jounal of Theoetical Physics 24, 361 [5] He J. (2005) PhD thesis, Depatment of Physics and Astonomy, The Univesity of Alabama. Publication Numbe: AAT ; ISBN: [6] He J. (2010) vixa: , [7] He J. (2011) vixa: , [8] He H. (He, Bo) and He J. (2012) vixa: , [9] He J. (2012) vixa: , [10] He J. (2012) vixa: , [11] He J. (2013) vixa: , 5

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS

DEVIL PHYSICS THE BADDEST CLASS ON CAMPUS IB PHYSICS TSOKOS LESSON 6- THE LAW OF GRAVITATION Essential Idea: The Newtonian idea of gavitational foce acting between two spheical bodies and the laws of mechanics