N-body problem integration (N=2) displaying a perfect Keplerian orbit (an ellipse) [Intégration du problème des N-corps (N=2) montrant une orbite keplérienne parfaite (une ellipse)].




The mathematical newtonian model:

                    F = m.γ

                           m1.m2
                    F = G.-------
                            r2

and this equation (when staying strictly inside the newtonian context, one can demonstrate that the trajectory of a body around another one is a perfect ellipse):

                         2        2
                    | x |    | y |
                    |---|  + |---| = 1
                    | a |    | b |

and this picture are a "synthesis" of a huge amount of numerical values -X and Y coordinates-:
                    
                    X=-800000000000.000000        Y=        +1000.000000
                    X=-799166000064.454468        Y= +27989568947.760650
                    X=-796663511901.509888        Y= +55921375246.897300
                    X=-792491283632.184937        Y= +83735923255.243881
                    X=-786647243443.405396        Y=+111373744767.720016
                    X=-779128521231.340820        Y=+138774353113.066803
                    X=-769931489097.738647        Y=+165875883044.374756
                    X=-759051804715.996460        Y=+192614711478.117554
                    X=-746484479038.770020        Y=+218925054332.794769
                    X=-732223953778.206543        Y=+244738533244.007599
                    X=-716264213954.533447        Y=+269983706706.834137
                    X=-698598919432.062622        Y=+294585557945.559204
                    X=-679221575849.836548        Y=+318464929193.731323
                    X=-658125753714.453125        Y=+341537896320.715393
                    X=-635305359835.672241        Y=+363715071637.104004
                    X=-610754984887.974731        Y=+384900821220.337158
                    X=-584470346608.554565        Y=+404992390454.005859
                    X=-556448846633.977905        Y=+423878913452.105347
                    X=-526690275857.960571        Y=+441440297714.340515
                    X=-495197717087.342590        Y=+457545961486.339233
                    X=-461978695533.236389        Y=+472053411434.564392
                    X=-427046653020.436279        Y=+484806639343.538879
                    X=-390422834068.982605        Y=+495634329810.908386
                    X=-352138716161.846497        Y=+504347874400.330322
                    X=-312239139907.355164        Y=+510739199645.671082
                    X=-270786351349.391632        Y=+514578458131.797607
                    X=-227865229686.255005        Y=+515611666175.225647
                    X=-183590042709.856995        Y=+513558468956.451233
                    X=-138113159832.700897        Y=+508110328739.113464
                    X= -91636235028.870025        Y=+498929666769.876892
                    X= -44424416024.877166        Y=+485650807662.503113
                    X=  +3175900065.465378        Y=+467884075341.501648
                    X= +50715503185.226310        Y=+445225103997.960083
                    X= +97617427472.923400        Y=+417272362288.405457
                    X=+143150528185.577606        Y=+383656913569.580444
                    X=+186406172868.677582        Y=+344089133453.590576
                    X=+226286945182.115662        Y=+298426404636.323669
                    X=+261521714723.657501        Y=+246761858210.234467
                    X=+290725629051.373169        Y=+189524738428.388153
                    X=+312520841585.724304        Y=+127567417275.454803
                    X=+325716668536.934021        Y= +62198223006.654739
                    X=+329515043551.962524        Y=  -4882226246.836296
                    X=+323674532868.917603        Y= -71755092708.735641
                    X=+308564150133.509460        Y=-136528805597.224564
                    X=+285081892772.509705        Y=-197575237592.599060
                    X=+254475501947.702972        Y=-253681601590.071869
                    X=+218137658787.323669        Y=-304090926985.294800
                    X=+177436906761.184479        Y=-348453819930.926392
                    X=+133610597143.845917        Y=-386735626516.374207
                    X= +87716052194.003341        Y=-419117050514.681030
                    X= +40622578393.841774        Y=-445909525249.911804
                    X=  -6973667863.918034        Y=-467492196848.978088
                    X= -54525136275.164947        Y=-484269211220.109741
                    X=-101606497534.667068        Y=-496642941958.444824
                    X=-147890330250.330505        Y=-504998521330.766052
                    X=-193126365338.586426        Y=-509695854117.710144
                    X=-237124520192.660980        Y=-511066339505.118835
                    X=-279741380978.299683        Y=-509412401795.952881
                    X=-320869592701.490845        Y=-505008611894.748901
                    X=-360429601866.614075        Y=-498103619840.776733
                    X=-398363259766.155457        Y=-488922441210.968323
                    X=-434628874995.758789        Y=-477668816546.808472
                    X=-469197382259.000793        Y=-464527498768.808533
                    X=-502049380352.338501        Y=-449666385627.008789
                    X=-533172829268.901184        Y=-433238466668.945557
                    X=-562561259638.667480        Y=-415383573394.559753
                    X=-590212378315.997192        Y=-396229942333.709900
                    X=-616126969700.465210        Y=-375895603252.519348
                    X=-640308042395.343994        Y=-354489608547.058411
                    X=-662760159839.397949        Y=-332113120234.844666
                    X=-683488909924.952026        Y=-308860374532.823303
                    X=-702500482089.756958        Y=-284819536244.112122
                    X=-719801340182.548706        Y=-260073461792.595642
                    X=-735397962263.524780        Y=-234700379460.007568
                    X=-749296632401.443970        Y=-208774502202.248444
                    X=-761503277891.523193        Y=-182366580523.182190
                    X=-772023340802.756470        Y=-155544404924.997314
                    X=-780861679188.498535        Y=-128373267044.422150
                    X=-788022488122.065308        Y=-100916386548.792847
                    X=-793509238390.982666        Y= -73235308198.392166
                    X=-797324630363.287231        Y= -45390273860.971466
                    X=-799470563564.701050        Y= -17440583527.914199



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