// fltk 7Fl_Tile 36 -2091 901 53 20
[
// fltk N4xcas23Comment_Multiline_InputE 36 -2091 901 52 20
On remplit tout d'abord les colonnes B et C avec les données, puis la colonne D  avec  ln(B), E avec ln(C) et£F avec C^2/B^3, G1 est la moyenne de F1:F8  et H1 le graphe du nuage de points B1:C8.
,
// fltk N4xcas10Log_OutputE 36 -2039 901 1 20

]
,
// fltk 7Fl_Tile 36 -2036 901 462 20
[
// fltk N4xcas13Tableur_GroupE 36 -2036 901 462 20
1 1 1 0 spreadsheet[[["PLANETE","PLANETE",[P,[0.78,60.22,88.0,60181.0],8,[5.0,5000.0],1,1,2]],["ga GRAND AXE en ua","ga GRAND AXE en ua",2],["dr DURÉE REVOLUTION en jours","dr DURÉE REVOLUTION en jours",2],["x=ln(ga)","x=ln(ga)",2],["y=ln(dr)","y=ln(dr)",2],["","",2],["","",2],["","",2],["","",2],["","",2],["","",2]],[["Mercure","Mercure",2],[0.78,0.78,2],[88.0,88.0,2],[=ln(B1),-0.248461359298,2],[=ln(C1),4.47733681448,2],[=((C1)^2)/((B1)^3),16318.5488629,2],[=mean((F1):(F8)),16653.3941258,2],[=polygonscatterplot(matrix(8,2,(B1):(C8))),pnt(pnt[0.78+88.0*i,0,""]),pnt(pnt[1.44+225.0*i,0,""]),pnt(pnt[2.0+365.25*i,0,""]),pnt(pnt[3.04+687.25*i,0,""]),pnt(pnt[10.4+4332.75*i,0,""]),pnt(pnt[19.1+10759.25*i,0,""]),pnt(pnt[38.44+30688.0*i,0,""]),pnt(pnt[60.22+60181.0*i,0,""]),pnt(pnt[[0.78+88.0*i,1.44+225.0*i,2.0+365.25*i,3.04+687.25*i,10.4+4332.75*i,19.1+10759.25*i,38.44+30688.0*i,60.22+60181.0*i],0,""]),2],[0,0,2],[0,0,2],[0,0,2]],[["Venus","Venus",2],[1.44,1.44,2],[225.0,225.0,2],[=ln(B2),0.364643113588,2],[=ln(C2),5.4161004022,2],[=((C2)^2)/((B2)^3),16954.2100694,2],[nop(0),0,2],[0,0,2],[0,0,2],[0,0,2],[0,0,2]],[["Terre","Terre",2],[2.0,2.0,2],[365.25,365.25,2],[=ln(B3),0.69314718056,2],[=ln(C3),5.90058205063,2],[=((C3)^2)/((B3)^3),16675.9453125,2],[0,0,2],[0,0,2],[0,0,2],[0,0,2],[0,0,2]],[["Mars","Mars",2],[3.04,3.04,2],[687.25,687.25,2],[=ln(B4),1.11185751542,2],[=ln(C4),6.53269812705,2],[=((C4)^2)/((B4)^3),16811.5883079,2],[0,0,2],[0,0,2],[0,0,2],[0,0,2],[0,0,2]],[["Jupiter","Jupiter",2],[10.4,10.4,2],[4332.75,4332.75,2],[=ln(B5),2.34180580615,2],[=ln(C5),8.37395772333,2],[=((C5)^2)/((B5)^3),16688.8820004,2],[0,0,2],[0,0,2],[0,0,2],[0,0,2],[0,0,2]],[["Saturne","Saturne",2],[19.1,19.1,2],[10759.25,10759.25,2],[=ln(B6),2.94968833505,2],[=ln(C6),9.28352112868,2],[=((C6)^2)/((B6)^3),16613.6055852,2],[0,0,2],[0,0,2],[0,0,2],[0,0,2],[0,0,2]],[["Uranus","Uranus",2],[38.44,38.44,2],[30688.0,30688.0,2],[=ln(B7),3.6490985841,2],[=ln(C7),10.3316269777,2],[=((C7)^2)/((B7)^3),16580.0957393,2],[0,0,2],[0,0,2],[0,0,2],[0,0,2],[0,0,2]],[["Neptune","Neptune",2],[60.22,60.22,2],[60181.0,60181.0,2],[=ln(B8),4.09800452305,2],[=ln(C8),11.0051119669,2],[=((C8)^2)/((B8)^3),16584.2771284,2],[0,0,2],[0,0,2],[0,0,2],[0,0,2],[0,0,2]]]
,
// fltk N4xcas10Log_OutputE 36 -1574 901 0 20

]
,
// fltk 7Fl_Tile 36 -1572 901 302 20
[
// fltk N4xcas19Multiline_Input_tabE 36 -1572 901 30 20
polygonscatterplot(P[1..8,1..2])
,
// fltk N4xcas10Log_OutputE 36 -1542 901 1 20

,
// fltk 7Fl_Tile 36 -1541 901 271 20
[
// fltk N4xcas7Graph2dE 36 -1541 695 271 20
0.78,60.22,88,60181,[pnt(pnt[0.78+88.0*(i),0,""]),pnt(pnt[1.44+225.0*(i),0,""]),pnt(pnt[2.0+365.25*(i),0,""]),pnt(pnt[3.04+687.25*(i),0,""]),pnt(pnt[10.4+4332.75*(i),0,""]),pnt(pnt[19.1+10759.25*(i),0,""]),pnt(pnt[38.44+30688.0*(i),0,""]),pnt(pnt[60.22+60181.0*(i),0,""]),pnt(pnt[[0.78+88.0*(i),1.44+225.0*(i),2.0+365.25*(i),3.04+687.25*(i),10.4+4332.75*(i),19.1+10759.25*(i),38.44+30688.0*(i),60.22+60181.0*(i)],0,""])],-5,5,1,0,0,0,5,5000,1,0,1,5,0
,
// fltk 7Fl_Tile 731 -1541 206 271 20
[
// fltk N4xcas14Mouse_PositionE 731 -1541 206 40 20
[]
,
// fltk 8Fl_Group 731 -1501 206 115 20
[
// fltk 9Fl_Button 731 -1501 69 23 20
[]
,
// fltk 9Fl_Button 800 -1501 68 23 20
[]
,
// fltk 9Fl_Button 868 -1501 69 23 20
[]
,
// fltk 9Fl_Button 731 -1478 69 23 20
[]
,
// fltk 9Fl_Button 800 -1478 68 23 20
[]
,
// fltk 9Fl_Button 868 -1478 69 23 20
[]
,
// fltk 9Fl_Button 731 -1455 69 23 20
[]
,
// fltk 9Fl_Button 800 -1455 68 23 20
[]
,
// fltk 9Fl_Button 868 -1455 69 23 20
[]
,
// fltk 9Fl_Button 731 -1432 69 23 20
[]
,
// fltk 9Fl_Button 800 -1432 68 23 20
[]
,
// fltk 9Fl_Button 868 -1432 69 23 20
[]
,
// fltk 9Fl_Button 731 -1409 69 23 20
[]
,
// fltk 11Fl_Menu_Bar 800 -1409 137 23 20
[]
]
,
// fltk 8Fl_Group 731 -1386 206 116 20
[
]
]
]
]
,
// fltk 7Fl_Tile 36 -1268 901 31 20
[
// fltk N4xcas23Comment_Multiline_InputE 36 -1268 901 30 20
On observe que cette courbe resemble à une fonction puissance
,
// fltk N4xcas10Log_OutputE 36 -1238 901 1 20

]
,
// fltk 7Fl_Tile 36 -1235 901 380 20
[
// fltk N4xcas19Multiline_Input_tabE 36 -1235 901 30 20
polygonplot(P[1..8,3..4])
,
// fltk N4xcas10Log_OutputE 36 -1205 901 1 20

,
// fltk 7Fl_Tile 36 -1204 901 349 20
[
// fltk N4xcas7Graph2dE 36 -1204 901 349 20
-0.24846,4.098,4.4773,11.005,[pnt(pnt[[-0.248461359298+4.47733681448*(i),0.364643113588+5.4161004022*(i),0.69314718056+5.90058205063*(i),1.11185751542+6.53269812705*(i),2.34180580615+8.37395772333*(i),2.94968833505+9.28352112868*(i),3.6490985841+10.3316269777*(i),4.09800452305+11.0051119669*(i)],0,""])],-5,5,1,0,0,0,0.5,0.5,1,0,1,5,0
,
// fltk 7Fl_Tile 937 -1204 120 349 20
[
// fltk N4xcas14Mouse_PositionE 937 -1204 120 40 20
[]
,
// fltk 8Fl_Group 937 -1164 120 115 20
[
// fltk 9Fl_Button 937 -1164 40 23 20
[]
,
// fltk 9Fl_Button 977 -1164 40 23 20
[]
,
// fltk 9Fl_Button 1017 -1164 40 23 20
[]
,
// fltk 9Fl_Button 937 -1141 40 23 20
[]
,
// fltk 9Fl_Button 977 -1141 40 23 20
[]
,
// fltk 9Fl_Button 1017 -1141 40 23 20
[]
,
// fltk 9Fl_Button 937 -1118 40 23 20
[]
,
// fltk 9Fl_Button 977 -1118 40 23 20
[]
,
// fltk 9Fl_Button 1017 -1118 40 23 20
[]
,
// fltk 9Fl_Button 937 -1095 40 23 20
[]
,
// fltk 9Fl_Button 977 -1095 40 23 20
[]
,
// fltk 9Fl_Button 1017 -1095 40 23 20
[]
,
// fltk 9Fl_Button 937 -1072 40 23 20
[]
,
// fltk 11Fl_Menu_Bar 977 -1072 80 23 20
[]
]
,
// fltk 8Fl_Group 937 -1049 120 194 20
[
]
]
]
]
,
// fltk 7Fl_Tile 36 -853 901 68 20
[
// fltk N4xcas23Comment_Multiline_InputE 36 -853 901 68 20
En coordonnées logarithmiques la représentation de la durée de révolution en fonction£du grand axe semble une droite.£Cherchons l'équation de cette droite.
,
// fltk N4xcas10Log_OutputE 36 -785 901 0 20

]
,
// fltk 7Fl_Tile 36 -783 901 302 20
[
// fltk N4xcas19Multiline_Input_tabE 36 -783 901 30 20
A:=point(P[1,3..4]);B:=point(P[8,3..4]);D:=droite(A,B,affichage=rouge);polygonplot(P[1..8,3..4])
,
// fltk N4xcas10Log_OutputE 36 -753 901 1 20

,
// fltk 7Fl_Tile 36 -752 901 271 20
[
// fltk N4xcas7Graph2dE 36 -752 695 271 20
-0.24846,4.098,4.4773,11.005,[pnt(pnt[-0.248461359298+4.47733681448*(i),0,"A"]),pnt(pnt[4.09800452305+11.0051119669*(i),0,"B"]),pnt(pnt[line[-0.248461359298+4.47733681448*(i),4.09800452305+11.0051119669*(i)],1,"D"]),pnt(pnt[[-0.248461359298+4.47733681448*(i),0.364643113588+5.4161004022*(i),0.69314718056+5.90058205063*(i),1.11185751542+6.53269812705*(i),2.34180580615+8.37395772333*(i),2.94968833505+9.28352112868*(i),3.6490985841+10.3316269777*(i),4.09800452305+11.0051119669*(i)],0,""])],-5,5,1,0,0,0,0.5,0.5,1,0,1,5,0
,
// fltk 7Fl_Tile 731 -752 206 271 20
[
// fltk N4xcas14Mouse_PositionE 731 -752 206 40 20
[]
,
// fltk 8Fl_Group 731 -712 206 115 20
[
// fltk 9Fl_Button 731 -712 69 23 20
[]
,
// fltk 9Fl_Button 800 -712 68 23 20
[]
,
// fltk 9Fl_Button 868 -712 69 23 20
[]
,
// fltk 9Fl_Button 731 -689 69 23 20
[]
,
// fltk 9Fl_Button 800 -689 68 23 20
[]
,
// fltk 9Fl_Button 868 -689 69 23 20
[]
,
// fltk 9Fl_Button 731 -666 69 23 20
[]
,
// fltk 9Fl_Button 800 -666 68 23 20
[]
,
// fltk 9Fl_Button 868 -666 69 23 20
[]
,
// fltk 9Fl_Button 731 -643 69 23 20
[]
,
// fltk 9Fl_Button 800 -643 68 23 20
[]
,
// fltk 9Fl_Button 868 -643 69 23 20
[]
,
// fltk 9Fl_Button 731 -620 69 23 20
[]
,
// fltk 11Fl_Menu_Bar 800 -620 137 23 20
[]
]
,
// fltk 8Fl_Group 731 -597 206 116 20
[
]
]
]
]
,
// fltk 7Fl_Tile 36 -479 901 84 20
[
// fltk N4xcas19Multiline_Input_tabE 36 -479 901 30 20
equation(D)
,
// fltk N4xcas10Log_OutputE 36 -449 901 1 20

,
// fltk N4xcas8EquationE 36 -448 901 53 20
y=(1.50185813695*x+4.85049052866)
]
,
// fltk 7Fl_Tile 36 -393 901 31 20
[
// fltk N4xcas23Comment_Multiline_InputE 36 -393 901 30 20
Donc on a approximativement : ln(dr)=1.5*ln(ga)+4.85
,
// fltk N4xcas10Log_OutputE 36 -363 901 1 20

]
,
// fltk 7Fl_Tile 36 -360 901 98 20
[
// fltk N4xcas19Multiline_Input_tabE 36 -360 901 30 20
dr2:=exp2pow(exp(3*ln(ga)+2*4.85 ))
,
// fltk N4xcas10Log_OutputE 36 -330 901 1 20

,
// fltk N4xcas8EquationE 36 -329 901 67 20
16317.607198*ga^3
]
,
// fltk 7Fl_Tile 36 -260 901 31 20
[
// fltk N4xcas23Comment_Multiline_InputE 36 -260 901 30 20
Ce qui prouve que l'on a dr^2=116317.6*ga^3
,
// fltk N4xcas10Log_OutputE 36 -230 901 1 20

]
,
// fltk 7Fl_Tile 36 -227 901 84 20
[
// fltk N4xcas19Multiline_Input_tabE 36 -227 901 30 20
mean(P[1..8,5])
,
// fltk N4xcas10Log_OutputE 36 -197 901 1 20

,
// fltk N4xcas8EquationE 36 -196 901 53 20
16653.3941258
]
,
// fltk 7Fl_Tile 36 -141 901 53 20
[
// fltk N4xcas23Comment_Multiline_InputE 36 -141 901 52 20
On peut aussi utiliser la fonction power_regression qui renvoie (m,k) pour que y=k*x^m approche £au mieux les points (ga,dr).
,
// fltk N4xcas10Log_OutputE 36 -89 901 1 20

]
,
// fltk 7Fl_Tile 36 -86 901 84 20
[
// fltk N4xcas19Multiline_Input_tabE 36 -86 901 30 20
(m,k):=power_regression(P[1..8,1..2])
,
// fltk N4xcas10Log_OutputE 36 -56 901 1 20

,
// fltk N4xcas8EquationE 36 -55 901 53 20
1.49968810636,129.119804192
]
,
// fltk 7Fl_Tile 36 0 901 84 20
[
// fltk N4xcas19Multiline_Input_tabE 36 0 901 30 20
ln(129.119804192)
,
// fltk N4xcas10Log_OutputE 36 30 901 1 20

,
// fltk N4xcas8EquationE 36 31 901 53 20
4.86074068804
]
,
// fltk 7Fl_Tile 36 86 901 380 20
[
// fltk N4xcas19Multiline_Input_tabE 36 86 901 30 20
power_regression_plot(P[1..8,1..2]),polygonscatterplot(P[1..8,1..2],affichage=vert+point_width_3)
,
// fltk N4xcas10Log_OutputE 36 116 901 1 20

,
// fltk 7Fl_Tile 36 117 901 349 20
[
// fltk N4xcas7Graph2dE 36 117 901 349 20
0.78,60.22,88,60181,[pnt(pnt[curve(group[pnt[x+(i)*129.119804192*exp(1.49968810636*ln(x)),x,0.78,60.22],group[0.78+88.9546013691*(i),0.9286+115.543604535*(i),1.0772+144.353494881*(i),1.2258+175.224450527*(i),1.3744+208.026902203*(i),1.523+242.653036783*(i),1.6716+279.011310472*(i),1.8202+317.02272475*(i),1.9688+356.61819721*(i),2.1174+397.736644998*(i),2.266+440.323550143*(i),2.4146+484.329861296*(i),2.5632+529.711136754*(i),2.7118+576.426864588*(i),2.8604+624.439915416*(i),3.009+673.71609629*(i),3.1576+724.223782856*(i),3.3062+775.933612983*(i),3.4548+828.818229236*(i),3.6034+882.852060618*(i),3.752+938.011136205*(i),3.9006+994.272924917*(i),4.0492+1051.61619689*(i),4.1978+1110.02090284*(i),4.3464+1169.46806857*(i),4.495+1229.93970212*(i),4.6436+1291.41871192*(i),4.7922+1353.88883404*(i),4.9408+1417.33456751*(i),5.0894+1481.74111645*(i),5.238+1547.0943382*(i),5.3866+1613.38069663*(i),5.5352+1680.58721994*(i),5.6838+1748.70146259*(i),5.8324+1817.71147056*(i),5.981+1887.60574989*(i),6.1296+1958.3732379*(i),6.2782+2030.00327682*(i),6.4268+2102.48558976*(i),6.5754+2175.81025848*(i),6.724+2249.96770304*(i),6.8726+2324.948663*(i),7.0212+2400.74418002*(i),7.1698+2477.34558181*(i),7.3184+2554.74446719*(i),7.467+2632.93269231*(i),7.6156+2711.9023577*(i),7.7642+2791.64579636*(i),7.9128+2872.15556252*(i),8.0614+2953.42442126*(i),8.21+3035.44533869*(i),8.3586+3118.21147281*(i),8.5072+3201.716165*(i),8.6558+3285.95293192*(i),8.8044+3370.91545794*(i),8.953+3456.5975881*(i),9.1016+3542.99332134*(i),9.2502+3630.09680423*(i),9.3988+3717.90232501*(i),9.5474+3806.40430795*(i),9.696+3895.59730807*(i),9.8446+3985.47600606*(i),9.9932+4076.03520356*(i),10.1418+4167.26981863*(i),10.2904+4259.17488146*(i),10.439+4351.74553034*(i),10.5876+4444.97700773*(i),10.7362+4538.86465668*(i),10.8848+4633.40391727*(i),11.0334+4728.59032329*(i),11.182+4824.41949913*(i),11.3306+4920.88715668*(i),11.4792+5017.98909251*(i),11.6278+5115.7211851*(i),11.7764+5214.07939221*(i),11.925+5313.05974837*(i),12.0736+5412.65836251*(i),12.2222+5512.8714156*(i),12.3708+5613.69515852*(i),12.5194+5715.1259099*(i),12.668+5817.16005417*(i),12.8166+5919.79403953*(i),12.9652+6023.02437619*(i),13.1138+6126.84763453*(i),13.2624+6231.2604434*(i),13.411+6336.25948848*(i),13.5596+6441.84151074*(i),13.7082+6548.00330483*(i),13.8568+6654.74171773*(i),14.0054+6762.05364724*(i),14.154+6869.93604072*(i),14.3026+6978.38589372*(i),14.4512+7087.40024875*(i),14.5998+7196.97619406*(i),14.7484+7307.11086249*(i),14.897+7417.80143034*(i),15.0456+7529.04511627*(i),15.1942+7640.83918024*(i),15.3428+7753.18092255*(i),15.4914+7866.0676828*(i),15.64+7979.49683897*(i),15.7886+8093.46580653*(i),15.9372+8207.97203752*(i),16.0858+8323.0130197*(i),16.2344+8438.58627574*(i),16.383+8554.68936242*(i),16.5316+8671.31986983*(i),16.6802+8788.47542063*(i),16.8288+8906.15366936*(i),16.9774+9024.35230166*(i),17.126+9143.06903366*(i),17.2746+9262.30161128*(i),17.4232+9382.04780958*(i),17.5718+9502.30543218*(i),17.7204+9623.07231059*(i),17.869+9744.34630371*(i),18.0176+9866.12529716*(i),18.1662+9988.40720282*(i),18.3148+10111.1899582*(i),18.4634+10234.471526*(i),18.612+10358.2498937*(i),18.7606+10482.5230726*(i),18.9092+10607.289098*(i),19.0578+10732.5460283*(i),19.2064+10858.2919446*(i),19.355+10984.5249504*(i),19.5036+11111.2431711*(i),19.6522+11238.4447536*(i),19.8008+11366.1278656*(i),19.9494+11494.2906958*(i),20.098+11622.931453*(i),20.2466+11752.0483661*(i),20.3952+11881.6396831*(i),20.5438+12011.7036717*(i),20.6924+12142.2386182*(i),20.841+12273.2428274*(i),20.9896+12404.7146222*(i),21.1382+12536.6523435*(i),21.2868+12669.0543496*(i),21.4354+12801.9190162*(i),21.584+12935.2447357*(i),21.7326+13069.0299172*(i),21.8812+13203.2729862*(i),22.0298+13337.9723844*(i),22.1784+13473.126569*(i),22.327+13608.734013*(i),22.4756+13744.7932044*(i),22.6242+13881.3026466*(i),22.7728+14018.2608574*(i),22.9214+14155.6663693*(i),23.07+14293.5177292*(i),23.2186+14431.8134979*(i),23.3672+14570.55225*(i),23.5158+14709.732574*(i),23.6644+14849.3530715*(i),23.813+14989.4123575*(i),23.9616+15129.9090598*(i),24.1102+15270.8418191*(i),24.2588+15412.2092888*(i),24.4074+15554.0101345*(i),24.556+15696.2430341*(i),24.7046+15838.9066775*(i),24.8532+15981.9997665*(i),25.0018+16125.5210144*(i),25.1504+16269.4691462*(i),25.299+16413.842898*(i),25.4476+16558.6410174*(i),25.5962+16703.8622625*(i),25.7448+16849.5054027*(i),25.8934+16995.5692178*(i),26.042+17142.0524982*(i),26.1906+17288.9540446*(i),26.3392+17436.272668*(i),26.4878+17584.0071896*(i),26.6364+17732.1564402*(i),26.785+17880.7192608*(i),26.9336+18029.6945017*(i),27.0822+18179.0810229*(i),27.2308+18328.877694*(i),27.3794+18479.0833933*(i),27.528+18629.6970089*(i),27.6766+18780.7174376*(i),27.8252+18932.1435849*(i),27.9738+19083.9743655*(i),28.1224+19236.2087025*(i),28.271+19388.8455276*(i),28.4196+19541.8837809*(i),28.5682+19695.322411*(i),28.7168+19849.1603745*(i),28.8654+20003.3966362*(i),29.014+20158.030169*(i),29.1626+20313.0599534*(i),29.3112+20468.4849781*(i),29.4598+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,
// fltk 7Fl_Tile 937 117 120 349 20
[
// fltk N4xcas14Mouse_PositionE 937 117 120 40 20
[]
,
// fltk 8Fl_Group 937 157 120 115 20
[
// fltk 9Fl_Button 937 157 40 23 20
[]
,
// fltk 9Fl_Button 977 157 40 23 20
[]
,
// fltk 9Fl_Button 1017 157 40 23 20
[]
,
// fltk 9Fl_Button 937 180 40 23 20
[]
,
// fltk 9Fl_Button 977 180 40 23 20
[]
,
// fltk 9Fl_Button 1017 180 40 23 20
[]
,
// fltk 9Fl_Button 937 203 40 23 20
[]
,
// fltk 9Fl_Button 977 203 40 23 20
[]
,
// fltk 9Fl_Button 1017 203 40 23 20
[]
,
// fltk 9Fl_Button 937 226 40 23 20
[]
,
// fltk 9Fl_Button 977 226 40 23 20
[]
,
// fltk 9Fl_Button 1017 226 40 23 20
[]
,
// fltk 9Fl_Button 937 249 40 23 20
[]
,
// fltk 11Fl_Menu_Bar 977 249 80 23 20
[]
]
,
// fltk 8Fl_Group 937 272 120 194 20
[
]
]
]
]
,
// fltk 7Fl_Tile 36 468 901 36 20
[
// fltk N4xcas19Multiline_Input_tabE 36 468 901 35 20

,
// fltk N4xcas10Log_OutputE 36 503 901 1 20

]