breed [bodys body] globals [ ; variavel global todos podem alterar body1 body2 body3 force ; modulo do vetor força ; vetores do copo 1 em relação ao corpo 2 fx1_2 ; x-component of force vector fy1_2 ; y-component of force vector ; vetores do copo 1 em relação ao corpo 3 fx1_3 ; x-component of force vector fy1_3 ; y-component of force vector ; vetores do copo 2 em relação ao corpo 1 fx2_1 ; x-component of force vector fy2_1 ; y-component of force vector ; vetores do copo 2 em relação ao corpo 3 fx2_3 ; x-component of force vector fy2_3 ; y-component of force vector ; vetores do copo 3 em relação ao corpo 1 fx3_1 ; x-component of force vector fy3_1 ; y-component of force vector ; vetores do copo 3 em relação ao corpo 2 fx3_2 ; x-component of force vector fy3_2 ; y-component of force vector vx ; x-component of velocity vector vy ; y-component of velocity vector ] to Clean ;; poem os valores padrao ca set X1 0 set Y1 0 set X2 5 set Y2 0 set X3 0 set Y3 4 set Mass1 1 set Mass2 1 set Mass3 1 set VelocityX1 0 set VelocityX2 0 set VelocityX3 0 set VelocityY1 0 set VelocityY2 0 set VelocityY3 0 ;; plot standard position set-default-shape turtles "circle" create-bodys 1 [set body1 self set color white setxy X1 Y1 set pen-size 1 pen-down ] create-bodys 1 [set body2 self set color yellow setxy X2 Y2 set pen-size 1 pen-down] create-bodys 1 [set body3 self set color red setxy X3 Y3 set pen-size 1 pen-down] end to Plot_bodies ca ;; plot standard position set-default-shape turtles "circle" create-bodys 1 [set body1 self set color white setxy X1 Y1 set pen-size 1 pen-down ] create-bodys 1 [set body2 self set color yellow setxy X2 Y2 set pen-size 1 pen-down] create-bodys 1 [set body3 self set color red setxy X3 Y3 set pen-size 1 pen-down] end to Stable ;; mostra um exemplo de orbita estavel dois sois e um planeta clear-all ;; poem os valores padrao ca set X1 -2 set Y1 0 set X2 2 set Y2 0 set X3 25 set Y3 0 set VelocityX1 0 set VelocityX2 0 set VelocityX3 0 set VelocityY1 0.1 set VelocityY2 -0.1 set VelocityY3 0.07 set Mass1 1 set Mass2 1 set Mass3 0.01 ;; plot position set-default-shape turtles "circle" create-bodys 1 [set body1 self set color white setxy X1 Y1 set pen-size 1 pen-down ] create-bodys 1 [set body2 self set color yellow setxy X2 Y2 set pen-size 1 pen-down] create-bodys 1 [set body3 self set color red setxy X3 Y3 set pen-size 1 pen-down] end to Stable_2 ;; two planets and one sun clear-all ;; set the default values ca set X1 -23 set Y1 0 set X2 8 set Y2 0 set X3 0 set Y3 0 set VelocityX1 0 set VelocityX2 0 set VelocityX3 0 set VelocityY1 1.5 set VelocityY2 3.5 set VelocityY3 0 set Mass1 1 set Mass2 1 set Mass3 1000 ;; plot position set-default-shape turtles "circle" create-bodys 1 [set body1 self set color white setxy X1 Y1 set pen-size 1 pen-down ] create-bodys 1 [set body2 self set color yellow setxy X2 Y2 set pen-size 1 pen-down] create-bodys 1 [set body3 self set color red setxy X3 Y3 set pen-size 1 pen-down] end to go ; integration time an improvement that can be added in the future ; every 0.1 ; [ ; check if the bodies are in the field of view if body1 = nobody [ stop ] if body2 = nobody [ stop ] if body3 = nobody [ stop ] ;Calculate force ask body1 [ update-force1_2 update-force1_3 ] ask body2 [ update-force2_1 update-force2_3 ] ask body3 [ update-force3_2 update-force3_1 ] ;; move the particles at the same time , to not influence the results ask body1 [move1] ask body2 [move2] ask body3 [move3] ; end ; bode1 to update-force1_2 ;body distance 1 to 2 let r distance body2 ; avoiding infinity if (r < 0.5 and r > -0.5) [set r 0.5] ;Calculating body force 1_2 set force 0.1 * (Mass1 * Mass2)/(r ^ 2) ;; has been multiplied by 0.1 so the particles don't leave the field of view ; separating the force in the components x and y face body2 set fx1_2 force * dx set fy1_2 force * dy end to update-force1_3 ;body distance 1 to 2 let r distance body3 ; avoiding infinity if (r < 0.5 and r > -0.5) [set r 0.5] ;Calculating body force 1_2 set force 0.1 * (Mass1 * Mass3)/(r ^ 2) ; separating the force in the components x e y face body3 set fx1_3 force * dx set fy1_3 force * dy end ; bode2 to update-force2_1 ;body distance 2 ao 1 let r distance body1 ; avoiding infinity if (r < 0.5 and r > -0.5) [set r 0.5] ;Calculating body force 2_1 (we know that is equal to - body strength 1_2, but in doubt, let's calculate) set force 0.1 * (Mass2 * Mass1)/(r ^ 2) ; separating the force in the components x and y face body1 set fx2_1 force * dx set fy2_1 force * dy end to update-force2_3 ;body distance 2 to 3 let r distance body3 ; avoiding infinity if (r < 0.5 and r > -0.5) [set r 0.5] ;Calculating body force 2_3 set force 0.1 * (Mass2 * Mass3)/(r ^ 2) ; separating the force in the components x and y face body3 set fx2_3 force * dx set fy2_3 force * dy end ; bode3 to update-force3_1 ;body distance 3 to 1 let r distance body1 ; avoiding infinity if (r < 0.5 and r > -0.5) [set r 0.5] ;Calculating body force 3_1 (we know that is equal to - body strength 1_3) set force 0.1 * (Mass3 * Mass1)/(r ^ 2) ; separating the force in the components x and y face body1 set fx3_1 force * dx set fy3_1 force * dy end to update-force3_2 ;body distance 3 to 2 let r distance body2 ; avoiding infinity if (r < 0.5 and r > -0.5) [set r 0.5] ;Calculating body force 2_3 (we know that is equal to - body strength 3_2) set force 0.1 * (Mass3 * Mass2)/(r ^ 2) ; separating the force in the components x and y face body2 set fx3_2 force * dx set fy3_2 force * dy end to move1 ; move the particles ;updates particle speed and adds force;; F=m.a, then have to divide by mass set VelocityX1 VelocityX1 + (fx1_2 / Mass1) + (fx1_3 / Mass1) set VelocityY1 VelocityY1 + (fy1_2 / Mass1) + (fy1_3 / Mass1) ; disappears if it goes off the edge if abs (ycor + vy) > max-pycor or abs (xcor + vx) > max-pxcor [ die ] ; update particle position set X1 X1 + VelocityX1 set Y1 Y1 + VelocityY1 setxy X1 Y1 end to move2 ; move the particles ;updates particle speed and adds force set VelocityX2 VelocityX2 + (fx2_1 / Mass2) + (fx2_3 / Mass2) set VelocityY2 VelocityY2 + (fy2_1 / Mass2) + (fy2_3 / Mass2) ; disappears if it goes off the edge if abs (ycor + vy) > max-pycor or abs (xcor + vx) > max-pxcor [ die ] ; update particle position set X2 X2 + VelocityX2 set Y2 Y2 + VelocityY2 setxy X2 Y2 end to move3 ; move the particles ;updates particle speed and adds force set VelocityX3 VelocityX3 + (fx3_1 / Mass3) + (fx3_2 / Mass3) set VelocityY3 VelocityY3 + (fy3_1 / Mass3) + (fy3_2 / Mass3) ; disappears if it goes off the edge if abs (ycor + vy) > max-pycor or abs (xcor + vx) > max-pxcor [ die ] ; update particle position set X3 X3 + VelocityX3 set Y3 Y3 + VelocityY3 setxy X3 Y3 end @#$#@#$#@ GRAPHICS-WINDOW 406 11 1337 553 -1 -1 13.0 1 10 1 1 1 0 1 1 1 -35 35 -20 20 0 0 1 ticks 60.0 TEXTBOX 13 123 248 167 Body characteristics 1 18 0.0 1 INPUTBOX 14 157 65 217 X1 0.0 1 0 Number INPUTBOX 66 157 126 217 Y1 0.0 1 0 Number INPUTBOX 140 157 197 217 Mass1 1.0 1 0 Number INPUTBOX 221 156 304 216 VelocityX1 0.0 1 0 Number TEXTBOX 23 275 226 319 Body characteristics 2 18 43.0 1 TEXTBOX 30 408 246 452 Body characteristics 3 18 15.0 1 INPUTBOX 304 156 390 216 VelocityY1 0.0 1 0 Number TEXTBOX 34 225 127 255 Posição inicial 12 0.0 1 TEXTBOX 283 230 433 248 Velocidade inicial 12 0.0 1 INPUTBOX 21 308 71 368 X2 5.0 1 0 Number INPUTBOX 71 308 121 368 Y2 0.0 1 0 Number INPUTBOX 139 309 200 369 Mass2 1.0 1 0 Number INPUTBOX 225 308 307 368 VelocityX2 0.0 1 0 Number INPUTBOX 307 308 393 368 VelocityY2 0.0 1 0 Number INPUTBOX 28 437 78 497 X3 0.0 1 0 Number INPUTBOX 78 437 128 497 Y3 4.0 1 0 Number INPUTBOX 142 437 197 497 Mass3 1.0 1 0 Number INPUTBOX 208 436 291 496 VelocityX3 0.0 1 0 Number INPUTBOX 291 436 375 496 VelocityY3 0.0 1 0 Number TEXTBOX 37 10 397 36 Gravitation, three-body system 20 0.0 1 BUTTON 10 51 76 84 Stable Stable NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 328 96 397 141 Go go T 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 243 96 325 140 Clean Clean NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 10 85 90 118 Stable_2 Stable_2 NIL 1 T OBSERVER NIL NIL NIL NIL 1 BUTTON 294 59 357 92 Plot Plot_bodies NIL 1 T OBSERVER NIL NIL NIL NIL 1 @#$#@#$#@ ## WHAT IS IT? This program simulates the gravitational attraction between three bodies. ## HOW IT WORKS The program will calculate the gravitational force acting between the bodies ## HOW TO USE IT Enter the settings of each body and put to start the simulation, there are two buttons that demonstrate stable orbits. ## THINGS TO NOTICE The orbits are rarely stable. ## THINGS TO TRY Try to place the bodies in the position of triangle rectangle or scalene triangle with zero initial velocity, the planets tend to rotate around a center of mass. ## EXTENDING THE MODEL Do in 3 dimensions put integration time to show that the shorter the integration time, more realistic the result ## RELATED MODELS (models in the NetLogo Models Library and elsewhere which are of related interest ) Electrostatics ## CREDITS AND REFERENCES Made by claudio.pavani@gmail.com @#$#@#$#@ default true 0 Polygon -7500403 true true 150 5 40 250 150 205 260 250 airplane true 0 Polygon -7500403 true true 150 0 135 15 120 60 120 105 15 165 15 195 120 180 135 240 105 270 120 285 150 270 180 285 210 270 165 240 180 180 285 195 285 165 180 105 180 60 165 15 arrow true 0 Polygon -7500403 true true 150 0 0 150 105 150 105 293 195 293 195 150 300 150 box false 0 Polygon -7500403 true true 150 285 285 225 285 75 150 135 Polygon -7500403 true true 150 135 15 75 150 15 285 75 Polygon -7500403 true true 15 75 15 225 150 285 150 135 Line -16777216 false 150 285 150 135 Line -16777216 false 150 135 15 75 Line -16777216 false 150 135 285 75 bug true 0 Circle -7500403 true true 96 182 108 Circle -7500403 true true 110 127 80 Circle -7500403 true true 110 75 80 Line -7500403 true 150 100 80 30 Line -7500403 true 150 100 220 30 butterfly true 0 Polygon -7500403 true true 150 165 209 199 225 225 225 255 195 270 165 255 150 240 Polygon -7500403 true true 150 165 89 198 75 225 75 255 105 270 135 255 150 240 Polygon -7500403 true true 139 148 100 105 55 90 25 90 10 105 10 135 25 180 40 195 85 194 139 163 Polygon -7500403 true true 162 150 200 105 245 90 275 90 290 105 290 135 275 180 260 195 215 195 162 165 Polygon -16777216 true false 150 255 135 225 120 150 135 120 150 105 165 120 180 150 165 225 Circle -16777216 true false 135 90 30 Line -16777216 false 150 105 195 60 Line -16777216 false 150 105 105 60 car false 0 Polygon -7500403 true true 300 180 279 164 261 144 240 135 226 132 213 106 203 84 185 63 159 50 135 50 75 60 0 150 0 165 0 225 300 225 300 180 Circle -16777216 true false 180 180 90 Circle -16777216 true false 30 180 90 Polygon -16777216 true false 162 80 132 78 134 135 209 135 194 105 189 96 180 89 Circle -7500403 true true 47 195 58 Circle -7500403 true true 195 195 58 circle false 0 Circle -7500403 true true 0 0 300 circle 2 false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 cow false 0 Polygon -7500403 true true 200 193 197 249 179 249 177 196 166 187 140 189 93 191 78 179 72 211 49 209 48 181 37 149 25 120 25 89 45 72 103 84 179 75 198 76 252 64 272 81 293 103 285 121 255 121 242 118 224 167 Polygon -7500403 true true 73 210 86 251 62 249 48 208 Polygon -7500403 true true 25 114 16 195 9 204 23 213 25 200 39 123 cylinder false 0 Circle -7500403 true true 0 0 300 dot false 0 Circle -7500403 true true 90 90 120 face happy false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 255 90 239 62 213 47 191 67 179 90 203 109 218 150 225 192 218 210 203 227 181 251 194 236 217 212 240 face neutral false 0 Circle -7500403 true true 8 7 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Rectangle -16777216 true false 60 195 240 225 face sad false 0 Circle -7500403 true true 8 8 285 Circle -16777216 true false 60 75 60 Circle -16777216 true false 180 75 60 Polygon -16777216 true false 150 168 90 184 62 210 47 232 67 244 90 220 109 205 150 198 192 205 210 220 227 242 251 229 236 206 212 183 fish false 0 Polygon -1 true false 44 131 21 87 15 86 0 120 15 150 0 180 13 214 20 212 45 166 Polygon -1 true false 135 195 119 235 95 218 76 210 46 204 60 165 Polygon -1 true false 75 45 83 77 71 103 86 114 166 78 135 60 Polygon -7500403 true true 30 136 151 77 226 81 280 119 292 146 292 160 287 170 270 195 195 210 151 212 30 166 Circle -16777216 true false 215 106 30 flag false 0 Rectangle -7500403 true true 60 15 75 300 Polygon -7500403 true true 90 150 270 90 90 30 Line -7500403 true 75 135 90 135 Line -7500403 true 75 45 90 45 flower false 0 Polygon -10899396 true false 135 120 165 165 180 210 180 240 150 300 165 300 195 240 195 195 165 135 Circle -7500403 true true 85 132 38 Circle -7500403 true true 130 147 38 Circle -7500403 true true 192 85 38 Circle -7500403 true true 85 40 38 Circle -7500403 true true 177 40 38 Circle -7500403 true true 177 132 38 Circle -7500403 true true 70 85 38 Circle -7500403 true true 130 25 38 Circle -7500403 true true 96 51 108 Circle -16777216 true false 113 68 74 Polygon -10899396 true false 189 233 219 188 249 173 279 188 234 218 Polygon -10899396 true false 180 255 150 210 105 210 75 240 135 240 house false 0 Rectangle -7500403 true true 45 120 255 285 Rectangle -16777216 true false 120 210 180 285 Polygon -7500403 true true 15 120 150 15 285 120 Line -16777216 false 30 120 270 120 leaf false 0 Polygon -7500403 true true 150 210 135 195 120 210 60 210 30 195 60 180 60 165 15 135 30 120 15 105 40 104 45 90 60 90 90 105 105 120 120 120 105 60 120 60 135 30 150 15 165 30 180 60 195 60 180 120 195 120 210 105 240 90 255 90 263 104 285 105 270 120 285 135 240 165 240 180 270 195 240 210 180 210 165 195 Polygon -7500403 true true 135 195 135 240 120 255 105 255 105 285 135 285 165 240 165 195 line true 0 Line -7500403 true 150 0 150 300 line half true 0 Line -7500403 true 150 0 150 150 pentagon false 0 Polygon -7500403 true true 150 15 15 120 60 285 240 285 285 120 person false 0 Circle -7500403 true true 110 5 80 Polygon -7500403 true true 105 90 120 195 90 285 105 300 135 300 150 225 165 300 195 300 210 285 180 195 195 90 Rectangle -7500403 true true 127 79 172 94 Polygon -7500403 true true 195 90 240 150 225 180 165 105 Polygon -7500403 true true 105 90 60 150 75 180 135 105 plant false 0 Rectangle -7500403 true true 135 90 165 300 Polygon -7500403 true true 135 255 90 210 45 195 75 255 135 285 Polygon -7500403 true true 165 255 210 210 255 195 225 255 165 285 Polygon -7500403 true true 135 180 90 135 45 120 75 180 135 210 Polygon -7500403 true true 165 180 165 210 225 180 255 120 210 135 Polygon -7500403 true true 135 105 90 60 45 45 75 105 135 135 Polygon -7500403 true true 165 105 165 135 225 105 255 45 210 60 Polygon -7500403 true true 135 90 120 45 150 15 180 45 165 90 sheep false 15 Circle -1 true true 203 65 88 Circle -1 true true 70 65 162 Circle -1 true true 150 105 120 Polygon -7500403 true false 218 120 240 165 255 165 278 120 Circle -7500403 true false 214 72 67 Rectangle -1 true true 164 223 179 298 Polygon -1 true true 45 285 30 285 30 240 15 195 45 210 Circle -1 true true 3 83 150 Rectangle -1 true true 65 221 80 296 Polygon -1 true true 195 285 210 285 210 240 240 210 195 210 Polygon -7500403 true false 276 85 285 105 302 99 294 83 Polygon -7500403 true false 219 85 210 105 193 99 201 83 square false 0 Rectangle -7500403 true true 30 30 270 270 square 2 false 0 Rectangle -7500403 true true 30 30 270 270 Rectangle -16777216 true false 60 60 240 240 star false 0 Polygon -7500403 true true 151 1 185 108 298 108 207 175 242 282 151 216 59 282 94 175 3 108 116 108 target false 0 Circle -7500403 true true 0 0 300 Circle -16777216 true false 30 30 240 Circle -7500403 true true 60 60 180 Circle -16777216 true false 90 90 120 Circle -7500403 true true 120 120 60 tree false 0 Circle -7500403 true true 118 3 94 Rectangle -6459832 true false 120 195 180 300 Circle -7500403 true true 65 21 108 Circle -7500403 true true 116 41 127 Circle -7500403 true true 45 90 120 Circle -7500403 true true 104 74 152 triangle false 0 Polygon -7500403 true true 150 30 15 255 285 255 triangle 2 false 0 Polygon -7500403 true true 150 30 15 255 285 255 Polygon -16777216 true false 151 99 225 223 75 224 truck false 0 Rectangle -7500403 true true 4 45 195 187 Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194 Rectangle -1 true false 195 60 195 105 Polygon -16777216 true false 238 112 252 141 219 141 218 112 Circle -16777216 true false 234 174 42 Rectangle -7500403 true true 181 185 214 194 Circle -16777216 true false 144 174 42 Circle -16777216 true false 24 174 42 Circle -7500403 false true 24 174 42 Circle -7500403 false true 144 174 42 Circle -7500403 false true 234 174 42 turtle true 0 Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210 Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105 Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105 Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87 Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210 Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99 wheel false 0 Circle -7500403 true true 3 3 294 Circle -16777216 true false 30 30 240 Line -7500403 true 150 285 150 15 Line -7500403 true 15 150 285 150 Circle -7500403 true true 120 120 60 Line -7500403 true 216 40 79 269 Line -7500403 true 40 84 269 221 Line -7500403 true 40 216 269 79 Line -7500403 true 84 40 221 269 wolf false 0 Polygon -16777216 true false 253 133 245 131 245 133 Polygon -7500403 true true 2 194 13 197 30 191 38 193 38 205 20 226 20 257 27 265 38 266 40 260 31 253 31 230 60 206 68 198 75 209 66 228 65 243 82 261 84 268 100 267 103 261 77 239 79 231 100 207 98 196 119 201 143 202 160 195 166 210 172 213 173 238 167 251 160 248 154 265 169 264 178 247 186 240 198 260 200 271 217 271 219 262 207 258 195 230 192 198 210 184 227 164 242 144 259 145 284 151 277 141 293 140 299 134 297 127 273 119 270 105 Polygon -7500403 true true -1 195 14 180 36 166 40 153 53 140 82 131 134 133 159 126 188 115 227 108 236 102 238 98 268 86 269 92 281 87 269 103 269 113 x false 0 Polygon -7500403 true true 270 75 225 30 30 225 75 270 Polygon -7500403 true true 30 75 75 30 270 225 225 270 @#$#@#$#@ NetLogo 6.1.1 @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ @#$#@#$#@ default 0.0 -0.2 0 0.0 1.0 0.0 1 1.0 0.0 0.2 0 0.0 1.0 link direction true 0 Line -7500403 true 150 150 90 180 Line -7500403 true 150 150 210 180 @#$#@#$#@ 0 @#$#@#$#@