Задача о двух телах
Материал из Department of Theoretical and Applied Mechanics
Описание[править]
Решение и визуализация задачи двух тел.
Файл:[[1]]
Код программы[править]
Текст программы на языке JavaScript:
1 var gravitationalConstant = 6.67*Math.pow(10,-11);//гравитационная постоянная
2 var point_x1 = 1200/6*3;
3 var point_y1 = 300;
4 var point_x2 = 1200/6*4;
5 var point_y2 = 300;
6 var sP = 1;
7 var k = 0;
8 var flag = 0;
9 function firstPaint(){
10 var canvas = document.getElementById('pole');
11 if (canvas.getContext){
12 var ctx = canvas.getContext('2d');
13 }
14 var img1 = new Image();
15 img1.src = "planet1.jpg";
16 img1.onload = function(){
17
18 var img = new Image();
19 img.src = "space.jpg";
20 img.onload = function(){
21 var pattern = ctx.createPattern(img,"repeat");
22 ctx.fillStyle = pattern;
23 ctx.beginPath();
24 ctx.clearRect(0,0,1500,800);
25 ctx.moveTo(1,1);
26 ctx.fillRect(0, 0, 1500, 800);
27 ctx.closePath();
28 ctx.beginPath();
29 ctx.fillStyle = "#F6F231";
30 ctx.arc(point_x1,point_y1,10,0,Math.PI*2);
31 ctx.fill();
32 var img2 = new Image();
33 img2.src = "planet2.jpg";
34 img2.onload = function(){
35 var pattern2 = ctx.createPattern(img2,"repeat");
36 ctx.beginPath();
37 ctx.fillStyle = pattern2;
38
39 ctx.moveTo(point_x2,point_y2);
40 ctx.arc(point_x2,point_y2,10,0,Math.PI*2);
41 ctx.fill();
42 }
43 }
44 }
45
46 }
47 function AddPlanet(x,y,mass,speed){
48 this.x = x;
49 this.y = y;
50 this.mass = mass;
51
52 this.M = this.mass*gravitationalConstant;
53 this.speed = speed;
54 }
55 function makePlanets(){
56 point_x1 = 1200/6*3;
57 point_y1 = 300;
58 point_x2 = 1200/6*4;
59 point_y2 = 300;
60 var mass =document.getElementById('firstMass').value*Math.pow(10,20);
61 var speed = 1;
62 var firstPlanet = new AddPlanet(point_x1,point_y1,mass,speed);
63 mass = document.getElementById('secondMass').value*Math.pow(10,20);
64 speed = 1;
65 var secondPlanet = new AddPlanet(point_x1,point_y1,mass,speed);
66
67
68 firstPlanet.r = Math.pow(10,7)*(point_x2 - point_x1 - (point_x2-point_x1)*firstPlanet.mass/(firstPlanet.mass + secondPlanet.mass));//радиус вектор 1 тела относительно центра масс системы
69 secondPlanet.r = Math.pow(10,7)*((point_x2-point_x1)*firstPlanet.mass/(firstPlanet.mass + secondPlanet.mass));//радиус вектор 1 тела относительно центра масс системы
70 firstPlanet.massCenterX = point_x2 - (point_x2-point_x1)*firstPlanet.mass/(firstPlanet.mass + secondPlanet.mass);//рассчет x координыты центра масс
71 firstPlanet.c = firstPlanet.speed*firstPlanet.r;//константы закона площадей
72 secondPlanet.c = secondPlanet.speed*secondPlanet.r;//константы закона площадей
73
74
75 firstPlanet.f = -firstPlanet.M + firstPlanet.speed*firstPlanet.c;//векторы Лапласса
76 secondPlanet.f = -secondPlanet.M + secondPlanet.speed*secondPlanet.c;//векторы Лапласса
77
78 firstPlanet.p = Math.pow(firstPlanet.c, 2)/firstPlanet.M/Math.pow(10,6); //фокальный параметр
79 secondPlanet.p = Math.pow(secondPlanet.c, 2)/secondPlanet.M/Math.pow(10,6); //фокальный параметр
80
81 firstPlanet.e = firstPlanet.f/firstPlanet.M;//эксцентриситет
82 secondPlanet.e = secondPlanet.f/secondPlanet.M;//эксцентриситет
83 console.log('e1=',firstPlanet.e,'e2=',secondPlanet.e);
84
85 drawPlanets(firstPlanet,secondPlanet);
86 }
87
88 function drawPlanets(firstPlanet,secondPlanet){
89 var canvas = document.getElementById('pole');
90 if (canvas.getContext){
91 var ctx = canvas.getContext('2d');
92 }
93
94 var img = new Image();
95 img.src = "space.jpg";
96 var img2 = new Image();
97 img2.src = "planet2.jpg";
98
99 var pattern2 = ctx.createPattern(img2,"repeat");
100
101 img.onload = function() {
102 var pattern = ctx.createPattern(img,"repeat");
103 ctx.fillStyle = pattern;
104
105 var angle = Math.PI;
106 var angle2 = 0;
107
108 firstPlanet.a = firstPlanet.p/(1 - firstPlanet.e)*6;
109 firstPlanet.b = firstPlanet.p/Math.pow((1 - firstPlanet.e),0.5)*3;
110 firstPlanet.c = Math.abs(firstPlanet.e*firstPlanet.a);//фокольное расстояние
111 secondPlanet.a = secondPlanet.p/(1 - secondPlanet.e)*6;
112 secondPlanet.b = secondPlanet.p/Math.pow((1 - secondPlanet.e),0.5)*3;
113 secondPlanet.c = Math.abs(secondPlanet.e*secondPlanet.a);//фокольное расстояние
114 firstPlanet.leftScope = firstPlanet.a*Math.cos(180);
115 secondPlanet.scope = secondPlanet.a*Math.cos(0);
116 point_x1 = firstPlanet.massCenterX + firstPlanet.c;
117 point_x2 = firstPlanet.massCenterX - secondPlanet.c;
118 var x = 10, y = 390;
119 var timerId = setInterval( function(){
120 if (k==2){
121 var a =1;
122 }
123 else{
124 angle = angle + Math.PI/360;
125 if (angle >= 2*Math.PI){
126 angle = 0;
127 }
128 angle2 = angle2 + Math.PI/360;
129 if (angle2 >= 2*Math.PI){
130 angle2 = 0;
131 }
132 firstPlanet.x = point_x1 + firstPlanet.a*Math.cos(angle);
133 firstPlanet.y = point_y1 + firstPlanet.b*Math.sin(angle);
134
135 secondPlanet.x = point_x2 + secondPlanet.a*Math.cos(angle2);
136 secondPlanet.y = point_y2 + secondPlanet.b*Math.sin(angle2);
137 ctx.fillStyle = pattern;
138 ctx.beginPath();
139 ctx.clearRect(0,0,1500,800);
140 ctx.moveTo(1,1);
141 ctx.fillRect(0, 0, 1500, 800);
142 ctx.closePath();
143
144 ctx.beginPath();
145 ctx.moveTo(firstPlanet.x,firstPlanet.y);
146 ctx.fillStyle = "#F6F231";
147 ctx.arc(firstPlanet.x,firstPlanet.y,10,0,2*Math.PI);
148 ctx.fill();
149
150 ctx.beginPath();
151 ctx.moveTo(firstPlanet.x,firstPlanet.y);
152 ctx.fillStyle = pattern2;
153 ctx.arc(secondPlanet.x ,secondPlanet.y ,10,0,2*Math.PI);
154 ctx.fill();
155
156 ctx.beginPath();
157 ctx.moveTo(firstPlanet.massCenterX,point_y1);
158 ctx.fillStyle = "#1D067F";
159 ctx.arc(firstPlanet.massCenterX,point_y1 ,4,0,2*Math.PI);
160 ctx.fill();
161
162 y = graph1(firstPlanet,secondPlanet,x,y);
163 x = x + 1;
164 if (k==1){
165 clearTimeout(timerId);
166 k = 0;
167 }
168 }
169 },sP);
170
171 };
172 }
173
174
175 function breakk(){
176 k = 1;
177 }
178
179
180 function pausee(){
181 if (k==0){
182 k = 2;
183 }
184 else{
185 k = 0;
186 }
187 }
188
189 function graph1(firstPlanet,secondPlanet,x,y){
190 var canvas = document.getElementById('pole2');
191 if (canvas.getContext){
192 var canvas = canvas.getContext('2d');
193 }
194
195
196 if ( flag == 0){
197 canvas.beginPath();
198 canvas.strokeStyle = "#000000";
199 canvas.moveTo(10,395);
200 canvas.lineTo(10,10);
201 canvas.lineTo(5,15);
202 canvas.moveTo(10,10);
203 canvas.lineTo(15,15);
204 canvas.moveTo(5,390);
205 canvas.lineTo(690,390);
206 canvas.lineTo(685,395);
207 canvas.moveTo(690,390);
208 canvas.lineTo(685,385);
209 canvas.moveTo(550,20);
210 canvas.lineTo(550,100);
211 canvas.lineTo(690,100);
212 canvas.lineTo(690,20);
213 canvas.lineTo(550,20);
214 canvas.strokeStyle = "#000000";
215 canvas.font = "20px serif";
216 canvas.fillText('R(t)',20,20);
217 canvas.stroke();
218 flag = 1;
219 }
220 return lengAndDraw(firstPlanet,secondPlanet,canvas,x,y)
221 }
222
223
224 function lengAndDraw(firstPlanet,secondPlanet,canvas,x,y){
225 var l = Math.sqrt( Math.pow(firstPlanet.x-secondPlanet.x,2) + Math.pow(firstPlanet.y - secondPlanet.y,2))/3.5;
226 // console.log(l);
227 canvas.beginPath();
228 canvas.clearRect(550,20,140,80);
229 canvas.strokeStyle = "#000000";
230 canvas.moveTo(x,y);
231 canvas.lineTo(x + 1, 390 - l);
232 canvas.font = "20px serif";
233 canvas.fillText('r = ' + Math.floor(l*3.5) + '*10^7', 570, 60);
234 canvas.stroke();
235 return (390 - l);
236 }
