Im trying to make a sketch to simulate the movement of a planet around the sun. I use as parameters the initial position, the initial speed, the gravity constant, an the angle of the initial speed.

Usually the trajectory is an ellipse, as it should, and the planet dont go away from the ellipse. I think that the sketch is ok, and the elipse is only the case of stable orbits. ¿Do you think the strange case of the parameters chosen below is due to any error in the code?

Code:

//parámeters
float g=20000;//gravity constant
float din=200;//Initial distance to the sun
float vin=5;//Initial speed
float ang=-PI/10;//angle respect perpendicular to the distance to the sun. downside is positive
//variables
Ball planet;
float X;
float Y;
float r2;

void setup(){
  size (700,700);
  background(0);
  smooth();
  planet =new Ball(width/2,height/2-din,1,vin*cos(ang),vin*sin(ang),10);
  frameRate(60);
}
void draw(){
  background(0);
  ellipse (width/2,height/2,30,30);
  planet.ecuation();
  planet.move();
  planet.paint();
}
class Ball {
  float radio;
  float x,y;
  int id;
  float vx,vy;
  Ball[] resto;
  Ball(float xin,float yin, int idin,float vxin, float vyin,float radin){
    x=xin;
    y=yin;
    id=idin;
    vx=vxin;
    vy=vyin;
    radio=radin;
   
  }
  void ecuation(){
    X=x-width/2;
    Y=y-height/2;
    r2=X*X+Y*Y;
    if (r2>0){
	vx-=g*X/(sqrt(r2)*r2);
	vy-=g*Y/(sqrt(r2)*r2);
    }
  }
  void move(){
    x+=vx;
    y+=vy;
  }
  void paint(){
    ellipse (x,y,radio,radio);
  }
} 

This for example is stable:

Code:

float g=10000;//gravity constant
float din=300;//Initial distance to the sun
float vin=5;//Initial speed
float ang=0;//angle respect perpendicular to the distance to the sun. downside is positive 

But try to increase the g value, it starts to be insestable, and I think it shouldn't and in some cases of stronger gravity it expel the earth away!

The parameters values are not taken from anywhere, I´ve been changing them till I found an stable orbit, and then start to change them again to see what happened.

I simply applied Newton formula

Of course there are stable parameters and inestable ones, but I think there are nonsense results. For example that of increase the gravity and a stable orbit transform in an insestable one, or that the ellipse axes rotate around.

The question are that according to my limited phisics knowledge, the trajectory of an object submited to gravity atraccion to other, should be an ellipse or an hyperbola.

My sketch is suposed to simulate this movement, and I think is ok, but the movement of my planet are not what it should be. There has to be an error in my code or an explanation for theese cases.

just found this sketch : http://www.openprocessing.org/visuals/?visualID=5152

To have a circular orbit, you need the distance and speed to form a special relations, plus the initial velocity has to be perpendicular to the radial line of the planet leading to the sun to begin with. If you have radius R multiply velocity squared V^2 equal to MG, then you're guaranteed to have a circular orbit.
R*V^2=MG
Here M is the mass of the sun and G is gravitational constant 6.67*10^-11.

I don't know where your numbers are from, possibly from your imagination of a different solar system but still the above condition has to be met to produce circular orbits, which is what you see for our solar system's planets.

I didn't try your program yet but if you have an ellipse that changes it orientation of major axis, there's a problem. It shouldn't, according to physics. Once set, the planets should not be changing their orbits.

I suggest you use the right constants say for planet and sun't mass and distance. You may scale the distance within your display.