Orbit mechanics

[2NywAqkS]

#define STAR_MASS 2000000

Asteroid::Asteroid()
{
	x = (rand() % 10000) - 5000;
	y = (rand() % 10000) - 5000;
	mass = (rand() % 20) + 2;
	randDir = (rand() % 360) * 0.0174532925;
	randVel = ((rand() % 20) + 2) + 0.01;
	velocity = 0;
}

void Asteroid::Calculate(int delta)
{
	// Calculate Gravity
	double direction = atan2(y, x);
	double distance = sqrt((x*x)+(y*y));
	double force = ((mass * STAR_MASS)/(distance*distance));
	double acceleration = force / mass;
	velocity += acceleration * ((double)delta / 64.0); // 64 times slower
	x -= cos(direction) * velocity;
	y -= sin(direction) * velocity;

	// Move in it's random direction
	x += cos(randDir) * randVel * delta;
	y += sin(randDir) * randVel * delta;
}

From this code I would have thought that some of the asteroids would orbit when they passed close to the star (0, 0). But instead they just flash on and off weirdly and slowly move away. I've tried altering the variables but they always do this when the get too close.

If this isn't enough source code, I've uploaded the rest here:
www.wizardchip.com/GravSimSource.zip

Any help is much appreciated!
Thanks,
Rowan.

[mik2718]

Shouldn't force, acceleration and velocity also be 2-vectors ?
(not just position)

[helios]

The problem is that on line 16 you're treating (x,y) as a position vector, while on lines 21 and 22 you're treating it as a velocity vector. You need at least two vectors per body to be able to simulate this.

[Chervil]

An interesting simulation. Thanks for sharing your code - which though not quite working, didn't take much to get going.

mik2718 is correct about treating the other quantities as 2-d vectors. I played around with your code and replaced the Asteroid velocity with xvelocity and yvelocity.

I'm not sure whether this was necessary, or simply my preference, I assigned initial random values (using your existing figures) to these velocity components, which meant there was no longer a need for lines 24-26 in your code above.

For my own purposes, I added a variable and keyboard detection to allow me to adjust the overall speed, this meant the "delta" value needed to be a double rather than an int. I also reduced the default star mass considerably to about 2000.

Also, I found the dots hard to see, so I changed the drawing to use a small polygon (hexagon or octagon) - my first attempt used a triangle but that looked ugly.

Here's some of my code (which may contain trivial changes as well as useful ones):

Asteroid::Asteroid()
{

	using std::cos;
	using std::sin;

	x = (rand() % 10000) - 5000;
	y = (rand() % 10000) - 5000;

	mass = (rand() % 200) + 2;
	randDir = (rand() % 360) * 0.0174532925;
	randVel = (((rand() % 20) + 2) + 0.01) / 500.0; 

	xvelocity = cos(randDir) * randVel;
	yvelocity = sin(randDir) * randVel;

}


void Asteroid::Calculate(double delta)
{
	// Calculate Gravity
	using std::atan2;
	using std::sqrt;
	using std::cos;
	using std::sin;

	double direction = atan2(y, x);
	double distance = sqrt((x*x)+(y*y));
	double force = ((mass * STAR_MASS)/(distance*distance));
	double acceleration = force / mass;

	double xacceleration = - acceleration * cos(direction);
	double yacceleration = - acceleration * sin(direction);

	xvelocity += xacceleration  / 64.0;
	yvelocity += yacceleration  / 64.0;

	x += xvelocity * delta;
	y += yvelocity * delta;

}

void Asteroid::Draw()
{

	glBegin(GL_POLYGON);
		glColor3d(((double)mass)/17, ((double)mass)/20, ((double)mass)/22);
		glVertex2f(x+  0.0   , y+  4.000 );
		glVertex2f(x+  2.8284, y+  2.8284);
		glVertex2f(x+  4.0   , y+ -0.0   );
		glVertex2f(x+  2.8284, y+ -2.8284);
		glVertex2f(x+  0.000 , y+ -4.000 );
		glVertex2f(x+ -2.8284, y+ -2.8284);
		glVertex2f(x+ -4.000 , y+  0.000 );
		glVertex2f(x+ -2.8284, y+  2.8284);
	glEnd();

}

It would be interesting to add code so that each object exerts a gravitational effect upon all the other asteroids, I may play with that as a separate version.

[2NywAqkS]

Wow thanks. Your last point was exactly what I had in mind! If you get anywhere with it it'd be cool to see it.