Visual Representation of a Kepler Orbit in 3D

[Warringer]

Hello.

I'm currently in a bit of a bind, as I want to develop a little Java tool to visualize the trajectory of a body around its parent body, using Keplers Laws and the Keplerian Orbital Elements. In a quest to learn Java3D.

May or may not be related to the KSP calculator

Having moved from a simple 2D plane into 3D is harder then I thought.

To integrate inclination was relatively easy, but now I am stuck with integrating the other three orbital elements

• Longitude of the ascending node
• Argument of periapsis
• Mean anomaly

Now I am hoping that you can help me out here as I already tried to find something via Google and Wikipedia as well as going through any page on Orbital Mechanics and programming I have found.

I think I'll just add the code as well...

/**
 * Keplerian Orbital Elements
 */
protected double eccentricity;		// Eccentricity e
protected double semimajor_axis;	// Semimajor Axis a
protected double inclination; 		// Inclination i
protected double asc_node;		// Longitude of the ascending node 
protected double per_arg;		// Argument of periapsis 
protected double mean_anomaly;		// Mean Anomaly

/**
 * Kepler Ellpise Calculaton Elements
 */
protected double kep_radius;
protected double kep_delta_angle;
protected double kep_angle_moved = 0;
protected double kep_delta_time = 0.1;

/**
 * Calculates the Radius and the angle of a Kepler ellipse moved during a delta t
 */
public void keplerMovedAngle() {
	// Calculate Radius
        kep_radius = (1 - eccentricity * eccentricity) / (1 - eccentricity * Math.cos(deg2rad(kep_angle_moved)));
       	// Calculate angle delta
        kep_delta_angle = 2 * Math.PI * Math.sqrt(1 - eccentricity * eccentricity) / (kep_radius * kep_radius) * (kep_delta_time * per_cor);
       	kep_angle_moved += kep_delta_angle;
}
	
/**
 * Calculates the position of an object in the Kepler ellipse at a specific time
 * 
 * @return Position Vector of orbiting object
 */
public Vector3d keplerPosition() {
	// Add deltas
	double rad = deg2rad(kep_angle_moved);
	double inc = deg2rad(inclination);
	
	// Calculate Coordinates
	double pz = dist_cor * kep_radius * Math.cos(rad);
       	double px = dist_cor * kep_radius * Math.sin(rad) * Math.cos(inc);
        double py = dist_cor * kep_radius * Math.sin(rad) * Math.sin(inc);
       
       	Vector3d keplerVector = new Vector3d(px, py, pz);
	return keplerVector;
}

Please note that dist_cor and per_cor are correction factors for scaling distances and orbital periods of the orbits.

I think that I may have nailed the Longitude of the ascending node by starting to calculate the orbit with starting at:

kep_angle_moved = -asc_node