steos · December 18, 2010 01:40 · Dec 19, 2010 · Dec 18, 2010 · Dec 18, 2010
diff --git a/Kepler.java b/Kepler.java
@@ -1,9 +1,25 @@
-import static java.lang.Math.pow;
-import static java.lang.Math.tan;
-import static java.lang.Math.toRadians;
+import static java.lang.Math.*;
 
 public class Kepler
 {
+	public static class Point2d
+	{
+		public double x;
+		public double y;
+
+		public Point2d(double x, double y)
+		{
+			this.x = x;
+			this.y = y;
+		}
+
+		public Point2d toCartesian()
+		{
+			return new Point2d((x * cos(y)), 
+				(x * sin(y)));
+		}	
+	}
+
 	/**
 	 * gravitational constant
 	 */

diff --git a/Point2d.java b/Point2d.java
@@ -1,20 +0,0 @@
-import static java.lang.Math.cos;
-import static java.lang.Math.sin;
-
-public class Point2d
-{
-	public double x;
-	public double y;
-
-	public Point2d(double x, double y)
-	{
-		this.x = x;
-		this.y = y;
-	}
-
-	public Point2d toCartesian()
-	{
-		return new Point2d((x * cos(y)), 
-			(x * sin(y)));
-	}	
-}

diff --git a/Kepler.java b/Kepler.java
@@ -1,3 +1,7 @@
+import static java.lang.Math.pow;
+import static java.lang.Math.tan;
+import static java.lang.Math.toRadians;
+
 public class Kepler
 {
 	/**

diff --git a/Point2d.java b/Point2d.java
@@ -1,3 +1,6 @@
+import static java.lang.Math.cos;
+import static java.lang.Math.sin;
+
 public class Point2d
 {
 	public double x;

diff --git a/Kepler.java b/Kepler.java
@@ -0,0 +1,107 @@
+public class Kepler
+{
+	/**
+	 * gravitational constant
+	 */
+	public static final double G = 6.67428E-11;
+
+	/**
+	 * 2 * pi
+	 */
+	public static final double TWO_PI = PI * 2;
+
+	/**
+	 * pi squared
+	 */
+	public static final double PI2 = pow(PI, 2);
+
+	/**
+	 * solves kepler (find position of satellite for given point in time)
+	 * 
+	 * @param majorAxis the semi-major axis of the satellites orbit
+	 * @param e the numeric eccentricity of the satellites orbit
+	 * @param T the total time of circulation
+	 * @param time time since satellite reached periapsis
+	 * @param iterations number of iterations to calculate eccentric anomaly
+	 * 
+	 * @return the cartesian coordinates of the planet in the orbital plane
+	 */
+	public static Point2d getOrbitalPosition(double majorAxis, double e, 
+			double T, double time, int iterations)
+	{
+		double mean = getMeanAnomaly(T, time);
+		double ecc = getEccentricAnomaly(e, mean, iterations);
+		double phi = getTrueAnomaly(e, ecc);
+		double r = getRadiusLength(majorAxis, e, phi);
+
+		return new Point2d(r, phi).toCartesian();
+	}
+
+	/**
+	 * returns the circulation time according to
+	 * keplers third law
+	 * 
+	 * @param majorAxis the semi-major axis of the orbit
+	 * @param M the mass of the central body
+	 * @param m the satellites mass
+	 * 
+	 * @return the total time of circulation
+	 */
+	public static double getCirculationTime(double majorAxis, double M, double m)
+	{
+		return sqrt((pow(majorAxis, 3) * 4 * PI2) / 
+				(G * (M + m)) );
+	}
+
+	/**
+	 * iteratively calculates the eccentric anomaly of an orbit for a given
+	 * mean anomaly and eccentricity (converges very fast - at about 4 iterations)
+	 */
+	public static double getEccentricAnomaly(double eccentricity, double meanAnomaly, int iterations)
+	{
+		double tempResult = meanAnomaly;
+		double numerator;
+
+		for (int i = 0; i < iterations; i++)
+		{
+			numerator = meanAnomaly + eccentricity * sin(tempResult)
+					- eccentricity * tempResult * cos(tempResult);
+			tempResult = numerator / (1 - eccentricity * cos(tempResult));
+		}
+
+		return tempResult;
+	}
+
+	/**
+	 * calculates the mean anomaly of an orbit for the specified point in
+	 * time
+	 * 
+	 * @param circulationTime total 
+	 * @param time time since periapsis
+	 */
+	public static double getMeanAnomaly(double circulationTime, double time)
+	{
+		return TWO_PI / circulationTime * time;
+	}
+
+	/**
+	 * calculates the true anomaly for a given orbits eccentricity and
+	 * eccentric anomaly
+	 */
+	public static double getTrueAnomaly(double eccentricity, double eccentricAnomaly)
+	{
+		return 2 * atan(sqrt((1 + eccentricity) / (1 - eccentricity))
+				* tan(eccentricAnomaly / 2));
+	}
+
+	/**
+	 * calculates the length of the radius vector
+	 */
+	public static double getRadiusLength(double majorAxis, double eccentricity, double trueAnomaly)
+	{
+		double nominator = majorAxis * (1 - pow(eccentricity, 2));
+		double denominator = 1 + eccentricity * cos(trueAnomaly);
+
+		return nominator / denominator;
+	}
+}
diff --git a/Point2d.java b/Point2d.java
@@ -0,0 +1,17 @@
+public class Point2d
+{
+	public double x;
+	public double y;
+
+	public Point2d(double x, double y)
+	{
+		this.x = x;
+		this.y = y;
+	}
+
+	public Point2d toCartesian()
+	{
+		return new Point2d((x * cos(y)), 
+			(x * sin(y)));
+	}	
+}