vis visa attempt 1

/* Princeton University Explorer Competition
 * Team: Sherlock Ohms */

import java.util.Scanner;
import java.util.ArrayList;
import java.io.*;

public class HorseshoeModelSimulation {
	static final double G = 6.67430 * Math.pow(10, -11); //Newton's gravitational constant
	static final double M_SOL = 1.989 * Math.pow(10, 30); //Mass of the Sun (Msol) in kg

	public static void main(String[] args) throws IOException {
		Scanner input = new Scanner(new File("CruithneData.txt"));

		ArrayList<Double> distances = new ArrayList<Double>(); //contains data for simulated distances of horseshoe asteroid to the Sun (in AU)

		double e, a;
		e = input.nextDouble(); //reads in eccentricity of asteroid
		a = input.nextDouble(); //reads in semi-major axis of asteroid (in AU)

		//populates radii ArrayList with data from Ephemeris simulation
		while(input.hasNextLine()) {
			distances.add(input.nextDouble());
		}

		ArrayList<Double> modeledDistances = checkModel(distances, a, e);

		double error;
		for(int i = 0; i < modeledDistances.size(); i++) {
			error = Math.abs(1 - (modeledDistances.get(i) / distances.get(i)));
			System.out.printf("%.4f %.4f %.4f%%\n", distances.get(i), modeledDistances.get(i), error * 100);
		}
		input.close();
	}

	public static ArrayList<Double> checkModel(ArrayList<Double> distances, double a, double e) {
		//  Formula: r(theta) = [a * (1 - e^2)] / [1 + e * cos(theta)]

		ArrayList<Double> modeledDistances = new ArrayList<Double>(); //contains model's calculated distance between horseshoe asteroid and the Sun for each day

		double distance; //current distance between horseshoe asteroid and the Sun (in AU)
		double b = a * (Math.sqrt(1 - Math.pow(e, 2))); //semi-minor axis (in AU)
		double theta = 0; //true anomaly: angle between current position of the orbiting object and periapsis (which is the first day of data in the text file) (in radians)

		double distanceSincePeriapsis = 0; //distance traveled along orbit since periapsis (in AU)

		//use approximation of ellipse circumference
		double orbitCircumference = calcCircumference(a, b);

		double velocity; //current orbital velocity of asteroid

		for(int i = 0; i < distances.size(); i++) {
			//Now, to obtain the anomaly angle (in radians), we take the percentage of orbit completed and multiply it by 2 pi
			theta = (distanceSincePeriapsis / orbitCircumference) * (2 * Math.PI);

			distance = (a * (1 - Math.pow(e, 2))) / (1 + e * Math.cos(theta));

			modeledDistances.add(distance);

			//update distance traveled since periapsis using velocity
			velocity = calcVelocity(distances.get(i), a);

			distanceSincePeriapsis += velocity; //Since velocity is in AU/day, adding it to distanceSincePeriapsis updates distance traveled to current day
		}

		return modeledDistances;
	}

	//performs approximation of elliptical circumference given semi-major axis and semi-minor axis; +/- 5% of true circumference
	public static double calcCircumference(double a, double b) {
		double circumference = Math.PI;

		circumference *= (a + b);

		double tempMult = 3;
		tempMult *= Math.pow(a - b, 2);
		tempMult /= Math.pow(a + b, 2);

		double tempDivisorPart = Math.pow(a - b, 2) / Math.pow(a + b, 2);
		tempDivisorPart *= -3;
		tempDivisorPart += 4;

		tempMult /= (Math.sqrt(tempDivisorPart) + 10);

		tempMult += 1;

		circumference *= tempMult;

		return circumference;
	}

	//uses vis-visa equation to calculate orbital velocity of horseshoe asteroid
	public static double calcVelocity(double r, double a) {
		double rInMeters = convertAUToMeters(r);
		double aInMeters = convertAUToMeters(a);
		double velocity = Math.sqrt(G * M_SOL * ((2 / rInMeters) - (1 / aInMeters))); //yields velocity in m/s
		velocity = convertToAUPerDay(velocity);
		return velocity;
	}

	//given velocity in m/s, converts to AU/day
	public static double convertToAUPerDay(double velocity) {
		double convertedVelocity = velocity;

		//convert from m to AU
		convertedVelocity /= (1.496 * Math.pow(10, 11));

		//convert from /sec to /day
		convertedVelocity *= 60 * 60 * 24;

		return convertedVelocity;
	}

	//converts AU to meters
	public static double convertAUToMeters(double inAU) {
		return (inAU * (1.496 * Math.pow(10, 11)));
	}
}