HorseshoeModelSimulation with RA * cos(DE) approach

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

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

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

		ArrayList<Double> motion = new ArrayList<Double>(); //contains data for apparent motion in RA (corrected by cos(DEC) = real motion in sky (in arcsec/min)
		ArrayList<Double> distances = new ArrayList<Double>(); //contains data for simulated distances of horseshoe asteroid to the Sun (in AU)

		//populates radii and motion ArrayLists with data from Ephemeris simulation
		while(input.hasNextLine()) {
			//When adding each new motion value in arcsec/min, it is automatically converted to AU/day by the convertMotion() method
		//	motion.add(convertMotion(input.nextDouble()));
			motion.add(input.nextDouble());
			distances.add(input.nextDouble());
		}

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

		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);
		}
		input.close();
	}

	public static ArrayList<Double> checkModel(ArrayList<Double> motion, ArrayList<Double> distances) {
		//  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 e = 0.51485; //eccentricity of orbit
		double a = 0.99774; //semi-major axis (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);

		for(int i = 0; i < motion.size(); i++) {
			//total distance traveled in period to current day is iterative sum of ArrayList<BigDecimal> motion to current day
			//distanceSincePeriapsis += motion.get(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);
			theta += motion.get(i) * 1440 / 3600 * Math.PI / 180;
			//System.out.println(theta);

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

			modeledDistances.add(distance);
		}

		return modeledDistances;
	}

	public static double convertMotion(double motion) {
		//motion is given in arcsec/min. First, we must convert it to arcsec/day.

		double convertedMotion = motion;

		convertedMotion *= 1440; //There are 1440 minutes in 1 day. Now, we have motion in arcsec/day.

		convertedMotion = 1 / convertedMotion; //To convert from arcsec/day to parsec/day, we compute 1 / motion.

		convertedMotion *= 206265; //There are 206265 AU in 1 parsec. Hence, we multiply motion by 206265.

		return convertedMotion;
	}

	//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;
	} */
}