/*    
    Euler's method for the Eart-Sun system, simplest possible code
*/ 
#include <cmath>
#include <iostream>
#include <fstream>
#include <iomanip>
using namespace  std;
// output file as global variable
ofstream ofile;
// function declarations
void output( double, double, double, double, double);

int main(int argc, char* argv[])
{
//  declarations of variables
  char *outfilename;
  // Read in output file, abort if there are too few command-line arguments
  if( argc <= 1 ){
    cout << "Bad Usage: " << argv[0] <<
      " read also output file on same line" << endl;
    //    exit(1);
  }
  else{
    outfilename=argv[1];
  }
  ofile.open(outfilename);

  int NumberofSteps = 1000;
  double FinalTime = 1.0;
  double Step = FinalTime/((double) NumberofSteps);
  double time = 0.0;
  // Initial values  x = 1.0 AU and vy = 2*pi
  double pi = acos(-1.0);
  double FourPi2 = 4*pi*pi;
  double x =  1.0; double y =  0.0; double vx = 0.0; double vy = 2.0*pi;
  double r = sqrt(x*x+y*y);

// now we start solving the differential equations using Euler's method
  while (time <= FinalTime){
    x += Step*vx;
    y += Step*vy;
    vx -= Step*FourPi2*x/(r*r*r);
    vy -= Step*FourPi2*y/(r*r*r);
    r = sqrt(x*x+y*y);
    time += Step;
    output(time, x, y, vx, vy);   // write to file 
  }
  ofile.close();  // close output file
  return 0;
}   //  End of main function 

//    function to write out the final results
void output(double time, double x, double y, double vx, double vy)
{
  ofile << setiosflags(ios::showpoint | ios::uppercase);
  ofile << setw(15) << setprecision(8) << time;
  ofile << setw(15) << setprecision(8) << x;
  ofile << setw(15) << setprecision(8) << y;
  ofile << setw(15) << setprecision(8) << vx;
  ofile << setw(15) << setprecision(8) << vy << endl;
}  // end of function output