Answer to 1 and 2 of HW implemented from git reposit orbit_bw.C

orbit_bw.C

+// orbit - Program to compute the orbit of a comet.
+#include <iostream.h>
+#include <fstream.h>
+#include <assert.h>  
+#include <math.h>
+         
+void main() {
+
+  //* Set initial position and velocity of the comet.
+  double r0, v0;
+  cout << "Enter initial radial distance (AU): "; cin >> r0;  
+  cout << "Enter initial tangential velocity (AU/yr): "; cin >> v0;
+  double r[2], v[2], accel[2];
+  r[0] = r0; r[1] = 0;  v[0] = 0; v[1] = v0;
+  
+  //* Set physical parameters (mass, G*M)
+  const double pi = 3.141592654;
+  double GM = 4*pi*pi;      // Grav. const. * Mass of Sun (au^3/yr^2)
+  double param[1];  param[0] = GM;
+  double mass = 1.;         // Mass of comet 
+  double F = .01*4*pi*pi/r0/r0;    // const outside force in one direction one percent of initial gravitational force
+  double time = 0;
+
+  //* Loop over desired number of steps using specified
+  //  numerical method.
+  cout << "Enter number of steps: "; 
+  int nStep;  cin >> nStep;
+  cout << "Enter time step (yr): ";
+  double tau;  cin >> tau; 
+  cout << "Choose a numerical method:" << endl;
+  cout << "1) Euler,       2) Euler-Cromer,   3) Verlet  "	<< endl;
+  int method;  cin >> method;
+  double *rplot, *thplot, *tplot, *kinetic, *potential, *totalE;  // Plotting variables
+  rplot = new double [nStep];  thplot = new double [nStep];
+  tplot = new double [nStep];
+  kinetic = new double [nStep]; potential = new double [nStep];
+  totalE = new double [nStep];
+  int iStep;
+  for( iStep=0; iStep < nStep; iStep++ ) {  
+
+    //* Record position and energy for plotting.
+    double normR = sqrt( r[0]*r[0] + r[1]*r[1] );
+    double normV = sqrt( v[0]*v[0] + v[1]*v[1] );
+    rplot[iStep] = normR;               // Record position for plotting
+    thplot[iStep] = atan2(r[1],r[0]);
+    tplot[iStep] = time;
+    kinetic[iStep] = 0.5*mass*normV*normV;   // Record energies
+    potential[iStep] = -GM*mass/normR+F*r0*mass;  // With the additional constant potential from the force 
+    totalE[iStep] = kinetic[iStep]+potential[iStep];
+    //* Calculate new position and velocity using desired method.
+    if( method == 1 ) {
+      accel[0] = -GM*r[0]/(normR*normR*normR)+.01*GM*r0;  // constant force effects the acceleration of the object   
+      accel[1] = -GM*r[1]/(normR*normR*normR)+.01*GM*r0;   
+      r[0] += tau*v[0];             // Euler step
+      r[1] += tau*v[1];             
+      v[0] += tau*accel[0]; 
+      v[1] += tau*accel[1]; 
+      time += tau;  
+    } 
+    else if( method == 2 ) {
+      accel[0] =-GM*r[0]/(normR*normR*normR)+.01*GM*r0; // constant force effects the acceleration of the object   
+      accel[1] =-GM*r[1]/(normR*normR*normR)+.01*GM*r0;   
+      v[0] += tau*accel[0]; 
+      v[1] += tau*accel[1]; 
+      r[0] += tau*v[0];             // Euler-Cromer step
+      r[1] += tau*v[1];             
+      time += tau;  
+    }
+    else if( method == 3 ) {
+    double accel[3]; double r[3]; r[0]=r0; r[1]=0; r[2]=0; v[1]=v0; double oldr;
+    accel[0] =-GM*r[0]/(normR*normR*normR)+.01*GM*r0; 
+    accel[1] =-GM*r[1]/(normR*normR*normR)+.01*GM*r0;
+    accel[2]=-GM*r[2]/(normR*normR*normR)+.01*GM*r0;
+    oldr = r[1];
+    r[0] = r[1] - tau*v[1]+tau*tau*accel[1];
+    r[1] = 2*r[1] - r[0]+tau*tau*accel[1];
+    r[2] = 2*r[1] - oldr+tau*tau*accel[2];
+    v[0] = .5*r[1]/tau +.5*r[0]/tau;
+    v[1] = .5*r[2]/tau +.5*oldr/tau;
+    time += tau;
+     
+                  
+}      
+  
+  }
+  
+//loop through data to find min and max for plotting purposes
+   double min, max;
+   min = kinetic[0]; max = kinetic[0];
+   for( iStep=0; iStep < nStep; iStep++ ) {  
+	if(kinetic[iStep] > max)
+		max = kinetic[iStep];
+	if(potential[iStep] > max)
+		max = potential[iStep];
+	if(totalE[iStep] > max)
+		max = totalE[iStep];
+	
+	if(kinetic[iStep] < min)
+		min = kinetic[iStep];
+	if(potential[iStep] < min)
+		min = potential[iStep];
+	if(totalE[iStep] < min)
+		min = totalE[iStep];
+	
+   }
+
+//Set up the canvas and divide it into two parts
+   TCanvas *MyC = new TCanvas("MyC", "lorenz", 1);
+   MyC->Divide(2,1);
+   MyC->cd(1);  
+
+//Graph the energy vs time
+   TGraph *graph = new TGraph(nStep, tplot, kinetic);
+   graph->SetName("gr1");
+   graph->Draw("A*");
+   graph->SetMinimum(min); //set graph's range
+   graph->SetMaximum(max);
+
+   TGraph *graph2 = new TGraph(nStep, tplot, potential);
+   graph2->SetName("gr2");
+   graph2->SetMarkerColor(2);
+   graph2->Draw("*");
+
+   TGraph *graph3 = new TGraph(nStep, tplot, totalE);
+   graph3->SetName("gr3");
+   graph3->SetMarkerColor(3);
+   graph3->Draw("*");
+
+//*Provide title and axis labels
+
+   graph->SetTitle("Energies for Orbiting Comet");
+   graph->GetXaxis()->SetTitle("Time(yr)");
+   graph->GetXaxis()->CenterTitle();
+   graph->GetYaxis()->SetTitle("Energy (M*AU^2/yr^2");
+   graph->GetYaxis()->CenterTitle();
+
+   // draw the legend
+   TLegend *legend=new TLegend(0.6,0.65,0.88,0.85);
+   legend->SetTextFont(72);
+   legend->SetTextSize(0.04);
+   legend->AddEntry(gr1,"Kinetic","P");
+   legend->AddEntry(gr2,"Potential","P");
+   legend->AddEntry(gr3,"Total","P");
+   legend->Draw();
+
+//switch to second half of canvas
+   MyC->cd(2);
+   
+//  convert polar coordinates to cartesian 
+   double *xplot, *yplot;
+   xplot = new double[nStep]; yplot = new double[nStep];
+   for( iStep=0; iStep < nStep; iStep++ ) {  
+	xplot[iStep] = rplot[iStep]*cos(thplot[iStep]);
+	yplot[iStep] = rplot[iStep]*sin(thplot[iStep]);
+
+   }
+//plot trajectory of comet in cartesian coordinates, with Sun at origin
+  TGraph *graph4 = new TGraph(nStep, xplot, yplot);
+  graph4->SetName("gr4");
+  graph4->Draw("A*");
+
+
+//*Provide title and axis labels
+
+   graph4->SetTitle("Trajectory of Comet");
+   graph4->GetXaxis()->SetTitle("x-axis(AU)");
+   graph4->GetXaxis()->CenterTitle();
+   graph4->GetYaxis()->SetTitle("y-axis(AU)");
+   graph4->GetYaxis()->CenterTitle();
+
+ 
+}