Can someone explain why my graph is not generating any lines. I copied my code from this video https://ww​w.youtube.​com/watch?​v=vaMiCkrR​C6Q

clear
clf 
%All Constants Used
G = 6.67408e-11;
M = 5.9722e24;
m = 1000;
%Changing Variables
r = [6.67e6, 0 , 0]; %Radius
v = [0, sqrt(G*M/norm(r(1,:),2)),0 ]; %Hohmann Equation
t = 0.0; %Start time
dt = 1; %Steps/Change in Calculation
DeltaV = 2420; %Change in Velocity
TtoDeltaV = 5431; 
%First Orbit
rplot = r; 
while t <= TtoDeltaV
    rlen = norm(r,2); %Radius Magnitude
    accel = -G*M/rlen^2;
    nextv = v + accel*dt*r/rlen;
    nextr = r + dt*v;
    t = t + dt;
    rplot = [rplot, nextr];
    v = nextv; 
    r = nextr;
    
end
hold on;
Orbit1 = plot(rplot(:,1), rplot(:,2),'b','LineWidth',1);
%Second Orbit
rplot = r;
theta = 0;
rp = r;
rplen = norm(rp,2);
nextv = v + DeltaV*[0 1 0];
v = nextv;
while  theta <= 3.14159 %Position Vector
    rlen = norm(r,2);
    accel = -G*M/rlen^2;
    nextv = v + dt*accel*r/rlen;
    nextr = r + dt*v;
    t = t + dt;
    rplot = [rplot, nextr];
    v = nextv;
    r = nextr;
    tempDot = dot(rp,r); %Dot product
    costheta = tempDot/(rlen*rplen);
    theta = acos(costheta);
    
end
disp("Sat reaches forbits at t = " + t + "s")

Sat reaches forbits at t = 24323s

Orbit2 = plot(rplot(:,1), rplot(:,2),'r','LineWidth',1);
%Orbit 3
rplot = r; 
tstart = t; %Start or Orbit
OrbitP = (2*pi)*sqrt(norm(r,2).^3)/(G*M);
OrbitV = sqrt((G*M)/norm(r,2));
DeltaV = OrbitV - norm(v,2);
nextv = v + DeltaV*[0 -1 0]; %-1 to add the direction of going down
v = nextv;
while t < (tstart +OrbitP);
    rlen = norm(r,2);
    accel = -G*M/rlen^2;
    nextv = v + dt*accel*r/rlen;
    nextr = r + dt*v;
    t = t + dt;
    rplot = [rplot, nextr];
    v = nextv;
    r = nextr;
end
Orbit3 = plot(rplot(:,1),rplot(:,2),'k','LineWidth',1);
title('Hohmanns Transfer Orbit');

Answer 1

[Walter Roberson]

clear
clf 
%All Constants Used
G = 6.67408e-11;
M = 5.9722e24;
m = 1000;
%Changing Variables
r = [6.67e6, 0 , 0]; %Radius
v = [0, sqrt(G*M/norm(r(1,:),2)),0 ]; %Hohmann Equation
t = 0.0; %Start time
dt = 1; %Steps/Change in Calculation
DeltaV = 2420; %Change in Velocity
TtoDeltaV = 5431; 
%First Orbit
rplot = r; 
while t <= TtoDeltaV
    rlen = norm(r,2); %Radius Magnitude
    accel = -G*M/rlen^2;
    nextv = v + accel*dt*r/rlen;
    nextr = r + dt*v;
    t = t + dt;
    rplot = [rplot, nextr];
    v = nextv; 
    r = nextr;
    
end
hold on;
Orbit1 = plot(rplot(:,1), rplot(:,2),'b','LineWidth',1);
%Second Orbit
rplot = r;
theta = 0;
rp = r;
rplen = norm(rp,2);
nextv = v + DeltaV*[0 1 0];
v = nextv;
while  theta <= 3.14159 %Position Vector
    rlen = norm(r,2);
    accel = -G*M/rlen^2;
    nextv = v + dt*accel*r/rlen;
    nextr = r + dt*v;
    t = t + dt;
    rplot = [rplot, nextr];
    v = nextv;
    r = nextr;
    tempDot = dot(rp,r); %Dot product
    costheta = tempDot/(rlen*rplen);
    theta = acos(costheta);
    
end
disp("Sat reaches forbits at t = " + t + "s")

Sat reaches forbits at t = 24323s

Orbit2 = plot(rplot(:,1), rplot(:,2),'r','LineWidth',1);
%Orbit 3
rplot = r; 
tstart = t; %Start or Orbit
OrbitP = (2*pi)*sqrt(norm(r,2).^3)/(G*M);
OrbitV = sqrt((G*M)/norm(r,2));
DeltaV = OrbitV - norm(v,2);
nextv = v + DeltaV*[0 -1 0]; %-1 to add the direction of going down
v = nextv;

t

t = 24323

tstart

tstart = 24323

OrbitP

OrbitP = 0.0045

dt

dt = 1

OrbitP is less than dt. When you add t = t + dt then the result is going to be more than tstart + OrbitP

while t < (tstart +OrbitP);
    rlen = norm(r,2);
    accel = -G*M/rlen^2;
    nextv = v + dt*accel*r/rlen;
    nextr = r + dt*v;
    t = t + dt;
    rplot = [rplot, nextr];
    v = nextv;
    r = nextr;
end

so you are only going to have one point to plot.

You also have the problem that v is a 1 x 3 vector, so nextr will be a 1 x 3 vector, so your [rplot, nextr] is horzontal concatenating together 1 x 3 vectors each time -- but you expect to extract columns out of the result.

Orbit3 = plot(rplot(:,1),rplot(:,2),'k','LineWidth',1);
title('Hohmanns Transfer Orbit');