Here is the corrected code (Note that the Initial Conditions were missing and some arbitrary values are taken. Therefore they need to be changed. Also, note that in figure 1 three solution sets overlap each other. Hence, they are plotted in separate) :
t0 = 0;
nrevs = 100;
Period = 2;
tmax = nrevs*Period;
mu = 2.5;
h0 = 0; %
r0 = 1; % use the given value
V0 = 0.5; % use the given value
x0 = [r0; h0; V0];
f = @(t,x) ([x(3); x(2).*x(3).^2./x(1)-mu./x(1).^2; -x(2).*x(3)./x(1)]);
settings1=odeset('RelTol',1e-4,'AbsTol',1e-4);
settings2=odeset('RelTol',1e-8,'AbsTol',1e-8);
settings3=odeset('RelTol',1e-11,'AbsTol',1e-11);
[T1,y1]=ode45(f,[0 tmax],x0,settings1);
[T2,y2]=ode45(f,[0 tmax],x0,settings2);
[T3,y3]=ode45(f,[0 tmax],x0,settings3);
% Plot the trajectories for each tolerance
figure;
plot(y1(:,1).*cos(y1(:,2)), y1(:,1).*sin(y1(:,2)), 'r-', ...
y2(:,1).*cos(y2(:,2)), y2(:,1).*sin(y2(:,2)), 'b--', ...
y3(:,1).*cos(y3(:,2)), y3(:,1).*sin(y3(:,2)), 'g-.');
legend('tol=1e-4', 'tol=1e-8', 'tol=1e-11');
title('Orbit Trajectories');
axis equal
figure
plot(y1(:,1).*cos(y1(:,2)), y1(:,1).*sin(y1(:,2)), 'r-')
legend('tol=1e-4');
title('Orbit Trajectories');
axis equal
figure;
plot(y2(:,1).*cos(y2(:,2)), y2(:,1).*sin(y2(:,2)), 'b--');
legend('tol=1e-8');
title('Orbit Trajectories');
axis equal
figure;
plot(y3(:,1).*cos(y3(:,2)), y3(:,1).*sin(y3(:,2)), 'g-.');
legend('tol=1e-11');
title('Orbit Trajectories');
axis equal