Drawing a rotating circle on a sphere

I am trying to rotate a sphere like the eye on MATLAB and would like to simulate the pupil on the sphere that moves with the rotations as well.

[X,Y,Z] = sphere;

s1 = surf(X,Y,Z, 'FaceColor', [1 1 1], 'EdgeColor', 'none');
set(gca,'Color','k')

xdir = [1 0 0];
ydir = [0 1 0];
zdir = [0 0 1];
rotate(s1,zdir,10);
rotate(s1,ydir,10);
rotate(s1,xdir,10);

I have written a code for a sphere that rotates but I cannot figure out how to get the pupil plotted on the sphere centre so that the final figure after rotation looks somewhat like this -

Answer 1

[Fabio Freschi]

The code should be self-explicative

[X,Y,Z] = sphere;

% figure 
figure, hold on
axis equal, view([1 1 1]);

% sphere with transparence
s1 = surf(X,Y,Z, 'FaceColor', [1 1 1], 'EdgeColor', 'none','FaceAlpha',0.5);
light

% I don't like black background
% set(gca,'Color','k')

% radius of the eye (to be more general)
R = max(sqrt(X(:).^2+Y(:).^2+Z(:).^2));

% radius of the pupil
r = 0.6;

% distance from the center
h = sqrt(R^2-r^2);

% create disc
n = 30;
a = linspace(0,2*pi,n);

s2 = fill3(h*ones(n,1),r*cos(a(:)),r*sin(a(:)),'b');

% rotation
xdir = [1 0 0];
ydir = [0 1 0];
zdir = [0 0 1];
rotate(s1,zdir,10);
rotate(s1,ydir,10);
rotate(s1,xdir,10);

% rotation of pupil
rotate(s2,zdir,10);
rotate(s2,ydir,10);
rotate(s2,xdir,10);

[Julian Blackthorne]

@Fabio Freschi Yes, it is! Thank you so much for your help.