function beta = Brightness(t)
% When you look at a circle at an angle, it appears as an ellipse.
% Consider the circle on the Earth defined by the terminator. That
% is an ellipse inside a unit circle that defines the full earth.
% The area of that ellipse is pi*1*a where a is the minor semiaxis.
% The minor semiaxis is sin(theta) where theta is the angle between
% vectors SE abd EM.
$ 
E = Earth(t);
M = Mars(t);
u = E; uNorm = norm(u);
v = M-E; vNorm = norm(v);
beta = -(uNorm*vNorm - u'*v)/(2*uNorm*vNorm^3);