With the new value of

*mu*, it seems that

*fsolve* failed to solve the system and, so, returns unevaluated.

restart: with(plots):
alpha:=Pi/3:
mu:=3.006*10^(-6):
rs:=((x+mu)^2+y^2)^0.5:
re:=((x+mu-1)^2+y^2)^0.5:
Q:=beta/10*(1-mu)*(cos(alpha))^2:
S:=(x+mu)*cos(alpha)+y*sin(alpha):
T:=-(x+mu)*sin(alpha)+y*cos(alpha):
eq1:=(1-mu)*(x+mu)/rs^3+mu*(x-mu+1)/re^3-x=Q*S/rs^3:
eq2:=(1-mu)*y/rs^3+mu*y/re^3-y=Q*T/rs^3:
plist:=[]:
for beta from 0 to 10 do
fsolve({eq1,eq2}, {x,y});
xx:=eval(x,%);
yy:=eval(y,%%);
plist:=[op(plist),[xx,yy,beta/10]];
end do:
Error, invalid input: eval received
fsolve({.9999969940*y/((x+0.3006000000e-5)^2+y^2)^1.5
+0.3006000000e-5*y/((x-.9999969940)^2+y^2)^1.5-y = 0.,
.9999969940*(x+0.3006000000e-5)/((x+0.3006000000e-5)^2+y^2)^1.5
+0.3006000000e-5*(x+.9999969940)/((x-.9999969940)^2+y^2)^1.5-x
= 0.}, {x, y}), which is not valid for its 2nd argument, eqns
kernelopts(version);
Maple 12.02, APPLE UNIVERSAL OSX, Dec 10 2008 Build ID 377066

Regards,
--Jean-Marc