c = {k0 -> 
          1.01867507, k1 -> 0.63802799 , sig0 -> 0.25007323, 
        sig1 -> 0.27052757, z -> 3.0}
ekin = 2.25*k0/P^2 + 9.0*k1/Q^2;
p = R + X;
vne = -3.0*z/P - (12.0 - (X/Q)^2 - 3.0*(R/Q)^2)/Q - 
          2.0/p;
vee = 
        3.0*sig0/P + 3.0*sig1/Q + 
          2.0*(3.0 - (R/Q)^2 - 0.6*(P/Q)^2)/
              Q;
vnn = z/p;
vir = -(vne + vnn + vee)/ekin  /.  
          c;
etot = ekin + vne + vnn + 
          vee /. c

N[t = FindMinimum[etot, {P, 0.6}, {Q, 3.0}, {R, 1.5}, {X, 1.5}], 
      20]
u = t[[2]];
plot1 = 
      Graphics[{Circle[{-R, 0}, P], Circle[{0, 0}, Q], 
            Disk[{-R, 0}, 0.08], Disk[{0, 0}, 0.03], 
            Disk[{X, 0}, 0.08],  Line[{{-R, 0}, {X, 0}}]}]  /.  
        u
Show[
      plot1, {AspectRatio -> 
          Automatic}]

Clear[vee, vir, etot, P, 
      Q, R, X, u]
vee = 
        3.0*sig0/P + 3.0*sig1/Q + 
          2.0*(3.0 - (R/Q)^2 - 0.6*(P/Q)^2)/Q - 
          12/(5*Q)*(P/Q)^2;
vir = -(vne + vnn + vee)/ekin  /.  
          c;
etot = ekin + vne + vnn + 
          vee /. c

N[t = FindMinimum[etot, {P, 0.6}, {Q, 3.0}, {R, 1.5}, {X, 1.5}], 
      20]
u = t[[2]];
plot1 = 
      Graphics[{Circle[{-R, 0}, P], Circle[{0, 0}, Q], 
            Disk[{-R, 0}, 0.08], Disk[{0, 0}, 0.03], 
            Disk[{X, 0}, 0.08],  Line[{{-R, 0}, {X, 0}}]}]  /.  
        u
Show[
      plot1, {AspectRatio -> Automatic}]

c1 = {k0 -> 1.01527946, 
        k1 ->  0.66361539, sig0 ->  0.24930702, sig1 ->  0.30149037, 
        z -> 3.0}
etot = ekin + vne + vnn + vee  /.  c1;
vir = -(vne + vnn + vee)/ekin  /.  
          c1;

N[t = FindMinimum[etot, {P, 0.6}, {Q, 3.0}, {R, 1.5}, {X, 1.5}], 
      20]
u = t[[2]];
N[(R + X)*0.529177  /.  u, 10]
N[vir  /.  u , 10]
N[-t[[1]] - 
plot1 = 
        Graphics[{Circle[{-R, 0}, P], Circle[{0, 0}, Q], 
              Disk[{-R, 0}, 0.08], Disk[{0, 0}, 0.03], 
              Disk[{X, 0}, 0.08],  
              Line[{{-R, 0}, {X, 
                    0}}]}]  /.  u
Show[
              plot1, {AspectRatio -> 
                  Automatic}]