Your equations are inconsistent
M1 = 1.87465;
R1 = 2.219975;
M2 = 0.32065;
R2 = 0.25694;
eq11 = (4 M1^4/R1^4 - v^2/R1 +
2 w^2/R1^2) (M1^2 - 1)^3 + (2 w^2/R1^2)*((2 M1^2) - 1)*(1 -
R1^4)*(M1^2 - 1);
eq12 = (4 M2^4/R2^4 - v^2/R1 +
2 w^2/R2^2) (M2^2 - 1)^3 + (2 w^2/R2^2)*((2 M2^2) - 1)*(1 -
R2^4)*(M2^2 - 1);
eq21 = (4 M1^2/R1^4 -
2*(s^2)*(g - 1)/(M1^(2*g)))*(M1^2 - 1)^3 - (4 w^2/R1^2)*
M1^2*(1 - R1^2)^2 ;
eq22 = (4 M2^2/R2^4 -
2*(s^2)*(g - 1)/(M2^(2*g)))*(M2^2 - 1)^3 - (4 w^2/R2^2)*
M2^2*(1 - R2^2)^2 ;
In[25]:= Reduce[
Rationalize [Thread[{eq11, eq22, eq12, eq21} == 0], 16], {g, v, w,
s}, Reals]
Out[25]= False