Galileo's experiment and equivalence principle

[AlonsoMcLaren]

Why do we say that Galileo's experiment at Pisa is an illustration of Equivalence Principle?

All we know is that

G* (mass of earth)*(gravitational mass of object)/(R^2) = (intertial mass of object)*a

Therefore,
a=G* (mass of earth)*(gravitational mass of object)/(R^2 * (inertial mass of object))

The experiment shows that a does not change for different objects.
But this only guarantees that (gravitational mass of object)/(inertial mass of object)= a constant, which is not necessarily 1.

 

[Nugatory]

But this only guarantees that (gravitational mass of object)/(inertial mass of object)= a constant, which is not necessarily 1.

We choose the value of G so that that constant is equal to 1. We don't have to - it just makes the math simpler. We could, if we wanted, say that that constant was equal to 2, and use a value of G which was greater by a factor of four to make the calculation match the force that we measure experimentally ... but why bother?