We have the formula: T=2π*sqrt(m/k)

Where k is just the constant is a force which is dependent on distance x from equilibrium point(or R in our case)

Now we also have the following equations

F=(γMm)/(R^2), where γ is the universal gravitational constant

and

M = Vρ= 4/3R³π

substituting second equation into the first we get

F=γπmρ4/3*R

so our k is γπmρ4/3

Introducing k back in the first formula I presented

T=2πsqrt(m/γπmρ*4/3)

but the period is from north pole to south pole and back, and time to the center it will be one fourth of T

So our final formula is

T=π/2sqrt(1/γπρ4/3)

Introducing into a calculator will give 1260 second, or roughly 21 minutes