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ds^2 = -dt^2 + a(t)^2 (dX^2 + X^2 dO^2) (O=omega)

And been told to show that radial geodesics obey:

a^2 (dX/dT) = k where k constant and T is proper time.

And hence (dt/dT)^2 = 1 + k/a^2

How do I introduce proper time? And where to I get an expression for dX/dT from? I'm completely stumped...and help would be much appreciated!