During a physics lecture, the professor demonstrated how to find the period of an object that was dropped through a hole drilled straight from one end of our planet to the other. He finished by saying "an object orbiting the earth near the surface will have a period of the same length as that of the transport tunnel". He backed this up with a=omega^2 * R => 9.81=omega^2 * 6.38(10)^6 => omega=0.00124 s^-1 => T=2pi/omega=84 mins (the period through the transport tunnel). I'm trying to figure this out intuitively, any suggestions on the practical logic behind this interesting concept? Thanks for reading this!