I think I stumbled across this a while back but I can't remember where. The classic freshman physics question is, assuming a uniform density for the Earth and a perfect, frictionless tunnel cut through the Earth in a straight line, how long would it take to travel between any two points on the surface of the Earth? The answer is interesting. It's the same no matter how far apart the two points are, 42 minutes.

In "The gravity tunnel in a non-uniform Earth," Am. J. Phys. **83**, 231-237 (2015), there is a new take on this using a non-uniform model for the Earth based on the actual data (the Preliminary Reference Earth Model, aka PREM). That model says the actual travel time is a bit different ranging from 38 to 42 minutes with longer distances taking less time.

The author found that you could actually model the trip as being under constant gravity and get pretty close to the same answer. Because the Earth is more dense in the core, the actual acceleration due to gravity increases slightly during the first part of the trip, up to about 1.09g.