Suppose that you were writing a science-fiction novel (or movie script).

In the story, a giant magnetic-levitation (mag-lev) train encircles the entire planet earth.

The ring-shaped train track is located in low-earth orbit.

Although earth is not a perfect sphere, this ring-shaped train track is close to perfectly circular.

The train track is 13,400 kilometers in diameter.

The track is located roughly 329 kilometers above earth sea-level, but that varies a little-bit depending where on the train-track you are.

The train-track exists in the vacuum of space and there is no air-resistance.

If you painted a smiley face on the train-track, that smiley face would go around planet earth once every 1 hour 31 minutes and 6.6 seconds. That is, even if a train-car is stationary relative to the train-track, the train-track itself is spinning around planet earth.

Suppose that the train orbits above earth's equator. Maybe that is not the best location, but it is going to make it easier to talk about how fast the train is traveling.

When we measure the speed of the train, we are measuring it relative to the prime meridian (zero-degrees longitude). The speed of the train is not measured relative to the train track. Recall that the circle-shaped train track is 13,400 km in diameter. Thus, a passenger-car is traveling at 100 kilometers per hour if the passenger-car departs zero-degrees longitude, circles all of the way around the earth, and returns to zero-degrees longitude, after 134 hours.

Okay.... that was more context than I expected.  

The follow are my actual ***questions***:

* How fast would a train-car have to travel (relative to the surface of planet earth) in-order for the centripetal force to feel to train passengers as if the passengers were walking on earth? Assume that the train track prevents the train-car from going into a higher orbit.
* Suppose that a passenger car is initially traveling 7.71 km/sec relative to the surface of planet earth. The passenger car is motion-less relative to the train-track. The train-car is initially accelerating at 1-g relative to earth's surface. Suppose that the train is engineered to ensure that the combination of centripetal force and train acceleration is always feels like 1 earth gravity to human passengers. Maybe the train car can tilt and swivel, so that the "ceiling" above passenger's heads is only tangent to earth's surface when the train is traveling at max-speed. How much time would pass untill 99% or more of the fake-gravity experienced by passengers on the train is due to centripetal force, and not the train accelerating along the track?
* Suppose that the train-car is traveling so fast along a ring in orbit around planet earth that the centripetal-force experienced aboard the passenger car feels like 1 earth gravity (or maybe 2 earth gravities total? 1g is needed to combat earth, and 1g for fake gravity aboard the train?)... anyway, how would time compare on the train to time on planet earth? 1 minute on the train equal 1.2 minutes on earth? Are we traveling at relativistic speeds at that point? Basically, there is 1-g of acceleration pulling the train into higher orbit, but the train is not allowed to move to a higher orbit, due to the train-track.