Why do particles in a falling coach get closer together?

[Ashshahril]

Homework Statement

You are launched upward inside a railway coach in a horizontal position with respect to the surface of Earth, as shown in the figure (attached pdf). After the launch, but while the coach is still rising, you release two ball bearings at opposite ends of the train and at rest with respect to the train.

Riding inside the coach, will you observe the distance between the ball bearings to increase or decrease with time?

Relevant Equations

F ∝ 1/R^2

As widely separated particles within a large enclosed space are differently affected by the nonuniform gravitational field of Earth, to use the Newtonian way of speaking, two particles released side by side are both attracted toward the center of Earth, so they move closer together as measured inside a falling long narrow horizontal railway coach. This has nothing to do with "gravitational attraction" between the particles, which is entirely negligible. (Spacetime Physics, Second Edition by Edwin F. Taylor and John Archibald Wheeler; ISBN:0-7167-2327-1)

So, when the coach fall toward Earth, the particles get attracted by the center of Earth. As a result, their distance decreases. But when the coach rise above, due to the Inverse Square Law, the gravitational force gets weaker and weaker. As a result, the particles mustn't change their position. But, in the case of this question, the distance will decrease according to the answer of “Spacetime Physics” book. But I don't understand why. I know that it is so, so that you cannot distinguish rising from falling (inertial reference frame) but how can the distance between the particles decrease in this particular case?

 

[jbriggs444]

But when the coach rise above, due to the Inverse Square Law, the gravitational force gets weaker and weaker. As a result, the particles mustn't change their position.

"Weaker and weaker" is not the same thing as non-existent.