What happens to objects falling freely in the earth's gravitational field?

We know objects accelerate, when they are dropped near the earth's surface, at 9.81 m per sec per sec.  But what about objects that are say 1000 km above the surface?  The force is less, we know that it varies inversely with the square of the distance, so the acceleration will be less at altitude.  

So what happens if 3 objects are dropped at the same time from 3 different heights, each one directly above the other.  (lets say the objects are 3 observers, you and 2 friends).  Let's also assume there is no atmosphere to offer any resistance and you happen to be located between your 2 friends at the intermediate height.  If you have a laser measuring tape and measure the distance between you and each of your friends at regular intervals, you will quickly determine that you are moving apart.  More accurate measurements at different points in time will show that you are not just moving apart but will reveal that your friends are actually accelerating away from you.   Objects free moving in a gravitational field accelerate away from each other in the direction of maximum gradient.  We see similar acceleration in the galaxies in our observable universe.  They are not merely moving away from us but acceleration with time under the influence of what we term "Dark Energy".