Short Tower model.
This tower is made up of 7 satellites chained together by 10,000 km cables, and is some 76,000 km in radius. This is insufficient for centrifugal forces to overcome gravitational forces. The base is in compression, and the tower collapses to Earth.
In this model, as each body falls, the tower is "reeled in", and remains connected to the planet tether point.
In the next applet, the height of the tower is increased to 150,000 km, so that there are more satellites pulling outwards on the tower.