How are objects kept free falling in the LISA experiment? I'm watching a video about the LISA experiment, which will be used to detect gravitational waves.
In there, three space stations will be launched and will follow the Earth in its revolution around the Sun.
To measure gravitational waves, the distance between two cubes of gold and platinum must be constantly measured.
To isolate the cubes from other influences (e.g. solar waves which would move them), they are kept in "free fall".
So, they levitate inside the station, and this is possible by rockets around the station which will move the station when the walls become too close to the cubes.
I don't understand how that is possible.
When the cubes are levitated inside the station (how?), there would still be the inertial force, which would have the cube move together with the station.
It's like saying that I am inside an airplane, I jump, and I become in "free fall" with respect to the airplane, so that while I'm on air the airplane moves beneath me and I end up crashing against the tail of the airplane (suppose I'm jumping opposite to the direction of movement).
What am I missing?
 A: 
When the cubes are levitated inside the station (how?)

Remember that the satellites are in orbit about the earth-sun system.  Orbit is a special case of free fall, because the only force acting on an orbiting object is gravity.  If a composite object is in free fall and its parts separate, the different parts can free-fall independently.
Note that minimizing the gravitational and electrostatic interactions between the satellite and the free-falling test masses is a nontrivial problem. The LISA experiment may not have to worry too much about this, since they are searching for oscillatory effects and can isolate motions with a particular frequency.

there would still be the inertial force which would have the cube move together with the station.

This is the idea.  Your options are

*

*the cubes move together with the satellite

*the cubes hit the wall of the chamber inside the satellite where they are housed

*the cubes escape from the satellite out of some window, and are lost into the emptiness of space.

Only one of these is amenable to a long-running experiment.

so that while I'm on air the airplane moves beneath me and I end up crashing against the tail of the airplane

As you have already said, this isn’t how inertia works. Since you mentioned airplanes, you might be amused by this OK Go music video, shot in a “zero-gee” airplane where the airplane itself follows a series of parabolic free-fall arcing paths. While the airplane is following a free-fall trajectory, objects which are not in contact with the inside of the airplane maintain a small relative velocity with its walls, seats, ceilings, etc.
The fundamental idea behind LISA is that gravitational waves from a distant orbiting system will cause the distance between the free-falling test masses to change, with the same frequency as the distant orbit.
