The Geostatonorrery would be an exhibit in a planetarium or science museum.
In the centre of a large, darkened space is suspended a scale model of your puny little planet, correctly tilted to the plane of the ecliptic.
A spotlight fixed on one wall represents your system's sun.
fine black threads are tiny, shiny metallic objects, each of which is a scale model of a geostationary satellite. These are attached to a ring high above, which rotates in synchrony with the model planet. The strings are manipulated by stepper motors to correctly simulate the azumuthal movement of the satellites.
Other rings are placed within the geostationary ring to allow other objects like the ISS etc. to be "flown" into the environment.
Your moon is not shown per se, but an appropriately scale-adjusted mirror mounted on a robotic stalk tracks round so as to reproduce the moon's illumination.
If the model is completely accurate, more informed visitors may be puzzled as to why there appears to be a large cubic structure lurking in the shadow of one of your communications platforms ...