Sidereal clock
Turn the middle pair of discs until your longitude faces today's date on the calendar ring; then point the index at a civil hour and read the local sidereal time facing it. The zone offset registers the civil ring (pre-filled from your browser, daylight time included).
The sidereal ring is drawn in phase with the calendar: every date points, towards the centre, at the sidereal time of its own midnight.
With the calendar and the sidereal ring both running clockwise, the geometry forces East on the left of the longitude ring.
Reading tolerance: about ±2 minutes at the far end of the day (the solar/sidereal rate difference is absorbed at the alignment instant).