Any Time for Pebble
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Any Time uses a configuration program that requires internet access in order to change the second time zone. The background of each time zone switches to white at 0600 and switches to black at 1800 in order to indicate day vs night.

If you’re traveling and are going to be without a connection, remember to make your selections ahead of time. Any Time will remember all those selections, even if you don’t have a bluetooth connection to the phone. When comparing my watch face to the other multi-time zone watch faces on the App store, it’s a good idea to experiment with how it behaves when bluetooth is turned off. I took special care to make sure Any Time won’t lose its settings.

If you travel to a different time zone, or daylight savings time changes locally, it may take a few minutes for your phone to inform your Pebble of the new time. The latest version of AnyTime will recognize the time shift and attempt to determine your new location. If you don’t have an internet connection on your phone when this occurs, it could skew the other time zone. To correct, get your phone onto the internet, then restart Any Time so that it will relocate itself. You only have to do this once per time zone change or daylight savings change happening either locally or in the other time zone.

Local Sidereal Time is essentially the right ascension at the meridian. It requires an accurate longitude reading. The Pebble Watch is actually doing the calculation! My values match the Navy’s sidereal time website. Other sidereal websites are off by a few minutes. If you’re setting up a telescope, make sure that you can get internet access at your viewing location, or not worry if it’s a few degrees off.