This article lays em all out.
The Hebrew Calendar, Is It Reliable?
http://www.cogeternal.org/text/HEBCAL.htm
More opinions at...
http://www.karaite-korner.org/
This site will aid in the 'Signs in the Heavens' department, and it's fun city!
Welcome to Your Sky, the interactive planetarium of the Web. You can produce maps in the forms described below for any time and date, viewpoint, and observing location. If you enter the orbital elements of an asteroid or comet, Your Sky will compute its current position and plot it on the map. Each map is accompanied by an ephemeris for the Sun, Moon, planets, and any tracked asteroid or comet. A control panel permits customisation of which objects are plotted, limiting magnitudes, colour scheme, image size, and other parameters; each control is linked to its description in the help file
http://www.fourmilab.ch/yoursky/
The view is always from Jerusalem!