The program Winstars 2 can be used to check out this prediction of the observation of Orion from Panama:
Here is a simultaneous observation as the sky would appear in Montreal:
At the Geographical Position (GP) of Panama at 5:20 Local Time on March 1st 2008 the foot of Orion will be directly overhead. Move away from this GP and Orion will be lower in the sky: compare for Montreal. Follow the link on the contacts page in order to download the superb Winstars software, which is shareware.
As you move away from the GP at which the star is at the zenith it becomes possible to chart out CIRCLES OF POSITION for which the departure of that star from the zenith is the same size for all points around the circumference of that circle.
The objective of astro navigation is to plot a small section which is related to a circle of position onto a chart in order to obtain a POSITION LINE. The intersection of two or more position lines reveals the GP of the observer. The process is analogous to transferring a bearing from a hand bearing compass onto a chart.
This diagram shows my very first position line observation made in August 2005. The following rules are used to select the chosen position in order to construct a position line when working with printed sight reduction tables:
(i) Latitude a whole number (ii) Longitude such that the local hour angle of the object (the Sun in this case) becomes an integer value and so can be used with the sight reduction tables.
The tables then return the azimuth and intercept values which enable a position line to be constructed. With any luck the true position will not be far off the position line!
The help file which is supplied with Pangolin's excellent Astrocalc application (included with the trial version of the software) provides an in depth analysis of the methodology. There is a link to Pangolin from the contact page on this site.