Actually there things called TLEs which are available for satellites to track them easily, GPS sats are in very stable orbits and are maintained in them so the system will stay accurate.
Here is the TLE for a GPS satellite it includes all of the information needed to track the satellite as long as you know the exact date and time
GPS BIIA-10 (PRN 32)
1 20959U 90103A 13104.01737920 -.00000014 00000-0 00000+0 0 9362
2 20959 54.4045 226.4577 0116480 337.4908 315.2123 2.00558664163919

here is a very nice QT sat tracking app for the old Zaurus
http://www.qsl.net/n1vtn/petittrack.html
which you could grab source(or even pre-alpha compile for maemo?) and strip out what you need.
The TLEs of the GPS sats are available here
http://www.celestrak.com/NORAD/elements/
http://www.celestrak.com/NORAD/elements/gps-ops.txt

As long as you are playing with the GPS a cool add-on would be setting the phone clock from GPS satellite time.

I currently use gpredict with chroot Debian to track amateur radio communication sats and use a handheld yaggi antenna and an older five watt UHF/VHF dual band radio to chat other ground stations via satellites and sometimes, when there is a amateur licensed astronaut, the space station even non hams can monitor the ISS especially when they are transmitting slow scan TV or doing a school interview.