Want to see something really neat and amazing? First off, you should have Google Earth loaded on your PC. Go to the listed URL below, and half way down the page you'll see a reference to the AGI Satellite database. Click on it and download it, to your Desktop or where you can locate it. Now either double click it or open it from within Google Earth and be amazed.
It's over 13,000 satellites that are being tracked in real time. You'll see the orbits and positions change as time moves on. You can hover over a satellite icon and left click to see more info on it. You can spin around the globe and see satellites over other countries. As you zoom out from earth, you'll see smaller points of light, those are the Geo-Sync sats, etc. I find it amazing and hope you do too !
There are a number of good satellite tracking programs available for almost any software platform. I used to use a couple of different one even back in the DOS days before windows. You can do a Google search for terms like "satellite tracking programs". You'll also want to find reasonably current "Keplerian Elements" or TLE (two line elements) for whatever satellites you are interested in. Often you'll download TLE files that contain thousands or ever tens of thousands of orbiting items, everything from space junk to the International space station.
Ham radio operators who use satellites often use tracking programs so that they can know when a satellite will be "visible" to a particular location and to get aiming information for pointing directional antennas. But even with non directional antennas you can reach some satellites or even the International Space Station if you know when to listen and what frequencies to use. I know several hams that have had contact with the ISS, one with just a radio mounted in his car and antenna sticking up on the hood.
Tracking programs are also helpful if you want to reach someone else on the earth through a satellite link. The program can easily show you when the satellite will be in line of sight communication range of each location, and of course you want to try to make contact when you both can contact the satellite.
There is an amateur radio group that has a lot more information on this called AMSAT, their website is AMSAT.ORG.
Of course, almost any good TLE set will contain Keplerian Elements for all of the GPS and similar satellites.
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