I hadn't realised that the Argos satellite network existed and animal trackers communicated with it.
Does anyone know how much it costs and what level of power is required to communicate with GPS satellites?
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The closest thing to what you appear to be looking for is probably the Iridium satellite network. This system is used by tracking/data logging products that need to work pretty much everywhere (including the middle of the ocean where there is no cell coverage).
Examples of systems using Iridium include things like the Rock7 RockBLOCK. The link provides details of power/cost requirements
your host needs to supply a minimum of 100mA @ 5V.
Line rental costs £10.00 per month
Credits are used each time you transmit. 1 credit is used per 50 bytes (or part thereof) of message sent or received.
Your question is based in a fundamentally erroneous premise.
Uplink communication to GPS satellites is not permitted, period. For public users and indeed most government ones, the system is downlink-only. It is intended to allow receivers to figure out where they are, but has no capability for sharing that information with others. For that, other means of communication are required.
The only people who are actually supposed to be transmitting uplink data to the satellites are the staff of the GPS Operation Center of the US Air Force, who manage them, and perhaps any authorized manufacturer or contractor personnel supporting that mission. The uplinked information would be satellite control commands, along with a catalog of data to be broadcast, which includes updates to base information receivers require to calculate a position fix, and also correlation-search hinting data on how all of the satellites are moving across the sky.
Note that the GPS system mentioned in your link for tracking songbirds is actually a recording system, not a realtime tracking one
Marra and Hallworth tagged ovenbirds from both Maryland and New Hampshire in June 2013 and recaptured them in April and May 2014 to download the GPS data.
They had to actually retrieve the recorders to find out where they had been.