A bunch of websites have live tracking of satellites, e.g. this one. Where are they getting the satellite ephemerides data for all of the iridium satellites?
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$\begingroup$ see also this answer to How to find the numerical positions of objects in the sky $\endgroup$– uhohCommented Jun 2, 2023 at 21:49
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The ultimate source for almost all freely available orbit data is the U.S. Space Force's https://www.space-track.org/ . It requires registration to create a user account, but is free to use. Services like the one you linked are mainly just repackaging that data into alternate formats, and adding images or different search methods. To minimize the size of the transmission, the original US Government data is distributed not as ephemerides but rather as very short text files (138 characters) called Two-Line Elements (TLE), from which ephemerides can be computed.
Many questions on this site have asked about how to do things with TLEs by hand, but that is a terrible idea. What you need to do instead is go back to space-track.org, download SGP4, and use it to compute ephemerides, and make whatever other calculations you want done to your TLEs. TLEs have lots of drawbacks, but they are free and cover almost everything, so we put up with the problems as best we can.
There is better data out there, in rawer formats, but it is not provided for free to anyone who asks! Operators like Iridium, Inmarsat, and so on make measurements of their own satellites in order to operate them safely, but I don't know of any operator who makes that data available to anyone else. There are a few commercial "space situational awareness" businesses which sell observations from their radars and telescopes, but they are not cheap.
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2$\begingroup$ Might not the websites of which the OP speaks be getting them from Celstrak as well, which in addition to being free doesn't require a token (or password)? $\endgroup$– uhohCommented Jun 2, 2023 at 21:47
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1$\begingroup$ @uhoh yes, but Celestrak, like n2yo and the others, is getting their TLEs from space-track, so it's just a question of the number of hops. The immediate source may be any of them, but the ultimate source — the source's source, or the source's source's source's source — is the U.S. Space Force. $\endgroup$– Ryan CCommented Jun 3, 2023 at 0:38
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2$\begingroup$ This is important enough to note that you might include it in your answer. Unlike Celestrak, Space-Track says: The User agrees not to transfer any data or technical information received from this website, or other U.S. Government source, including the analysis of data, to any other entity without prior express approval. See, 10 USC 2274(c)(2). So for someone reading your answer making a new website, it might be helpful to remind them that they can get them from Celestrak freely, or if they want to use Space-track a PW & written autho.. $\endgroup$– uhohCommented Jun 3, 2023 at 2:13
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$\begingroup$ Also relevant: How (the heck) are military satellites with (apparently) classified TLEs still showing up on sat map websites? $\endgroup$– uhohCommented Jun 3, 2023 at 2:15
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$\begingroup$ Celestrak should be the place to go by default. Only go to Spacetrack when you need to, and the terms of service is acceptable. The whole point of Spacetrack was to limit access to the data after the 9/11 attacks. Showing that people use the alternative sources more than the restricted one will be the primary evidence that the law needs to change. $\endgroup$ Commented Jun 3, 2023 at 14:42