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I understand that TLEs are used with SGP to predict future positions/velocities of a Earth-orbiting satellite. However, how are these sets obtained in the first place? Is it based on ground observations?

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In short, yes. The U.S. Air Force uses the Space Surveillance Network to track all observable objects in space. They have a system in place which attempts to correlate tracks with existing objects.

If the system encounters tracks which do not match up with an existing object, they create a new object to track. The system then continues to correlate tracks to this new object. After collecting multiple tracks (which could take a few days depending on the geometry of the orbit), the object is assigned a static catalog ID number, and finally released to the public (assuming they designate the object as unclassified).

I simplified the process somewhat, but that's the general idea.

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