In the absence of any communication satellite in 1958, back in Mercury times, how did the tracking centers, which were spread world across, communicated with each other, passed on their data to the next tracking station, and thus kept a track of the spacecraft?
NASA report SP-6, chapter 2 describes the tracking network in detail. It provides this overview schematic explaining how the various stations communicated with each other:
(source: NASA SP-6, chapter 2, figure 2-8)
Communications were via the following channels:
- Submarine cable
- Land line
The submarine lines and land lines were direct-line links, used exclusively by NASA. It was a mix of leased existing lines and newly installed lines.
The NASA report "Historics of the Space Tracking And Data Acquisition Network (STADAN), the Manned Space Flight Network (MSFN), and the NASA Communications Network (NASCOM)", available here as PDF download (100MB), provides a ton of background information.