Apollo program diagnostics

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How did the Apollo Program support technicians run diagnostics on a vehicle in space without modern computer technology and internet?

I know very little about this stuff so bare with me, but for instance Apollo 13, how could the ground crew spot faulty N2 and O2 tanks? How was the data transferred?

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They weren’t “running diagnostics” in the sense that they were running software programs like you might run on your computer. The computers of that era were far too rudimentary to be able to do anything like that. What they were doing was looking at telemetry and coupling that with their understanding of the spacecraft systems.

Every system of every spacecraft (then and now) is full of sensors that measure things like temperature, pressure, voltage, current, the status of every electrical circuit, guidance system readouts, and other physically measurable things. All of this data was monitored in real time and transmitted back to mission control via the spacecraft’s radio antennas. (The same antennas that they used to communicate by voice also transmitted this data as well as TV broadcasts, just on slightly different frequencies. Giant radio dishes on Earth picked up these radio waves.) f you look at a picture of mission control from that era, you can see each controller station has a video monitor, which displayed this data in text format.

So for example, the mission controller responsible for the spacecraft’s life support system would have a video display showing things like the pressure in the oxygen tanks, cabin pressure, carbon dioxide levels, the status of the various cabin pumps and fans…etc. The mission controllers knew what those numbers should be at any given time, and knew how the spacecraft system works so that if the numbers were off, they could figure out why.

So take Apollo 13. At the moment of the explosion, 1 of the oxygen tanks ruptured, and the other one got punctured. The sensors on those tanks detected that one had 0 pressure and the other was losing pressure. This data got sent back to mission control in real time, and the mission controller could see that one O2 tank was gone and another was losing pressure, so they knew there had to be a seriously catastrophic leak *somewhere* in the O2 system, and with some more data and commanding the astronauts to do certain things, they were able to figure out where the leak happened, although they didn’t know the full extent until the astronauts were able to see service module after it was separated.

So there was no message that told them exactly what had happened and no software program that they could run, they had to use their knowledge and the telemetry from the sensors (as well as communicating with the astronauts themselves) to figure it out.