So Will earned 12 Arx on the livestream, 9 for 'Exploration' and 3 for 'Other'. Considering that Will spent a around 34 minutes in the pilot's seat (they re-log around the 9 minute mark, and log out around the 43 minute mark), we can assume that the Arx earned per hour for being somewhat active (there are periods where Will is talking to the camera rather than actually doing anything) will probably be around 20 Arx/hour, meaning 20 hours per week to reach the 400 Arx cap. Note that it will probably be possible to earn more Arx than this by actually playing the game without stopping to talk to the camera.
As for what the minimum Arx/hour would be for sitting AFK, if we assume that the 'Other' category is based entirely on time spent in game, we get a total of 5-6 Arx per hour for just being in the game. This means that the upper limit for the amount of time needed to reach the weekly 400 Arx cap would be around 70-80 hours, or about 10-12 hours every day sitting AFK. Again, it is important to note that it will be possible to improve your Arx per hour by actually playing the game.
On a side note, Will spent about 8 minutes of the livestream either sitting on the landing pad doing nothing or sitting in space not moving. With the entire time spent in the sidewinder coming to just under 34 minutes, we can assume that the amount of Arx earned on the livestream is only ~80% of what players would normally earn in the same period of time. If we take the new value (15 Arx for 34 minutes), the amount of Arx per hour increases to over 25 Arx per hour, meaning that the weekly Arx cap of 400 could be reached in 16 hours.
Will's account (it was Adam flying) undocked, flew around a bit, used SC to go 240 ls, killed five megaship targets and three drone targets, scanned two things, made one hyperjump of 7 ly flew another 338 ls and docked.
For that, CMNDR WIlliam earned 9 Arx for exploring and 3 Arx for "other".
If there is an "Exploring" category, I think it is safe to say that there is also "Combat" and "Trading" categories, neither of which Adam earned. He did do combat, but only on sitting ducks, so it might be reasonable to not throw Arx at him for that. He did spend proper time flying and scanning though.
So it seems to me that two scans, seven lightyears, and 578 lightseconds adds up to 9 Arx. We don't know how it adds up of course. It probably isn't one Arx per lightyear and one per scan, much as that might be nice. It seems likely that exploring awards Arx for jumping and that a single seven lightyear jump earns at least one Arx. Whether that is for each jump or per lightyear, that is eminently earnable. I am going to be getting lots of Arx flying 500ly in 30 jumps to a void opal hotspot. If the per jump Arx is very low, then the per scan Arx will be very high. Assuming FSS earns the same as the data link scanner, then I can earn maybe four Arx per system when exploring. Only 100 systems per week to max out Arx.
As for the "other" category, I can't see how that is earned. It could be one per dock/undock and one per half-hour, but with 168 hours in a week, that would be 336 Arx for just sitting in the game. That seems rather high. Or you could just grind dock and undock. So I doubt that is how it works. Even one per minute in SC would seem to pay out far too much going to Hutton Orbital, but it's over four trips per week to get the cap, six hours and forty minutes in SC, so that might be reasonable.
