Actually I see my math problem on the drive plume detection. Space hexes are 18,000 meters, not 18,000

*kilometers*. Recalculating! Stand by

Actual space distance is ~1,944,444 space hexes. That'll be significantly longer than 45 mins

Still, it's only mathemetically possible to detect (according to SO rules) at 35 million km, which is not only a fraction of an AU, it's a teeeeny fraction of an entire transit. No way are you tracking dropships prior to their beginning "final approach", even by watching the drives.

That's a max detection (getting 12s) of about 24 hours out at 1g. Hilariously, 23 hours and 59 minutes would cover 1,946,000 space hexes. but we can round to a nice neat 24 hours. 1/36 = about a 3% chance of picking up the hostiles this early, however.

1 hour later, another check can be made. At T minus 23 hours, the dropships are still >34 million km, so another nat 12 or 3% to detect. Or, a cumulative ~5% percent chance to pick them up by this point.

22 hours from planetfall: TN to detect is now 11+, or ~8.33% chance to detect

21 hours from planetfall: TN to detect is now 10+, or 16.67%

20 hours from planetfall: TN to detect is now 10+, or 16.67%

19 hours from planetfall: TN to detect is now 9+, or 27.8%

18 hours from planetfall: TN to detect is now 9+, or 11.1%

17 hours from planetfall: TN to detect is now 8+, or ~41.67%

so on.

So, with roughly a 2/3rds probability to pick hostiles up 19 hours out at 1 g, that's probably about when they "usually" are detected. Assuming there's anyone actually looking. I'm not on board with that being a safe presumption.

BTW: I've piqued my own curiosity with nonstandard times, such as 1.5g and 2g. Since the lore does afterall support harder burns to catch defenders more off-guard. I'll post what I find in a bit.

EDIT: Fixed math error with cumulative probability