Unfortunately, there is no explanation for that rule, so we don't know how to refine it when we go from the level of detail of the [RbS:37] tables (very crude) to the level of detail of the
Striker rules (a little less crude). We can conjecture what's behind it, but that's all it will be: conjecture.
Is it ten times more expensive to maintain a trooper on worlds with air breathing problems? Or do you only need one tenth the number of troopers on a world with air problems? The ramifications of the two explanations are very different (In the second case you get a concomittant increase in the navy budget when you reduce the army budget -- total military spending remains the same).
If it's the first, is the rule actually reasonable? Does it really cost ten times as much to maintain a vacc suited trooper as it takes to maintain a freely breathing trooper? And if it costs ten times as much to maintain a vacc suited trooper (atmospheres 0, 1, 2, and 3), does it also cost ten times as much to maintain a filter-masked trooper (atmospheres 4, 7, and 9) or an air-masked trooper (atmosphere A)? And is it really no more expensive to maintain a trooper in a corrosive or an insidious atmosphere than in a vacuum?
And looking at TL15 armies, is it really ten times more expensive to maintain a vacc-suited trooper than a battle-dressed one?
I think perhaps those rules are more suited to making up counters for an FFW scale boardgame than for serious setting-building. (And could use some refinement too :smirk

.
My advice would be to take inspiration from the
Striker rules
1 and pretty much ignore the RgS rules.
1 Though not to follow them slavishly.
Hans
Let's start with breathable world troops...
Let's see - a typical trooper has a salary of Cr300, and dismal lodgings (equal Cr60/mo on the economy), and is getting fed, usually, Cr140 worth of home prep, but buying in wholesale, that's probably Cr70. Add some incidentals, like the provided hand soap and TP in the barracks, and data service... we get to about Cr500 per month per private; NCO's are easily double, and SNCO's triple that.
Gear replacement on a 5 year schedule makes troops considerably more expensive. Assuming a 50% wholesale discount, and 100 rounds per month continued fam fire in barracks (rounded up next clip)...
ACR: Cr1000, clips x 4 = Cr120/mo
CES: Cr1000
Short Range Commo (TL8+): Cr75
Tent: Cr 200 per 2 men
IR and LI goggles: Cr500 each. Assume one or the other.
Uniforms, office/barracks/dress - probably about Cr200
Weather Gear: Cr200
Bayonet: Cr10
Backpack: probably Cr50.
About KCr3.2 per 5 years about Cr55/month for gear replacement, and about Cr120/month in fam-fire.
Add salary of Cr300, plus share of barracks space, and said trooper is about Cr500/mo.
Now, for the vacuum trooper...
Add LS: the Oxygen tank listed isn't a rebreather; we can get about 10x the efficiency. Which leads to about 1/13Td and Cr150 of air for the whole month, assuming a 50% bulk discount, on a world where it's readily created. If we assume a neighboring world, that's a base of Cr1500/Td, probably bought at an average of 80% that, then shipped, for about KCr2.2/Td, and that's about Cr170 per month. For simplicity, we'll assume the air is always available within one KCr1/ton shipping hop.
Filters: we'll assume the filter mask is good for a month - and use it as the basis for the filtration scrubbers for the suits. Cr10/mo
Combat Armor - the standard for vacuum troops - KCr20. Cr330/mo
The add-ins for vision are no difference from standalones cost-wise.
The Tent is replaced with a vacuum tent Cr2000 (Cr33/mo, per 2 men)
So we get an extra Cr600 per month or so, adding incidentals like air lost out the airlocks.
A bit over double the cost per trooper.
And that doesn't include hazardous assignment pay - which vacuum should - and that should be about Cr30 for a basic trooper.
Jr. NCO's and veteran privates (PFC's) should be about double the base cost - housing, additional gear, increased pay - but the vacuum additions don't get multiplied. NCO's triple, Senior NCOs and junior officers about quadruple. Specialists add about Cr50 to Cr100 per month - additional training and gear.
High Energy Heavy Weapons troops add considerably more - FGMP's are KCr120+ and thus add upwards of KCr2/mo.
So, logically, it needs to be both increased costs (about 2-3 times the costs), and fewer needed (the vacuum or acids prevent long term occupation of the outlying areas), as well as fewer tolerated by the locals, plus the deletion of the wet and air portions of the Army, leaving only the COACC and Ground components.