The expense cuts both ways. Are you saying that every one of the invading troops is going to be a combat soldier equipped with the gear that you mention? If they are not, all those that are not become very nice targets for guerilla activity.
Well, they'll be a combat soldier in that they received the same basic training and know which end of the gun to point at the enemy but, no, not every clerk and cook will be fully armored, though one expects they'd at least have access to some arms in case the base got overrun. However, the maintenance needs of higher tech units are greater than that of lower tech units: the need to maintain the vehicles and the IR goggles and the other tech translates to more rear-area support troops, which means the unit has to be somewhat larger to put the same number of equipped troops on the front-line.
Also, how acclimatized are your landing troops to the planet? What are the atmospheric, gravitational, and weather differences between the attacker and the defender?
I'm not sure how that relates to the number of men a given planet puts under arms.
Also, I assume that the invasion is intended to capture the planet and not simply engage in deliberate destruction of the planet's infrastructure. Dropping rocks is easy, assuming that they do not take action to destroy the rocks coming down. But then you do have to occupy the planet. How many millions of men do you think are going to be required to hold a planet with a populous in the billions? The Germans and Italians combined had over 250,000 men in Yugoslavia alone, and did not have full control of the country. And then you have the Russian partisan movement, which also tied up large numbers of German troops.
Your assumption depends on political and larger scale military considerations. Our conduct during WW-II was not predicated on the idea of holding onto and exploiting the Axis powers after the war; we pretty well smacked the hell out of them with whatever was available and figured - at least while we were doing it - that the postwar rebuilding was their problem, not ours. Interstellar political considerations might justify a ground invasion to seize the world with infrastructure reasonably intact, or they might be satisfied by simply rendering the world incapable of projecting military power into space.
In any event, the question was how many troops were needed for invasion. Garrisoning's a different issue and is likely to generate different answers. Might be less expensive since you don't need battledress and FGMPs to deal with partisans wielding hunting weapons; might be a lot more since you have to cover more territory rather than striking specifically to take key objectives and reduce opposing military force concentrations - and one guy in battledress can still only be in one place at a time.
Taking the capital may win the war, but it doesn't give one control of the countryside. However, how many people are needed to hold a captured world will depend on what you intend to gain by holding it. It may be sufficient to allow the surrendered government to deal with its own local problems and then extract whatever it is you want out of the surrendered government, or it may be that boots-on-the-ground is the only way for you to hold the place and achieve your objectives.
Except you don't have to outfit your militia/irregulars to the same level as your full-time troops. It depends on the world's political situation - if the people are sheep under the almighty hand of Zorg and have nothing but wooden pitchforks with which to defend their homes, then, yeah, you get 9 million sheep to add to the 1 million military. If it's a well-to-do constitutional republic with a long history of militias and occasional drills of the "citizen soldiers", then you get 99 million well-armed, psyched-up, disciplined troops who each brought their own combat armor. But, either way, the numbers will up massively once you invade their home turf.
Actually, I apply that differently. A combat environment suit (CES) and chameleon cover are the minimum adequate protection for the battlefield - 'cause the chameleon cover gives you protection against IR detection, preventing you from standing out like a sore thumb while the other guy remains harder to spot. Also provides good protection from HE artillery fragmentation hits, making the unit more resistant to indirect fire, historically a big battlefield killer. And, while the slug weapons are generally pretty hopeless against combat armor, their attached grenade launchers helps keep the rifleman in the fight - though ammo and supply become big issues. IMTU, planetary regulars stick to CES/CC and slug throwers, with the slug thrower equipped with a much smaller 25-30mm grenade launcher to deal with combat-armored foes, while the mobile forces run around in combat armor and energy weapons, the energy weapons reducing the need for supply since they can be recharged from the power plants of any handy vehicle or generator.
As to militia: how many Americans own a set of ballistic cloth armor? Or Europeans, or Latin Americans, or so forth? If the citizen soldier is outfitted at the state's expense, you haven't solved the problem of budget, and the Traveller CES with slug thrower come to a fair fraction of an average person's annual income. Historically, militia on the large scale tended to either cheaply armed or drew on arms the militiaman brought with him, arms that were often useful in his day-to-day life - farm tools turned polearms, hunting rifles, and such. In England, a bow cost a fair chunk of a commoner's annual income; under the assizes and similar laws, the responsibility to own arms of war fell to freemen with property beyond a certain value and to knights and higher status folk.
(Besides, the way Traveller generates government types, the citizen soldier of a constitutional republic is the resident of a fairly low pop world. The high-pop worlds under discussion run to more authoritarian and restrictive high-law governments, the kind where the army's big role is keeping the citizenry in line and discouraging revolt.)
Future-tech populations have higher per capita incomes. I can't lay my hands on my copy of Striker Book 2 right now, but IIRC a TL15 world produces four or five times as much as a TL 7 world. How does that compare to the increased cost of outfitting soldiers?
(Mind you, future-tech worlds have to pay for a space/star navy on top of the groundside military, so that reduces the percentage of the military budget going to groundside forces from 100% to something like 40%).
Hans
I looked at that. Per Striker, it's 2k credits per capita per TL after 4: 2k at TL5, 4k at TL6, 6k at TL7 and so forth. A TL10 world has double the per capita income of a TL7 world, 12k verses 6k. So it costs 5 or 6 times as much, but they have twice the tax base. A TL15 world has almost twice as much as a TL10 world, 22k vs 12 k, and - well, combat armor and a laser are much more than twice the cost of the CES outfit.
But, I wasn't talking about America, but an extreme that went beyond any modern-day examples. Just to point out that there's lots more things to consider than any rule can answer.
