You ever stop an think we write too much... say right about the time we have to quote all this? :rofl:
Yes, but my point was that I'd use calculations to get a ballpark figure and then guesstimate the rest of the way, rather than redo the calculations over and over again.
Same here, I wouldn't figure the budget too tightly, leave some leeway for "misc expenses".
Agreed on the rest of the system not getting any coverage, but I disagree about the planet. There is no convenient horizon to hide smugglers and pirates as they slip past the defenders and hide in mangrove swamps. In space, there's no place to hide. Put a handful of sensors in orbit, and you can see everyone as they approach. Four patrol ships would be plenty to provide cover. One to guard the main settlement, one to patrol the jump limit, one in reserve, and one down for repairs/maintenance. Supplement with a handful of small craft for close orbit work and a couple of laser cannon emplacements at the downport.
Maybe, maybe not. Maybe some specific examples would be in order. Your example world is size 4, a small planet of about 5,600 km diameter.
That means the minimum jump distance is 560,000 km above the planet. Looking at MT rules for sensors the max range on most is 500,000 km so without satellites the jump point is just beyond sensor range. If they put satellites at 400,000km up (borrowing from CT, B2, p11) then they'll have good coverage of the minimum jump perimeter. Doing some quick math, the orbit perimeter / circumference at that range would be pi x (2 x (400,000 + (5,600 / 2))) = Orbit
3.141593 x (2 x (400,000 + (5.600 / 2))) =
3.141593 x (2 x (400,000 + 2,800))
3.141593 x (2 x 402,800)
3.141593 x 805,600
2,530,867 km = Orbit
So assuming we allow for some overlap in sensor coverage you'd need at least 6 satellites. Course Traveller conveniently only deals in 2D along the solar plane so we don't have to worry about coverage above or below the planetary equator ;-)
This also tells us something about the ETA for patrol ships moving about. If you have just four in orbit they are spaced out over 630,000 km apart if they are patroling at the same altitude as the satellites. At a 4 G burn, back up is going to be just over an hour away. If a smuggler times it right, they should be able to lift off and make a burn for the jump point before those patrol ships can intercept which means smuggling things on or off this world isn't going to be much of a problem.
For an earth-like planet with a diameter of around 12,000 km things get more difficult. The minimum jump range is 1,200,000 km out. You'd need two layers of satellites to maintain sensor coverage and a lot more than just six. You'd also need more patrol craft, etc.
Main point to keep in mind is that planet size will affect things significantly.
Once you get out of orbit, there's almost certainly no pirate close enough to intercept you before you reach the jump limit. If there had been, they would have been intercepted and inspected by one of the patrol ships (This admittedly ignores the possibility of lazy or complicit system defenders). And, no, the pirates aren't lurking around pretending to be innocent merchants, because innocent merchants wouldn't lurk, they'd be going straight towards the starport to conduct merchant-type business.
Depends on the size of the planet, how many sensor satellites they have, etc. With an earth sized planet, if they didn't have the extra layer of satellites you very well could lurk at the jump perimeter (100D limit) and not be on planetary or regular orbit (400,000km) sat sensors. Just depends on what the system has which any good pirate or smuggler would check out first

I think the important point to keep in mind is that depending on what the system can afford tells us something about where there would likely be piracy or smugglers... pirates want easier targets... if there are lots of sensor sats, patrol craft, etc. I would think they would go somewhere else.
I also think we need to design and price some sensor sats! LOL
All this also assume one inhabited planet that is the only point of interest in the system. If there are moon bases, outposts or colonies on outer planets, mining operations at asteroid belts... things get considerably more complicated for the patrols.
Fuel skimming is hugely inefficient anyway. The loss of revenue due to wasting a week moving between the gas giant and the mainworld is more than you save in fuel bills. Starships are expensive and any minute they're not transporting freight or passengers, they're losing money.
I agree, it really only makes sense if you had to jump in system at the outer edge of the system or the gas giant is the only potential source of hydrogen. Being able to jump in closer to your destination cuts out the practicality. There are also other sources of hydrogen that are probably safer than the risking the high winds of a gas giant... course Marc probably didn't know that back in the 70s. Ice asteroids, polar ice on moons and outer planets (turns out there is even a little on Earth's moon... probably not enough to be practical to extract for a Traveller ship, but its interesting), or just land on a world with water.
BTW, if I were running a small system, I'd hollow out an an asteroid, set up my own refinery and a fuel tanker to gather ice or hydrogen from whatever source was availble, refine it and sell it at my make-shift starport / downport. Extra income for the system.
No, it could buy 0.48 patrol ship outright or pay the maintenance on 10x that.
Ah, I misread the budget as having an extra zero... my mistake.
That said, I would think they'd have maybe two patrol boats (400 dT cruiser with jump drives and extra fuel removed, add some more guns, maybe higher G rating... guess we need to design this thing too :rofl: ). Make up the balance with armed pinnaces which would be much cheaper. If its a freighter or something, the pinnace could take care of the inspections, etc. If something else shows up you have a couple of patrol cruisers in geo-sync over the capital that make a 4-6G burn (depending on how much the engines can be "super-charged" after removing the jump drive) hoping to back up the pinnace before it gets shot to pieces by a corsair or some such. If that happens to be the other side of the planet... might be a few hours before they can get there which means its probably going to be too late.
Which takes me back towhy I said it wouldn't be much problem for smugglers to run the system. Its also why I suggested most of the population would be concentrated around the capitol. Even on a small planet, that's still a LOT of space to cover and a system this poor just can't effectively defend it. Even with sensor sats, they might see you, but that still doesn't mean they can get to you in time.
Really illustrates just how BIG space is.