The Jump Shadow Knows!

 Jump drives are a staple of RP games in space (unless you're playing Spelljammer or using one of those sissy warp drives). We know the particulars - it takes 168 hours to initiate a jump (plus or minus a bit), you travel 1-6 parsecs. You can set a course or buy a jump tape (not really a tape but we still refer to dialing a number for a call or rolling down a car window). 

Oh there's a jump shadow too. You cannot safely initiate jump within 100 diameters of a significant object -planet, moon, stars... When you are traveling in jump space, you will emerge when you encounter such an object, or you reach te end of your journey. Either way it takes a week.

Some rules have determined that you require a jump limit, a moon or something at your endpoint to emerge from jump. Jump into an empty hexagon and you'll find something, a rock or a stray comet. If it has ice on it winner winner chicken dinner. If not, you have a long trip to a star system. I hope you brought a long book or a low berth. 

Other options include the jump failing (with or without fireworks). The ship stays where it is and you kiss your fuel good-bye. It's the gravito-electro equivalent of holding in a sneeze. Or you do an in system jump. Really, you can make stuff up. In the OG approach, you jetted off in a random direction and traveled up to 36 parsecs, optionally emerging near a star (yeah, you want to ask your ref about that). 

So what are these Jump Limits? Some people believe it reflects the safe amount of micro-gravity you can have in your jump. A size 8 planet would have 1/10,000 of a g at 100 diameters. The hundred diameters limit approximates this. Except it doesn't.

It doesn't work for stars at all. Our own beloved Sol has a surface gravity of 274 m/s^2 so Sol would exert 1/10,000 g 520 diameters away (surface gravity ^0.5*100). Or 731 million kilometers or about five AUs. Wow. At least you can fill your tanks at Jupiter before beginning the long journey sunward to Earth. Typically between 4.5 and 6 days. A like time is required to exit Sol's jump shadow figured by gravity. G-stars may not be popular for free traders, or they may have extensive ports on their outer worlds to accommodate traders in a hurry. Even an M class star typically has a mass of  0.2 that of Sol and a jump shadow .44 its size or about 2 AUs. If you reduce the diameters needed for a safe jump then you have ships emerging 20 diameters from a planet, say and that means attackers have a much shorter run to drop bombs on a planet. Governments will not like this.

If you keep the rigid 100D rule things can get dicey for explorers. Assuming the hundred diameter rule reflects only the physical dimensions of the object, a poorly calculated jump could lead to you emerging near a white dwarf star. Now, a white dwarf star can have the mass of the sun, with  a diameter of 12,000 km. A ship emerging 1,200,000 km from such a star is subjected to 28,000 gs. A ship might be able to plot a slingshot maneuver to escape, and might be able to slow down after (and it would make a hell of a story!) Keep in mind ships exiting jump usually do so with little velocity for safety reasons and they often have nearly empty tanks.

Exiting near a neutron star, or Ancestors help you, a black hole is even worse. You'll be within a few hundred to a few thousand kilometers of an object as massive as a few Sols (with a number of other interesting properties). 

Another question to ask yourself, does every object cast a shadow? What if we got a mylar balloon or a solar sail a kilometer across? Would it have a 100 kilometer jump shadow? Towing a 100 kilometer asteroid to block a jump point is doable for a large, wealthy, and advanced culture. Any clown could buy a solar sail and voila, instant jump negation! And it's in your budget! 

I note a bunch of pirates have their hands, paws, claws and manipulators raised. Hold your questions till later please. 

FWIW: it is easier to Base jump shadows on physical size. Not gravity. Using gravity requires a lot of adjustments to the way systems are colonized and I don't want to do all that. As for neutron stars and black holes, there ain't that many. They're more story elements than navigation hazards. Solar sails and such could cause problems and they could be fun. They'd also be easy to spot and remove. 

Effects of jump blocks vary. My hard and fast rule would be an object in the way before your jump causes the jump to fail. Objects in the path of the ship after it enters hump space will either cause a misjump, or cause the ship to exit Jump Space nearby. There is a lot of wiggle room for missing a ship in Jump Space. An old JTAS article by the Emperor himself said Jump was accurate to within 30,000 Km per parsec. Filling 30,000 square kilometers, even with solar sails is no easy feat. You'd need a 300 km sail. 

I made the chart below to indicate micro gees (µ), gees, misjump number, a modifier for multiple jump shadows and effects. The µ and gee columns are just to make it look hard sciency. The misjump number is the number rolled to indicate a misjump based on the number of diameters distance from a massive object. Now if you have stars with huge jump shadows you might be jumping within 40 diameters. That's a 7+. Say you also are within 40 diameters of the main world. that is a +2 to the misjump roll for a 5+ indicating a misjump. Now Navigator levels will reduce this number. Perhaps Intelligence or Education or the mark of computer will as well. It's your table. I'm already screwing canon with no official endorsement. At a guess, Int/Edu 9 -1, Int/Edu 12 -2 DM to Jump plottage. 

Size 8 Equivalent	µ gees	Gees	Misjump	Adder	Effects
10D	100.00	0.01	4+	+4	Off by 1d6*Jump # Pc. **
20D	25.00	0.00	5+	+3	Off by 1d6*10 AUs**
30D	11.11	0.00	6+	+3	Off by 1D6 AUs°
40D	6.25	0.00	7+	+2	Reset/fuel lost
50D	4.00	0.00	9+	+2	Reset 1d6*10% fuel lost.
75D	1.78	0.00	11+	+1	Reset
100D	1.00	0.00	13+	0	Delay 1d6 turns
					**J-Drive Damaged 2D6 days to repair
					*J-Drive Damaged 1D6 days to repair
					ºJ-Drive Damaged 1D6 days to repair

The effects tell what the misjump does. Find the misjump number or lower. As you can see, most misjumps result in delays or lost fuel. The results are way easier to take, unless you have a navigator as sharp as a bag of wet mice. Optionally spending a day on computing your course instead of an hour or so will give a -2 to the number. 

For reference, you can figure out the jump shadow using micro gees with √(MPlanet/MEarth) *1,280,000 Km. MP = mass of the planet. ME = Mass of Earth (1 for most purposes). Figure the jump shadow of stars using √(M*/MSol) *.86 AUS. M*= mass of your star. MSol = Mass of the Sun (again 1 for most purposes.) I invite you to screw with multi body systems and do your own bad math.