The Core Expeditions Errata

This is where the game runs into reality and you need to decide what is more important to you.

I am going off memory but I believe that when the first Traveller subsector maps were being created it was unknown in which direction the Milky Way Galaxy rotated. The designers had a 50/50 guess and guessed wrong, so Spinward is Trailing and Trailing is Spinward.

I should add that this was fixed once the real direction of rotation was known.

The 100d rule exists because diameter is a far easier number to come up with than mass. A planet's mass is determined by its average density and that can vary considerably.

Stars vary in density as well.

Couple this with the fact that exactly what Jump Space is has never really been explained in scientific terms and 100d is good enough for a game.

Pick a random Traveller planet - say Lanth - and then ask what is its mass? I can answer that - 5.86E+24 kg - because I created it in a software program. The diameter is 12,783 km. Lanth is a water world and slightly less dense on average than the Earth - 5.35 g/cm3 vs. 5.51 g/cm3.

Which figure is easier to use?

Also you have books - The World Builders Handbook and The Great Rift mentioned above - that not a huge number of players or referees will own. I own 15 Mongoose books but have neither of those.

Of course it always comes down to your table = your rules, so people can use whatever method suits them.
 
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Please bear in mind that medication has been taken (nice, passive tense, blaming nobody), but my assumption would be:
View attachment 7675
assuming that F is what we want to start with.
I use the cube root (rather than the square root) because the relationship between diameter and volume (and thus mass) is a cubic one. To double the diameter (and the 100D limit), the volume of the stellar object would increase by a factor of 8, assuming the density is held constant. (Obviously, the density of dead stellar objects does not hold constant, but according to what's been published, we're treating the jump shadow of such objects as if they were stars of the appropriate mass. But it's an undefined area at the moment; it can be played either way without breaking the game.)

I will note, though, that working proportionately with the cube root of the mass gives a smaller jump shadow than using the square root. This might become important when dealing with intermediate and super-massive black holes. For example, using your method for Sagittarius A*, you get a jump shadow radius of 1884 AU, while using mine gives a jump shadow radius of just short of 149 AU. I'm not sure how important that might become (hey, gamers are seriously unpredictable!), but it might be something to keep in mind.

Edited to clarify: the square root only increases faster than the cube root when your initial quantity is above 1. For stars of smaller mass than Sol (not applicable for neutron stars or black holes), the reverse holds true.
 
The formula Geir gave uses stellar mass, not stellar volume.
At those distances, the body acts like a point source. Light, other radiation and gravity vary with the square root of distance.
The use of 100D is just an approximation. The gravity well is generated by mass. Also, the formula was presented due to the discussion of black holes, and requiring the accurate formula without resorting to D. Volume and diameter are not going to give good results on objects that dense, and yes, your way will have gravity appearing to fall off faster than it actually would. Result: starships precipitate from jump space sooner than calculated (at the distance calculated by using the square root).
 
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