The 100 planetary diameter rules for safe jump distance has always
seemed to be a rule of thumb requirement where the exact distance
can be figured out, it is easier to be safe.
The Starship operators manual states that the 100 diameter is due
to gravitational effects. "...the gravitational effects of nearby
massive bodies must be considered. Within 10 diameters of a world
or any massive body (even another starship), the proximity of the
mass so distorts the fabric of space (and jumpspace) ...."
I decided to calculate the gravitational effects for some unusual
situations, massive stars, habitable worlds orbiting a gas giant,
black holes, battleships, etc. and come up with safe jump distances.
Using the formula g=G*M/r^2, the gravity can be calculated at
any point. For earth at standard orbit it is 0.952g, at 10 diameters
0.00226g, and at 100 diameters 0.0000247g the earth is a size 8 world.
We could say that the safe limit is 0.00003 g, and 0.0025 g for a
"10 diameter" limit. This allows for a 10% error on the large planets
for differing densities, etc.
Let's look at the moon, a "typical?" size 2 world. The force of gravity
at 10 diameters is 0.00445g and at 100 0.00000487g. If in fact we use
the speculative values from above, a safe jump could be done at 40
diameters (gravity < 0.00003g). This is quite a variation for a
thumbnail guide to be used in practice, in fact as the travel times are
given in a chart in the imperial encyclopedia (pp. 92, 93), a new chart
could be developed for worlds with reasonable densities giving more
accurate jump distances.
However considering the earth situation, traveling out to 100 diameters
(directly away from the sun), the ship is experiencing 0.0000247g from
the earth, however from the sun the pull is 0.0005987, or some 24 times
as powerful. Jumping from that point would be like jumping from a
distance of 20 diameters. One could argue that the sun's effects are
already calculated in but the variation in the jump distance due to
planetary size would be insignificant. In fact in order to get down to
0.00003g one would have to travel out to over 4.5 AU distance from the
sun. At 1g this would not take 6-8hours, but near 127, or over 5 days!
Either something is wrong with the 100 diameter limit, or the explanation
about gravity being the cause, though I cannot think of anyother reason.
-Dan
Dan Corrin, System Manager, Mechanical Engineering, UWO, London, Ontario
TML FTP site coordinator: [email removed] ...!watmath!julian!engrg!dan