[email removed] writes:
>But who's to say the gravitons behave similar to quantum mechanics? It may
>be that the "size" of the graviton is dependent on the size of the "radiating"
>body. Then the explanation for the 100 diameter rule could read something
>like this...
(details deleted)
The problem with your argument is that greater mass NECCESSARILY implies
greater flux (i.e. density) of gravitons in the vicinity of that mass. Thus
more massive bodies will always require greater distances to safe jump points
(all other things being equal...). The idea that the SIZE of the body matters
is rubbish. (It can be demostrated that a spherical mass distribution can be
treated as a point mass located at the center of the distribution, as long as
you remain outside the radius of the object.) Only mass, and the distance from
that mass, are of concern. That's why, as a physicist, I have always disliked
the idea of travelling "X" diameters to the jump point.
With this in mind (a solar system composed entirely of effective point
masses), the problem is to develop a suitable mearure for the degree of local
space-time curvature due to gravitational influnces. Clearly, stars will have a
large influence ( with mass scales about 1E+5 to 1E+7 times larger than planet
a large influence (their mass scale is about 1E+5 to 1E+7 times larger than
planetary scales). In order to minimize their affect, curvature should fall
off very rapidly with distance. As an earlier article pointed out, a 1/r**2
fall-off (obtained by measuring gravitational FORCE) has some setbacks. It is
obvious that a 1/r fall-off (the result of measuring gravitational POTENTIAL)
would be even worse. Perhaps by defining a gravitational "CURVATURE" which
falls off as 1/R**3, we can get better results.
What would such a fall-off do? It just might solve our problems. Look:
Mass is given by Density*(Radius**3). Thus a curvature like Mass/(Distance**3)
would be the same as:
Curvature = Density/(RELATIVE Distance)**3
where relative distance is really just the number of DIAMETERS away.Sum this
expression over all bodies in the system (in practice, we need sum only over
stars and the planet or gas giant involved) to find the total curvature. If
this sum is less than a critical value, jump is possible. If we ignore the
affect of stars (say we are sufficiently far away) ,we can invert the equation
above to get the jump distance:
N = (density/curvature constant)**0.333
This actually explains the 100 diameter rule: because curvature falls off as
1/R**3, we can calculate jump distance as a constant distance relative to the
planetary diameter (although the diameter really HAS NOTHING TO DO WITH IT)!
However, there is a small correction due to the density of the planet, but that
is no great problem.
For example consider a jump from Terra. (Density=1.00, Diam.=12,740 km).
Suppose than it exactly 100 diameters to the jump point (travelling straight
away from Terra and Sol). This implies a critical curvature constant (CCC)
of 1.2E-6 (Sol has density about .25 Terran, and 1 AU is about 108 solar
diameters). Or for a "10 diameter" jump, the CCC is 1E-3. For simplicity,
say the two CCC's are 1E-6 and 1E-3, respectively. Then risky jump is still
at 10 diameters (127,400 km), while safe jump is at 108 Terran diameters
(1,375,920 km). Note the coincidence: safe jump is 108 Terran diameters away
from Terra, and 108 SOLAR diameters from Sol. This is a true coincidence,
but I LIKE IT. Cosmic Synergy and Synchronicity and Fabulous Portents of the
Unknown....
Any way the only trick left is to find out how far one must go in a
given direction away from the planet in order to get curvature below the
critical level. It will, of course vary with direction, if you want to pick
nits with me. There's two options: get a computer whiz to come up with a code
(I ALMOST did), or do what I did--stick with the 10/100 diameter rule ( you
can use the (density)**0.333 effect if you like), because otherwise you can
get bogged down in overly technical scientific mumbo-jumbo (like I do at the
office), rather than enjoy the role-playing (which I do in my SPARE time).
Any way. I've vomited my two cents worth. That's why nobody likes us
physicists--we overkill science.
Marty Jarrio (Physicist at large)
" Ray, get that tranquilizer gun..he's a vicious one"