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Date: Thu, 2 Jul 1998 08:12:51 EDT

Subject: Orbits, Detailed (Long!) repost

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To add a little more detail to orbits;
Some of this is really simplified, but as real space combat takes
some
heavy math, this should do. It only has medium math, and I'll include
some
tables.
Given: that 1 Manuver Unit (MU, 1" or 1cm) = 1000 km.
Given: that 1 turn = 15 minutes (to fit neatly with DS2)
Then: 1 Thrust over 1 turn = 1/15th of 1 g (1 standard Terran gravity,
set to
10m/s/s), or 0.0167 g, or 66.67 cm/s^2
OK, this may seem kind of slow - Traveller had accels up to 6 gs, &
2300's stutterwarp was blindingly fast (60,000 km/sec! for some BIG
ships).
But this may not be so bad - it could easily represent high-efficiency
low-
thrust ion drives, good chemical rockets (for 1-shot surface-to-orbit
stuff),
thermonuclear pulse-drives, or even solar sails (got some rules on the
cooker
for those - really neat, & fun to model). I would call this a tradeoff
for
having cheap, efficient FTL. It would also require such an FTL - long
insystem trips would otherwise take forever. I also like the idea of
big,
slow, stately behemoths. Makes spun sections necessary too, assuming
long-
term 0-g is still bad for humans. I am also assuming no contra-grav
(CG;
screening from planetary gravitic attraction) and for details sake, no
interior artificial grav (always hated that). If you have CG, you only
have
to follow orbit rules when you want to, or are forced to due to damage.
Given: Beam Weapons (Batteries and HBWs) are Neutral Particle Beams, and
have
real trouble with atmosphere
Given: Needle Beams & the various defense systems are lasers, probably
deep
UV/soft X-ray, and also have trouble with atmosphere
Given: Pulse Batteries, Pulse torpedoes and other plasma/fusion-based
weapons
have real trouble with atmophere
Given: To find anything in the clutter of a planetary environment (space
is
_clean_ by comparison), ships will have to be really close to find &
accurately target surface features (buildings, tanks, people, your left
big
toe...)
These are some technological assumptions that I made, pretty much
flat-
out arbitrarily. They represent some level of 'hardness', and seem to
fit
rather well. It also gives a good reason for ships to get close to the
surface, as opposed to uncontested space bombardment. If you change
these, it
doesn't matter that much, except that low orbits won't matter that much
to
you.
Given: Terra's diameter is approximately 13,000 km (12, 734 km, really)
Given: Terra's atmosphere is essentially 100 km thick for these rules
(sort of
off, but close enough for general orbit principles)
Given: Terra's 1g threshold is at the planet's (real) surface.
Thus: Terra is represented by a planet 13 MU in diameter on the playing
surface.
Thus: Terra's atmosphere extends 0.1 MU from the surface of the planet -
pretty much when the stand touches the planet's surface.
Now for the math: we know how far away your object is from the
planet in
cm, right? (MU x 10^8) We also know how much the planet masses in
grams,
right? (check an astronomy text - cheats given below) We also know the
gravitational constant, right? (in the same text, and below) OK, here's
the
equation:
A planet's attraction, in Thrust points (T), is equal to (the
gravitational constant multiplied by the planet's mass in grams divided
by
(the distance from the center of the planet to the object in
centimeters)
squared) divided by 66.67.
It looks like this (I hope this works)
T = (GM)
____
(R^2)
_______
66.67
Wow, text is bad for doing these equations. Sorry if it's jumbled.
OK, Terra's mass in grams is 5.974x10^27, the gravitational
constant is
6.67x10^-8 dynes (1 dynes = 1 gram accelerated at 1 centimeter per
second per
second), and our object 1 MU above the surface of Terra is 8x10^8 cm
from the
point source we assume Terra is.. Solving as above, we get:
9.34 Thrust, or 9 Thrust, if you don't want to use half-thrust units.
So when
calculating that object's move, apply a thrust of 9 towards the center
of the
planet. The distance that is used is the one when all other thrusts are
applied. So this object had better be going pretty fast, or it will
make a
pretty light show for the folks on the ground.
Here's where things begin to get tricky. Figuring that an orbit
low
enough to get good bombardment possibilities is about 1 MU from the
planet's
surface (you've got to have some leeway), you're going to end up with a
path
that looks like it will take the ship through the planet. Oops. Here
comes
the fudge: If the endpoint is not IN the planet, and the vector is not
true
straightline travel (some thrust/pull was applied to change course), the
object can be considered to have curved around the planet.
Of course, if you've got CG, you can just be at rest relative to the
map,
and you are totally stationary. The planet will turn under you, and
eventually, unless you manuver or allow the planet to tug you a little
bit, it
will curve off in its orbit around its primary, and you will zip along
in a
straight line. Bye!
Where is the wonderful geostationary orbit? It should be at about
42 MUs
from the center of Terra - from where measurements are made. What sort
of
pull does that give us? .34 Thrust, or 1 every third turn. How fast
should
the object be going to maintain the orbit properly? Heck, that's what
playtesting is for! I'm working on it, I'm working on it.
To give you an idea of scale at this scale (1 MU = 1000 km):
Terra - Luna: 384 MUs (3.84 m, or 32 feet)
Luna is 3.5 MUs in diameter, and has a mass of 7.35x10^25 g
Terra - Mars: 78,600 MUs (786m, or 6550 feet (1.24 miles)
Mars is 7 MUs in diameter, and has a mass of 6.4x10^26 g.
Jupiter - A long way away. Jupiter is 137 MU in diameter (1.37 m, or
11.4
feet). Near it's 'surface', it has a pull of almost 40 Thrust. Zoiks.
Terra's Gravity Table
Distance from Center Thrust Applied towards Center
8 (LEO) 9
9 7
10 6
11 5
12 4
13 4 (3.5)
14 3
15 3 (2.5)
16 2
17 2
18 2
19 2 (1.5)
20 1 (1.5)
21 1
22 1
23 1
24 1
25 1
26 1
This will trail on for a while, reaching 0.5 Thrust, 0.34, 0.25, as low
as you
want to take it. For most gaming purposes, anything less that 1 is
meaningless. As you can see from the scale examples above, things are a
long
way apart. Most FTL ships will make short hops to save time. Most
non-FTL
ships will be limited to close planetary or satellite work. With
constant
acceleration to midpoint, and constant deceleration to the destination,
a
Thrust 2 ship on the Terra-Luna route will take 37.6 turns, or 9.4
hours.
Good, but not as fast as most SF games blaze around.
Have fun sliding around!
Noah V. Doyle
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