Orbits, Detailed (Long!)

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