Orbits, Detailed (Long!) repost

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

> On 2 Jul 98 at 8:12, NVDoyle@aol.com wrote:

> To add a little more detail to orbits;

Um, your math seems faulty to me.

1MU=1000km=1,000,000m 1 turn=15 minutes=900seconds One 'thrust point' of
acceleration over one turn gets you a distance of 1,000,000m

using s=vt + 0.5*at^2
where v is the starting velocity, zero in this case. so we only need to use
s=0.5*at^2

1,000,000=0.5*a*900*900 1,000,000=a*405,000 a=2.5 approximately. which is a
roughly a quarter of an earth gravity.

Alternatively you can use the game mechanic that by the end of the game turn
the ship has got to a speed of 1MU per turn, which would give a different
result.

v=at
1,000,000/900=a*900
a=1,000,000/(900*900)
a=1.25

which is about an eighth of a G.

Trouble is, FT isn't really consistent in it's model of movement. It has ships
that have accelerated continuously for a turn both ending up at a final speed,
but acting as if they had been travelling at that speed all the time. Ok, it's
a game, and I for one don't want to use these formulas all the time either;)
But this gives a range of about a quarter to an eighth of a g per thrust
point...

Which still feels horribly slow, yuk. I'd always thought it was far more. No
gravity compensators required. But you might want to recalculate everything
again for your system. I'm going to consider making one distance unit 10,000
kilometers. So each thrust point is
more like 1.25-2.5G, feels better to me. YMMV.

Alternatively keep your system, but don't try and use math to justify it, or
fudge the scale so it fits.

Alternatively, *I've* made a major mistake:)
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> In a message dated 98-07-03 19:21:17 EDT, Richard S. writes:

<< Um, your math seems faulty to me. >>

*SNIP*

> Trouble is, FT isn't really consistent in it's model of movement. It

> Which still feels horribly slow, yuk. I'd always thought it was far

> Alternatively keep your system, but don't try and use math to justify

Arrrrgh. You're right, AFAICT. I was so worried about getting the
gravitational attraction business right that I neglected the acceleration
problem. OK, everybody ignore that post, I'll come up with a cleaned up one
soon.

I still ike the 1000km/15 min turn - it seems to be pretty close on, and
it
makes the planets on-table into significant obstacles.  I liked GDW's
Brilliant Lances/Battle Rider system (30,000km/30mins), but it was more
suited to a hex game, as planets became more like terrain than objects at that
scale.
Actually, some of my math was reverse-engineered from some of GDW's
stuff -
that'll teach me to confirm my sources.

I would go with your second model,

v=at
1,000,000/900=a*900
a=1,000,000/(900*900)
a=1.25

providing a thrust of 1/8th g per thrust point.  I'll go with that for
now, cause that is the best observable result (I apply 1 thrust for 1 turn,
and am
then going 1 MU/turn).  Personally, I like the slower accelerations,
'cause I
have a hard time rationalizing interior artificial gravity (contra-grav,
a la Traveller, I can live with). It also allows some extreme ship designs to
exist without having squash-the-crew-syndrome.  A thrust of 16 is 2 gs -
fast,
in my universe.  Also, I find it easier to rationalize low-thrust
engines with
very high fuel efficiency - makes for better long patrols.

Finally, try out the planetary acceleration stuff - In the few games
that I've
used it in, it was a lot of fun, and became very important - it'll be
less so,
now that I'm scaling up the thrust/g ratio.

> On 3 Jul 98 at 22:11, Sabmason@aol.com wrote:

[snipped]

> providing a thrust of 1/8th g per thrust point. I'll go with that

You manage to rationalize FTL drives and non reaction mass normal drives, so
give limited contra inertia (not grav) effects on ships a chance perhaps? 1G
acceleration from purely accelerating can be thought of as different from the
1G force upon you from stading on earth. One is cause by gravity, the action
of a very big mass. The other because of inertia. So you don't need gravity
control exactly, just a way of divorcing the interial frame (PBS abounds). I'm
not advocating inertialess ships just partially inertial compensated. It cuts
down on inertial superweapons.

Hrrm, if we change 1MU=1,000km to 10,000km earth sized planets become an inch
across:( but hey, jupiter will be 8" instead of 80", the sun will be 70"
instead of 700";)

If we change the timescale to 1.5 minutes, there are ten turns per
stargrunt/dirtside turn :(

Trouble is, at such low accelerations, it takes FOREVER to get between planets
inside a solar system. <doublecheck> um, wait, you can use FTL inside systems
with FT can't you, just as long as you
are sufficiently far from the planetary surface / gravity well. Has
that distance been quantified?
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