Gravitational effects on orbits

Allan and I were discussing this offlist and realized there had been an
oversight in a formula, so the numbers given previously were not correct. Here
are the correct numbers and how to get them:

> From basic physics (ie the class we took 15 to 20 years ago) we

The Earth's radius we have determined to be approximately 6mu (6.375 to be
picky, but we'll call it 6). So at 6mu from the
center, the acceleration is 4mu/turn.  Gravity drops off as the
square of the increase of distance, so for a radius R from the
center of the planet, the gravitational effect is 4mu/turn *
(6/R)^2 .  Thus at 12 mu radius, the gravitational effect is 4 *
(6/12)^2 =1mu/turn.  7mu radius is close to 3mu/turn effect, and
8.5mu radius is about 2mu/turn effect.

Now, the other part of the problem is that if you make the endpoint of
movement the determining factor, you'll tend to crash. Let's say you swoop in
and end your turn at 7 mu radius. No matter how fast you're going and no
matter what the direction, gravity grabs you and pulls you 3mu towards the
center of the
planet.  7mu (your altitude) - 3mu (gravity effect) abruptly
meets 6mu (planetary radius) with a severe detrimental effect on
your hull.  Let me say it again--no matter how fast or what
direction you're going in, you crash.

Traveler took the critical point to be the midpoint of the move instead of the
endpoint, and I suspect that may work better.

> Traveler took the critical point to be the midpoint of the move

Though I know it's not as scientifically correct, I've always added gravity
"adjustments" to the end of the move based on the ship's position at the
beginning. In other words, if it starts in the gravity well, it has its end
point adjusted. Seems to work well, and you can get a stable orbit that way.

On Mon, 31 Jul 2000 21:57:36 -0400, Laserlight <laserlight@quixnet.net>
wrote:

> Allan and I were discussing this offlist and realized there had

To be honest, I was the one making the oversight. The new formula looks
correct. Large gas giants would still be a pain, though, depending on density
(as I mentioned, Uranus actually has slightly less gravity than Earth at the
surface).