Re: Terminal velocity and orbits. (was: Spelljammer on planar walkabout)

>[nods] Gotcha.
>
[sighs] Finaly :)

[snip]
>>Both your physics and math are right as, it is your description of a
>>forced orbit that is wrong. This because you need to apply thrust
>>along the orbit as well as towards the planet in order to increase
the
>>centripetal force that is keeping you from smashing into the planet.
>
>But you don't _want_ to affect centrifugal "force." You want to get
closer
>to the planet by applying a constant force, so that if the force
drops off
>(you lose power, run out of fuel, etc.) you'll return to your
previous
>orbit. If you thrust along the orbit, you'll just affect the
>unpowered-orbit distance, which is not what you want to do. This is a
>convention used fairly regularly in hard SF (well, okay) and I think
it may
>have been used in real life as well--in any case, if my math _is_
correct,
>it would be impossible to achieve a stable orbit, because of positive
>feedback. Too close, and gravity increases faster than centrifugal
force
>and you fall even further in. Too far out, and gravity falls off and
you
>spin out into space. I _know_ my conclusions are wrong. I just can't
figure
>out where the error is.
>
Your error is that you do not take into account the fact that when the
situation changes the rules governing it also change.

For 'forced' orbits you need to be moving faster than is allowed in
your target orbit so if the force that 'forces' you into that orbit
(in this case your ships engines) ceases you will be 'thrown' back
into a higher orbit (probably but not necessarily the one you started
in).

You are right that stable orbits are effectively impossible but it is
possible to achieve an orbit that will only decay extremely slowly
(i.e. less than 1 millimetre per century).  Also you do not take into
account the following the equation that you are using to work out
centripetal force only applies when the object is moving in a circle
(or a good approximation thereof) and that an object if it is moving
out from its orbit it will lose energy due to gravity and if it moves
inwards for its orbit it will gain energy due to gravity.