> On Mon, May 29, 2006 at 11:09:30AM -0500, Doug Evans wrote:
> does
No, but I'm working on writing one. What sorts of problem are you trying to
solve? I've got reasonably decent solutions for the high
constant-thrust model and for Hohmann and other transfers, but the
multi-body slingshots and long-low-thrust systems (e.g. ion drives) are
proving more troublesome.
R
Crap, prolly over my head, but using the example of Earth to Mars, where we
accept that there's a close-enough-for-government-work ratio of one to
two for respective years, how would it be best to visualize the possible
paths?
Assuming constant, handwavium-amounts of thrust, of course.
The concept I was working with was move the distance of the Earth orbit, then
perpendicular up to the Mars orbit. Do the same in reverse, which, of course,
is only half the chord size of the other direction.
Also, I was considering allowing prograde or 'standing still' movement in
orbit, with the image of the ship 'standing on it's head or tail' with
relation to the center of the orbit. How much handwavium is necessary to do so
compared to changing orbits?
Shaking your head and walking away from the whole thing is acceptable,
perhaps even wise. ;->=
Now if you're REALLY crazed, try to suggest comparisons to combat burns.
The_Beast
Mr. Burton West wrote on 05/29/2006 11:19:25 AM:
> On Mon, May 29, 2006 at 11:09:30AM -0500, Doug Evans wrote:
are
> proving more troublesome.
> Crap, prolly over my head, but using the example of Earth to Mars,
I'd think you could more or less use a straight line for that (but I could be
wrong), because the trip doesn't take as long as you might expect.. Let's
assume it's NOT at closest approach...in fact let's say it's at 1.33 AU to
make my arithmetic easy. So half that distance (the acceleration
part--then you flip the ship and decel, so you end at zero speed) is
100,000,000 km or 1E11 meters. You're contantly accelerating at a slow
1/5
gee or 2m/sec^2:.
1E11m = 0.5* 2m/sec ^2 * t^2 = sqrt(1E11sec^2)
= 316227 seconds = 87 hours 50 minutes, more or less, for the first half of
the trip, or about a week for the whole trip.
(feel free to factcheck my arithemetic)
Multiply the thrust by four (ie 0.8 gee) and you cut the time in
half--you
can multiply the thurst by N and divide the time by sqrt N. If you have a 40
gee ship, which IIRC is what one of Vorkosigan's ships will do, then you can
make the trip in under 20 hours.
http://www.projectrho.com/rocket/rocket3i.html
http://www.projectrho.com/rocket/rocket3b.html
http://www.projectrho.com/rocket/rocket3o.html
Thanks, all!
I'll be having to chew on it awhile; I've already found some numbers different
than some of my sources.
Wonderful thing, the internet...
The_Beast
> On Mon, May 29, 2006 at 11:37:49AM -0500, Doug Evans wrote:
If you can do that, you can pretty much ignore solar gravity completely.
Let's assume an Earth-to-Mars trip on the simple profile:
(1) go from Earth's orbital speed to standstill. (2) go directly from Earth to
Mars. (3) accelerate to Mars' orbital speed.
This is obviously not the most efficient method in many cases, but it's a
useful approximation.
Stage 1 needs a delta V of 29.8km/s; stage 3 needs a delta V of
24.1km/s. (Orbital speed = sqrt (G * mass of primary / radius).) For a
1g ship, that's a total of about 1.5 hours' thrust. That's small enough to be
more or less ignorable.
A constant-thrust burn over distance S, with acceleration A and a speed
of zero at each end, takes T=sqrt(4*S/A). For the Earth-to-Mars trip,
that's between 49.7 hours and 109 hours depending on the relative position of
the planets. Even in the worst case, therefore, you're looking at less than
five days of travel time.
If you drop the acceleration to 1/4g, you double the stage 2 time and
quadruple the stage 1 time. You're still looking at a maximum of less than ten
days. Neither Earth nor Mars moves so far in that time that it's worth taking
their orbits into account.
The complicated trajectories are the really low-thrust ion-drive types
of orbit, where you've got 1/100g or less for an extended period.
> Also, I was considering allowing prograde or 'standing still' movement
Not quite sure what you mean here. Prograde means "in the direction of the
orbit". Do you mean the sort of thing I've been talking about above,
"hovering" with zero orbital speed? That's really no problem at all -
once you've burned down to that speed, all you need to do is exert enough
thrust to counteract solar gravity, and even a lightsail is
capable of that - all you need at 1 AU is 0.0006 gravity.
Does this answer the questions you were asking? :-)
R