From:	Bill Currie <bcurrie AT tssc DOT co DOT nz>
Newsgroups:	gac.physics.astronomy,nctu.club.astronomy,relcom.fido.su.astronomy,tw.bbs.sci.astronomy,comp.os.msdos.djgpp
Subject:	Re: Orbits, planets, PLEASE HELP!
Date:	Tue, 17 Mar 1998 09:18:11 +1200
Organization:	Telecommunication Systems Support Centre
Lines:	66
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To:	djgpp AT delorie DOT com
DJ-Gateway:	from newsgroup comp.os.msdos.djgpp

Gili wrote:
> 
> Hello,
> 
>         I have a science project due next week. I am programming something
> which will find the most efficient orbit given certain parameters.
> However, I have been unable to find the locations of all planets (and
> their moons) in our solar system at a fixed time. In order for my
> program to work, I must have the positions of all planets (and their
> moons) at a fixed time (so I know where they all begin off) and I also
> need to know their exact velocity at that given time.

I can't help you there, other than sugest asking NASA (poke around
http://www.nasa.gov/ for some contact addresses).  

>         My program will launch a rocket into space where it will be totally
> under the influence of gravity (which is why I need to know the
> positions/velocities of those planets.) However, I have run into
> another problem, how do I know the positions of the planets in the
> solar system after 1 second has past? The same goes for my rocket..

Does it realy have to be our solar system?  It seems that your project
is to demonstrate transfer orbits and sling-shots.  Why not just make up
a solar system (that makes sense) and use that.
 
>         I can resolve the force vectors being applied by all the
> planets/moons on my rocket, and I know its position and velocity. But
> where do I go from there? How do I know where it will be a second
> later?

Ouch, you're getting into numerical integration techniques here.  I
would suggest looking up runge-kutta (altavista gives some good links
and I imagine yahoo will as well).  However, I can give you some tips to
get started.

r is a vector

     GM
a= - -- * r
      3
     |r|

giving a as the accelleration vector.

nx (new x) and nv can be found with (t is actually change in time)

nx = x + v*t + a * t * t / 2 + b * t * t * t / 6
nv = v + a * t + b * t * t / 3

b can be fount by calculating nx for a very small t (dt) and
recalculating the acceleration (na)

b = (na - a) / dt

The above isn't Runge-Kutta (RK is much better AFAIK) and it has some
problems, but it does work so long as things don't get to close for your
t.

Also, you might want to poke around
http://www.astro.virginia.edu/~eww6n/author.html
It has some exelent math and physics papers.

HTH
Bill
-- 
Leave others their otherness

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