Plotting Inclination

I failed Geometery. At my best my average in simple Algebra was a C- to D. I only mention this so that you might have an understanding of how much suckage I have trying to figure out orbital formula's.

I've actually figured out all of it but one portion and that's inclination (the angle of the orbital plane relative to the suns equator).

Here are my X/X formula's -
oa = orbital angle (degree)
dist = semi Major Axis (distance from Sun)
ecc = eccentricity (ellipsoid amount)

x# = (Cos(oa) * dist + 0) * (1-ecc)			
z# = (Sin(oa) * dist) * -1 + 0

By changing the value of oa I can move my planet along its orbit (oa is derived by the passage of time and the position of orbit). In this way I can get my X and Z coordinate and easily plot my orbital line on a flat plane ... but planets dont move on a flat plane.

I need a formula for the Y location. I know the Inclination value for each planet/moon .. I just dont know what the formula is to plug it in. I've been to site after site looking at formula's and theories but nothing is registering with me - its either too complex for me to understand enough to break down into a useful formula, or it so complicated that I cant even begin to break the formula down.

Responces to this are kinda non existant .. maybe if I defined it in more visual terms? I'm solving for y on this thing. I know the inclination angle, I know the distance, I can figure the 3rd angle from the 3 angle law (all = 180). How would I go about solving for Y with that information?



I'm checking sites as this seems like it should be a straightforward pythagorean theorom sort of thing but once they get past the sqr(c) = sqr(a) + sqr(b) portion then it usually goes off into a direction that quickly loses me (like fractal patterns, working out areas, force lines, etc)

So 'I' is the angle, not the length of the hypotenuse, yes?

If so, I think the length of 'Y' is Tan(I)*d.

I must stress, however, that I also suck the big one when it comes to maths so I could be wrong. :)

Don't lose hope, though - there are some pretty big math brains around here who should show up soon to sort things out. ;)

I'm pretty sure big10p is correct.

That was close, but it didnt take into effect where on my orbit (in degrees) I was so I was getting a level path again. That was my fault tho - I forgot to mention that I also had to work in where along the orbit I was

But that was what I needed to get a bit further. Tan(I)*d is the Y change I get when the orbit is at 0 degrees I believe. I postulated that I needed to then add in some kind of ratio so that Y's value would increase and decrease as the planet moved along its orbit.

I came up with this :

Y = (Sin(Degree) * (Tan (Inclination) * Distance))

This is damn close - My planet orbits appear to now exactly match my orbit lines along the inclination - my only problem now is there seems to be a problem with getting a little too large a number in my Y value. The planets are sitting above the orbit lines (rather than exactly on them) and the further out you go the more exagerated it becomes.

If it were merely a matter of all the planets being off by the same amount I could easily adjust it, but being a ratio thing I can see more tinkering with the formula is needed.

Sooner or later I'll stumble upon sticking the right numbers in the right place ;)

If you know the dI angle, (Theta)

Tan(Theta)=y/d

Do you know the simulation Orbiter? They have a forum for that kind of question (not blitz related, though): http://orbit.m6.net/v2/forum.asp?forumid=6

larsalt : Egads, that takes the wind outta ones sales doesnt it? I have to admit that a few minutes on that sight was quite disheartening to my little project.

Then I have to remember that I'm not being quite as ambitious as that project. I started working a 3d model of the Solar System for my daughter to be able to explore it and understand the concept of distances/sizes and to gain a visual representation of things she learns (she's 6 years old and is fascinated by astronomy).

There's also the side effect of me actually learning more of the Blitz language and techniques while doing it ;)

Malice : As I mentioned, the Tan(Theta)=y/d formula doesnt take into account where along the orbit the planet is so the value that produces is actually the planets Y value at its aphelion (furthest point in orbit from sun).
I have to take into account where along the orbit the planet is at any given time. The Y value at aphelion will be greater than if at perihelion (closest point in orbit to the sun).

Now to determine this I need to take into account on how I'm moving my planets. Realistically I would calculate the orbital velocity and move the planet ahead in its orbit. Since this would require another series of formula I chose to skip this and go with realistic LOOKING rather than MODEL. I take the average orbital speed and figure out how many degrees along the orbit the planet would move in a specific slice of time and update the X and Z coordinates.

Phew, what a mouthful heh ... my sollution was to go for a way to distribute the Y value from aphelion to perihelion. So far the best sollution I found was to add a Sin(deg) to the formula to work in where along the orbit the planet is

Y = (Sin(Degree) * (Tan (Inclination) * Distance))

This matches the orbits up perfectly with their orbit lines. Using Dragon57's Torrus creator code I've created Torruses to represent the orbit lines and have tilted those Torruses to represent inclination. My math isnt far off as the planets ride exactly on top of those "Orbit Lines". The only deviation is the height in which the planets sit above their orbit lines. It appears that the greater the inclination the greater the deviation (Mercury and Pluto have the largest inclination values of 7 and 17 degrees repspectively).

So ... right now I'm plugging in various ideas to work out that deviation. At this point the simplest sollution would be to hard-code-adjust the planet's Y coordinate to place them on the line, which I've actually done and all the planets orbit pretty as pie. However, I still need to solve this deviation because I plan on plugging in the moons of these planets, various Major and Near Earth asteroids, and a few comets or whatever else might come to mind for someone to go explore.

larsalt : Thanks for the link to that sight. I'll definatly post a question there if I cant figure out the right sollution here. I'm not sure if they can help as that site is dedicated to very realistic mathmatics and such and I'm trying to merely LOOK authentic ;) I feel like a guy who draws a stick figure and asks an artist if the proportions of the fingers are correct.

Thanks for the help everyone!