On Mon, Oct 10, 2011 at 4:02 PM, Alaconius <[email protected]> wrote:
> Hi Jonathan, > The nice thing about the "methodology" that I'm attempting, is that it > doesn't require calculus so much as it requires that I be able to determine > the area of a triangle, and solve for the third leg of the triangle in > question. > As such, it only works when the amount of movement is small enough that a triangle is still a reasonable approximation of a pie slice. Once the curvature of the path starts adding a significant amount of area outside of the triangle, your approximation will start having significant error in it. > So. > > Step One: Determine the smallest unit of time that is desired for purposes > of the simulation. > Step Two: Determine the area of orbit itself > Step Three: divide the total area of the Ellipse/orbit by the smallest unit > of time being used in the simulation. > Technically, you'd want to divide the total area of the ellipse by the orbit's period, and then multiply that by your minimum length of time. > Step Four: Determine what the triangle's measurements must be to equal the > area of the triangle for the smallest sweep in step 3. > > Step Five: Determine WHERE the planet is now after the given amount of time > based on the calculations from Steps 1-4. Presto. Planet is in the > approximate vicinity of the third junction of the triangle (the other two > junctions being the sun itself, and the last known position of the planet in > question. > You're going to run into a chicken-and-egg problem with steps four and five, in part because the legs will generally end up having different lengths. THAT was what I was hoping to discover as a solution without having to > actively use calculus outright. I know it emulates derivatives to a degree, > but it doesn't REQUIRE it. :) > The reason why people learn and use calculus is that it makes some problems easier to solve (and it makes other problems possible to solve). This is one such problem. Feel free to try out your triangle approach; far be it from me to stop someone from practicing math. But be warned: it won't be as easy as you think. -- Jonathan "Dataweaver" Lang _______________________________________________ GurpsNet-L mailing list <[email protected]> http://mail.sjgames.com/mailman/listinfo/gurpsnet-l
