----------------------------------- Cervantes Fri Oct 15, 2004 3:39 pm Solar System Simulation ----------------------------------- I've recently been thinking about making a solar system simulation, using Newtonian physics. Could anyone perhaps give me a quick rundown of what I'll need to know (in terms of the physics, not the coding :wink:) ----------------------------------- josh Fri Oct 15, 2004 3:51 pm ----------------------------------- by simulation do you mean a mathematical one or a 2D or a 3D one??? that is a sick idea by the way :D :idea: ----------------------------------- Cervantes Fri Oct 15, 2004 3:58 pm ----------------------------------- 2D, using math. Just the basics, at first. ----------------------------------- josh Fri Oct 15, 2004 4:12 pm ----------------------------------- I might have some books that mention it, I will try and find some info ----------------------------------- Martin Sat Oct 16, 2004 2:15 am ----------------------------------- Newton's equations are wrong. ----------------------------------- Cervantes Sat Oct 16, 2004 6:30 am ----------------------------------- I know, but I still want to use them. Using Newton's equations, don't we end up with circular orbits? And with the General Theory of Relativity, we end up with elliptical oribts? ----------------------------------- Andy Sat Oct 16, 2004 1:41 pm ----------------------------------- just use centripetal acceleration formulas... where MAc=Fg... with Ac=V^2/r or Ac=4pi^2rf^2 ----------------------------------- Martin Sun Oct 17, 2004 1:29 am ----------------------------------- Yeah, ignore friction (it's physics, real world forces don't apply), and just give them an initial velocity perpindicular to the object they're to be orbitting, and it should work. Remember, planets pull on each other ;) And for god's sake, make it OO. ----------------------------------- Cervantes Mon Oct 25, 2004 6:37 pm ----------------------------------- just use centripetal acceleration formulas... where MAc=Fg... with Ac=V^2/r or Ac=4pi^2rf^2 would you mind explaining that a little more please? :? Remember, planets pull on each other "wink: Oh god, I know! I plan on making an initialization section of the program where you can edit the mass of the planets (along with various other things), in which case some funky things could happen.. perhaps with the right mass, the solar system will orbit earth! :lol: Tony showed me a way of creating a gravity field a while back, and it worked well enough for its purpose at that time, but what would it do in a solar system simulation? View.Set ("graphics:600;600,nobuttonbar") var ball : record x, y, dx, dy, GFdist, GFxdist, GFydist, GFangle, GFforce : real end record ball.x := 300 ball.y := 500 ball.dx := 0.5 ball.dy := 0 var gravityfield : record x, y, strength : int end record gravityfield.x := 300 gravityfield.y := 300 gravityfield.strength := 150 const highestspeed := 3 const ballradius := 6 function MathDistance (x1, y1, x2, y2 : real) : real result (((x2 - x1) ** 2) + ((y2 - y1) ** 2)) ** 0.5 end MathDistance setscreen ("offscreenonly") loop cls ball.x += ball.dx ball.y += ball.dy if ball.x > maxx - ballradius or ball.x < ballradius then ball.dx := -ball.dx ball.x += (2 * ball.dx) %move it 2 steps ahead to help prevent sticking end if if ball.y > maxy - ballradius or ball.y < ballradius then ball.dy := -ball.dy ball.y += (2 * ball.dy) %move it 2 steps ahead to help prevent sticking end if %%%%%%%%%GRAVITY FIELD EFFECTS%%%%%% ball.GFdist := MathDistance (gravityfield.x, gravityfield.y, ball.x, ball.y) ball.GFforce := gravityfield.strength * (1 / (ball.GFdist * ball.GFdist)) if ball.x not= gravityfield.x then ball.GFxdist := gravityfield.x - ball.x ball.GFydist := gravityfield.y - ball.y ball.GFangle := arctand (ball.GFxdist / ball.GFydist) else if ball.y > gravityfield.y then ball.GFangle := 90 else ball.GFangle := 270 end if end if if ball.x < gravityfield.x then ball.GFangle := ball.GFangle + 180 end if ball.dx -= ball.GFforce * cosd (ball.GFangle) ball.dy -= ball.GFforce * sind (ball.GFangle) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% if ball.dx > highestspeed then ball.dx := highestspeed elsif ball.dx < -highestspeed then ball.dx := -highestspeed end if if ball.dy > highestspeed then ball.dy := highestspeed elsif ball.dy < -highestspeed then ball.dy := -highestspeed end if drawfilloval (round (ball.x), round (ball.y), ballradius, ballradius, red) drawfilloval (gravityfield.x, gravityfield.y, 11, 11, black) View.Update delay (10) end loop See how the ball goes right, then left, then back? Gravity shouldn't do that! :o or should it? One of those good ol' fashioned "Educational Films" showed that our solar system is not revolving around the centre of the galaxy in a 2D plane, it is revolving around it and going up and down as well. Picture the Milky Way as a disc, totally flat (close enough..) then the sun and our solar system would be, at one point, below that disc, and then, as time passes, it moves up, passing through the disc, continues upwards, reaches its peak, and then comes back down. Kinda like a sine wave. :P Why, oh, why, is that? :eh: ----------------------------------- Tony Mon Oct 25, 2004 6:48 pm ----------------------------------- well you need to give the ball a little push at first to make it spin around the center... ball.dx := 1.75 ball.dy := 0 gravityfield.strength := 200 that works out much nicer :wink: though the code is still not perfect, as you can tell yourself from the resulting animation... Though it was enough back in the day :lol: ----------------------------------- Cervantes Mon Oct 25, 2004 6:51 pm ----------------------------------- Oh, I know, in order to get the orbit it would need that push. But, what I was trying to show, is that, without the push, you'd think it would go straight towards the gravity field, but in fact it wavers back and forth on its way there. ----------------------------------- Catalyst Mon Oct 25, 2004 7:42 pm ----------------------------------- this might be of some interest ----------------------------------- Paul Mon Oct 25, 2004 10:20 pm ----------------------------------- Orbits as I understand them are the result of a warping of spacetime due to a large mass present. Since there isn't friction to slow an object down, and given an initial velocity, the object just follows the simplest path, in an orbit. And wasn't there the gravitational force formula, y'know with the mass, distance and the universal gravitational constant. http://www.earth.ox.ac.uk/~tony/watts/teaching/mendips/2001/Image232.gif It doesn't sound easy though, but you like math ;) and if you look at catalysts program wouldn't the direction and magnitude of the force being exerted on the moving circles have to be somehow balanced with the circle's initial velocity to have an orbit? ----------------------------------- Cervantes Tue Oct 26, 2004 5:53 pm ----------------------------------- What is the universal gravitational constant? And, catalyst, is what you posted [url=http://www.compsci.ca/v2/viewtopic.php?t=3242]this only open source instead of .exe? My winRAR hates me, and gives me annoying error messages whenever I try to extract something. Could you, or anyone willing, perhaps send it to me as a winzip? I don't want to get offtopic here, but does anyone know where to get a free full version of winRAR (not a trail version)? ----------------------------------- Andy Tue Oct 26, 2004 6:17 pm ----------------------------------- 6.67300 × 10-11 m3 kg-1 s-2 kepler discovered that ----------------------------------- Catalyst Tue Oct 26, 2004 7:32 pm ----------------------------------- yes it is open source that heres a zip :) ----------------------------------- zylum Tue Oct 26, 2004 11:17 pm ----------------------------------- hey thats pretty cool... but over 400 lines? here's a simpler gravitation class i made: class SYSTEM export ADDBODY, DRAWSYSTEM, UPDATEBODY, UPDATEBODIES, SIMULATE, CHANGEG type BODYDATA : record _X : real _Y : real _VX : real _VY : real _AX : real _AY : real _MASS : real _COLOR : int end record var BODY : flexible array 1 .. 0 of BODYDATA var _G := 3.0 fcn GETANGLE (x1, y1, x2, y2 : real) : real var dx, dy, ratio, angle : real dx := x1 - x2 dy := y1 - y2 if dx not= 0 then ratio := dy / dx else ratio := dy / 0.00000001 end if angle := arctand (abs (ratio)) if dx < 0 then angle := 180 - angle end if if dy < 0 then angle := 360 - angle end if result angle end GETANGLE proc CHANGEG (g : real) _G := g end CHANGEG proc ADDBODY (x, y, vx, vy, mass : real, clr : int) var i := upper (BODY) + 1 new BODY, i BODY (i)._X := x BODY (i)._Y := y BODY (i)._VX := vx BODY (i)._VY := vy BODY (i)._MASS := mass BODY (i)._COLOR := clr BODY (i)._AX := 0 BODY (i)._AY := 0 end ADDBODY proc UPDATEBODY (i : int) BODY (i)._AX := 0 BODY (i)._AY := 0 for j : 1 .. upper (BODY) if i ~= j then BODY (i)._AX += ((_G * BODY (i)._MASS * BODY (j)._MASS) / ((BODY (i)._X - BODY (j)._X) ** 2 + (BODY (i)._Y - BODY (j)._Y) ** 2)) * (cosd (GETANGLE (BODY (j)._X, BODY (j)._Y, BODY (i)._X, BODY (i)._Y))) / BODY (i)._MASS BODY (i)._AY += ((_G * BODY (i)._MASS * BODY (j)._MASS) / ((BODY (i)._X - BODY (j)._X) ** 2 + (BODY (i)._Y - BODY (j)._Y) ** 2)) * (sind (GETANGLE (BODY (j)._X, BODY (j)._Y, BODY (i)._X, BODY (i)._Y))) / BODY (i)._MASS end if end for BODY (i)._VX += BODY (i)._AX BODY (i)._VY += BODY (i)._AY BODY (i)._X += BODY (i)._VX BODY (i)._Y += BODY (i)._VY end UPDATEBODY proc UPDATEBODIES for i : 1 .. upper (BODY) UPDATEBODY (i) end for end UPDATEBODIES proc DRAWSYSTEM for i : 1 .. upper (BODY) drawfilloval (round (BODY (i)._X), round (BODY (i)._Y), ceil (sqrt (BODY (i)._MASS)) + 1, ceil (sqrt (BODY (i)._MASS)) + 1, BODY (i)._COLOR) end for end DRAWSYSTEM proc SIMULATE var x, y, b : int loop mousewhere (x, y, b) UPDATEBODIES DRAWSYSTEM View.Update exit when b = 1 cls end loop end SIMULATE end SYSTEM setscreen ("offscreenonly, graphics:max;max, nobuttonbar") var SS : ^SYSTEM new SYSTEM, SS SS -> ADDBODY (maxx / 2, maxy / 2, 0, 0, 5000, 7) SS -> ADDBODY (maxx / 2 + 400, maxy / 2, 0, 5, 20, 7) SS -> ADDBODY (maxx / 2 + 420, maxy / 2, 0, 6.5, 1, 7) SS -> SIMULATE ----------------------------------- Tony Wed Oct 27, 2004 12:28 am ----------------------------------- your object representation is quite a bit off... based on mass, radius does not equate to ceil (sqrt (BODY (i)._MASS)) + 1 :? density of a 3D object should be considered. V = (4/3)(pi)(R^3) (for the sphere) where V could be replaced by _MASS (assuming same density for all objects)... thus we get R = (3*pi*_MASS/4)**(1/3) I'd recommend calculating that value just once and keeping it in object's record as well :wink: ----------------------------------- Cervantes Wed Oct 27, 2004 7:49 am ----------------------------------- Ahh, but the densities are not all the same. Earth has the highest density, Saturn has the lowest. I was thinking of hardcoding the values of each planets density and radius and mass. Thanks very much for the zip catalyst, and also thanks to zylum. This will indeed be a complex program for me to make, but I'll try my best :) ----------------------------------- wtd Wed Oct 27, 2004 10:21 pm ----------------------------------- I like your use of data structures, but if I may suggest... there are lots of places where you have x, y pairs. Create a Point or Coordinate, or Vector record type and group them together.