When you are ready heres some more code which demonstrates 2d gravitation in free space. its not entirely accurate as Ive played with the formulii to give pleasing results (IE it doesnt take half a year for a satelite to orbit a gravity well)
its based on the principle that the force on an object from a well varies inversely proportional to the distance of the object from the well. again its code ive posted before but a long time ago now.
Interestingly enough this program also displays chaotic behaviour in that small changes to the satelites starting position/angle can create radical changes in its flight path. in the code I have given the 2 satellites do not interact with each other. they are only there so you can compare different settings. basically this is a toy.
its based on the principle that the force on an object from a well varies inversely proportional to the distance of the object from the well. again its code ive posted before but a long time ago now.
Open in online IDE;A simple program to demonstrate 2d gravitational physics ;the physics is not entirely accurate but more to the point ;it looks acceptable and produces nice patterns. ;incidentally this system also displays chaotic behaviour ;in that a small change in a satelites starting paramaters ;produces a large change in its path trail as you will see by the ;two demonstration satelites having a difference of 0.1 degree in their ;start angle and everything else identical Type satelite Field x#;statelite position x and y coord Field y# Field dx#;speed of the satelite in x and y dir Field dy# Field fx#;forces acting on the satelite in x and y directions Field fy# Field mass; mass of the satelite Field pathStart.pathpoint Field colour ; colour of path Field crashed End Type Type well Field gravity#; gravitational force of the well Field x#; wells xy coords Field y# End Type Type pathpoint Field n.pathpoint Field x Field y End Type Graphics 800,600,32,2 Global period# Global pathLength Global maxLength = 1024 Global count = 0 Global maxmag#=0 Global this_time=MilliSecs() Global Last_time=MilliSecs() ;make a satelite And set it with some initial values a#=110 s.satelite =New satelite s\x = 100 s\y = 150 s\dx=1*Sin (a) s\dy=- 1* Cos (a) s\mass = 5 s\colour=$FF0000 a2#=135 s2.satelite =New satelite s2\x = 150 s2\y = 150 s2\dx=1* Sin (a2) s2\dy=-1* Cos (a2) s2\mass = 4 s2\colour=$00FF00 ;create a gravity well w.well= New well w\x=400 w\y=300 w\gravity=90000 ;And another For good measure w2.well= New well w2\x=200 w2\y=300 w2\gravity=90000 ;And another For good measure w3.well= New well w3\x=350 w3\y=300-100*(Sqr(3)/2) w3\gravity=90000 SetBuffer BackBuffer() ;this is the time passed in each program loop ;idealy you would set this each loop using some realtime clock code ;but for simplicity here we will hard code it to 10 milliseconds period=0.01 While Not KeyHit(1) For s.satelite=Each satelite s\fx=0 s\fy=0 resolveForces(s,w) resolveForces(s,w2) resolveForces(s,w3) updateSatelite(s) ;dampSatelite(s) drawSatelite(s) Next drawWell(w) drawWell(w2) drawWell(w3) makepath() drawpath() If crashed And (First satelite)=Null Then Exit count=count +1 Text 10,10,period Flip Cls Last_time=this_time this_time=MilliSecs() ;calc the period To the nearest 10 ms period=(this_time-Last_time)/(10)/Float(100.0) Wend End Function dampSatelite(s.satelite) s\dx=0.999 * s\dx s\dy=0.999 * s\dy End Function Function resolveForces( s.satelite, w.well) ;the force on the satelite always works towards the well ;the force on the satelite is proportional to 1/r^2 ;where r is the distance between the satelite and the center of gravity ;find the wells position relative to the satelite Local dx#=w\x-s\x Local dy#=w\y-s\y ;calc r^2 Local r2#=((dx)^2+(dy)^2) ;calc r Local r#=Sqr(r2) ;calc mag of force at the satelites position Local f#= w\gravity * r2^-1 ;resolve in the x and y s\fy=s\fy+f*(dy/r) s\fx=s\fx+f*(dx/r) End Function Function updateSatelite(s.satelite) If s\crashed=1 Then Return ;apply newtons laws in x and y directions ;incrementing the satelites position proportional to the period dx#=s\dx ;newtons law f=ma re-arranged to be a=f/m ax#=s\fx/s\mass ;newtons law v=u+at s\dx=dx+ax*period dy#=s\dy ay#=s\fy/s\mass s\dy=dy+ay*period s\x=s\x+s\dx s\y=s\y+s\dy For w.well=Each well Local x=s\x Local y=s\y Local x1=w\x Local y1=w\y If ((x-x1)^2+(y-y1)^2)<25 Then s\x=w\x s\y=w\y s\dx=0 s\dy=0 s\crashed=1 End If Next End Function Function drawSatelite(s.satelite) ;just a dot will do mag#=Sqr(s\fx^2+s\fy^2) Plot s\x,s\y Text s\x,s\y,"*",1,1 l=50*(mag/80) ;If Not s\crashed Then Line s\x,s\y,s\x+(l*(s\fx/mag)),s\y+(l*(s\fy/mag)) End Function Function drawWell(w.well) ;a nice + to mark the center of gravitation Line w\x-5,w\y,w\x+5,w\y Line w\x,w\y-5,w\x,w\y+5 End Function Function makePath() If count = 3 For s.satelite = Each satelite If Not s\crashed Then p.pathpoint=New pathpoint p\n=s\pathStart p\x=s\x p\y=s\y s\pathstart=p pathLength=pathLength+1 End If Next count = 0 End If End Function Function drawPath() LockBuffer BackBuffer() For s.satelite=Each satelite idx=0 p.pathpoint=s\pathstart If p<> Null While p\n<> Null idx=idx+1 If p\x>0 And p\x<800 And p\y>0 And p\y<600 c=255*(maxlength-idx)/maxlength col=c Shl( 16) + c Shl(8) + c WritePixelFast p\x,p\y,s\colour And col End If p=p\n Wend End If If pathLength>maxLength Then Delete First pathPoint End If If pathlength>maxlength Then pathlength=pathlength -1 Next UnlockBuffer BackBuffer() End Function
Interestingly enough this program also displays chaotic behaviour in that small changes to the satelites starting position/angle can create radical changes in its flight path. in the code I have given the 2 satellites do not interact with each other. they are only there so you can compare different settings. basically this is a toy.