it works tm

body.lua

@@ -1,21 +1,26 @@
 BodyList = {}
 Body = class(nil,{type=0})
 
-function newBody(x,y,mass,color)
+function newBody(pos,vel,mass,color)
   local o = {}
+
   -- coordinates
-  o.x = x
+  o.x = pos[1] or 0
-  o.y = y
+  o.y = pos[2] or 0
+  o.z = pos[3] or 0
   -- velocities
-  o.vx = 0
+  o.vx = vel[1] or 0
-  o.vy = 0
+  o.vy = vel[2] or 0
+  o.vz = vel[3] or 0
   -- accceleration
   o.ax = 0
   o.ay = 0
+  o.az = 0
   -- mass
   o.mass = mass
   -- color
   o.color = color
+  o.max_distance = 0
 	table.insert(BodyList,o)
 end
 
@@ -23,25 +28,30 @@ function UpdateBodiesAcceleration()
   for n, body in pairs(BodyList) do
     local ax = 0
     local ay = 0
+    local az = 0
     for o_n, other_body in pairs(BodyList) do
       if n ~= o_n then
 
         local dx = other_body.x - body.x
         local dy = other_body.y - body.y
+        local dz = other_body.z - body.z
 
-        local d2 = dx*dx + dy*dy
+        local d3 = dx*dx + dy*dy + dz*dz
+        if math.sqrt(d3)/3 > body.max_distance then body.max_distance = math.sqrt(d3)/3 end
 
         local f =
           (CONST_G * other_body.mass) /
-          d2 * math.sqrt(d2 + CONST_S)
+          d3 * math.sqrt(d3 + CONST_S)
 
         ax = ax + dx * f
         ay = ay + dy * f
+        az = az + dz * f
       end
     end
 
     body.ax = ax
     body.ay = ay
+    body.az = az
   end
 end
 
@@ -49,6 +59,7 @@ function UpdateBodiesVelocity(dt)
   for _, body in pairs(BodyList) do
     body.vx = body.vx + body.ax * dt
     body.vy = body.vy + body.ay * dt
+    body.vz = body.vz + body.az * dt
   end
 end
 
@@ -56,5 +67,6 @@ function UpdateBodiesPosition(dt)
   for _, body in pairs(BodyList) do
     body.x = body.x + body.vx * dt
     body.y = body.y + body.vy * dt
+    body.z = body.z + body.vz * dt
   end
 end

main.lua

@@ -12,37 +12,101 @@ function love.load()
   CONST_S = 0.15
 
   T = 0
+  DT = 1/120
   TIME_SPEED = 0.25
 
+  VIEW = {}
+  VIEW.x = 0
+  VIEW.y = 0
+  VIEW.prints = {}
+
   require "class"
 	require "body"
 
-	newBody(0,0,300,{1,0,0})
+	newBody(
-	newBody(0,100,100,{0,1,0})
+	  {0, 0, 0},
-	newBody(100,0,200,{0,0,1})
+	  {0, 0, 0},
-	newBody(100,100,50,{1,1,0})
+	  40000,
-	newBody(100,200,250,{1,0,1})
+	  {1,0,0}
-	newBody(200,100,150,{0,1,1})
+	)
-
+	newBody(
+	  {10000, 0, 0},
+	  {0, 100000, 0},
+	  200,
+	  {0,1,0}
+	)
+	newBody(
+	  {20000, 0, 0},
+	  {0, 100000, 0},
+	  400,
+	  {0,0,1}
+	)
+	newBody(
+	  {0, 20000, 0},
+	  {-200000, 0, 0},
+	 3000,
+	  {0,1,1}
+	)
 end
 
 function love.update(dt)
-  T = T + dt * TIME_SPEED
+  T = math.floor((T + DT * TIME_SPEED)*1000)/1000
   UpdateBodiesAcceleration()
-  UpdateBodiesVelocity(dt * TIME_SPEED)
+  UpdateBodiesVelocity(DT * TIME_SPEED)
-  UpdateBodiesPosition(dt * TIME_SPEED)
+  UpdateBodiesPosition(DT * TIME_SPEED)
 end
 
 function love.draw()
+  -- center camera on bigger one
+  local vm = 0
+  for n, body in pairs(BodyList) do
+    if body.mass > vm then
+      vm = body.mass
+      VIEW.x = -body.x
+      VIEW.y = -body.y
+    end
+  end
+  local vm = 0
+  for n, body in pairs(BodyList) do
+    if body.max_distance > vm then
+      vm = body.max_distance
+      VIEW.size = math.sqrt(body.max_distance)
+    end
+  end
+
+  love.graphics.setColor(1,1,1)
   -- draw bodies
   for n, body in pairs(BodyList) do
-    love.graphics.setColor(body.color[1],body.color[2],body.color[3])
+    addPrint(body)
-    love.graphics.circle("line",body.x+SCREEN_WIDTH/2,body.y+SCREEN_HEIGHT/2,math.sqrt(body.mass))
   end
+  drawPrints()
   -- draw info
   love.graphics.setColor(1,1,1)
-  love.graphics.print(T)
+  love.graphics.print("x,y: " .. VIEW.x .. VIEW.y .. " size: " ..  VIEW.size .. " T: ".. T)
   for n, body in pairs(BodyList) do
-    love.graphics.print("mass: "..body.mass.." x,y: "..body.x..", "..body.y,0,15*(n))
+    love.graphics.setColor(body.color[1],body.color[2],body.color[3])
+    love.graphics.print("mass: "..body.mass..", x,y: "..body.x..", "..body.y..", vx, vy:"..body.vx..", "..body.vy,0,15*n)
+  end
+end
+
+function addPrint(body)
+  VIEW.print_time = 10
+  table.insert(VIEW.prints,{
+    pos = {
+      x = body.x,
+      y = body.y
+    },
+    mass = body.mass,
+    color = body.color,
+    time = VIEW.print_time
+  })
+end
+
+function drawPrints()
+  for n, print in pairs(VIEW.prints) do
+    love.graphics.setColor(print.color[1],print.color[2],print.color[3],print.time/VIEW.print_time)
+    love.graphics.circle("line",(VIEW.x+print.pos.x)/VIEW.size+SCREEN_WIDTH/2,(VIEW.y+print.pos.y)/VIEW.size+SCREEN_HEIGHT/2,(print.time/VIEW.print_time)*math.sqrt(print.mass)*5/VIEW.size)
+    print.time = print.time - 1
+    if print.time < 1 then VIEW.prints[n] = nil end
   end
 end