BodyList = {}
Body = class(nil,{type=0})

function newBody(x,y,mass,color)
  local o = {}
  -- coordinates
  o.x = x
  o.y = y
  -- velocities
  o.vx = 0
  o.vy = 0
  -- accceleration
  o.ax = 0
  o.ay = 0
  -- mass
  o.mass = mass
  -- color
  o.color = color
	table.insert(BodyList,o)
end

function UpdateBodiesAcceleration()
  for n, body in pairs(BodyList) do
    local ax = 0
    local ay = 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 d2 = dx*dx + dy*dy

        local f =
          (CONST_G * other_body.mass) /
          d2 * math.sqrt(d2 + CONST_S)

        ax = ax + dx * f
        ay = ay + dy * f
      end
    end

    body.ax = ax
    body.ay = ay
  end
end

function UpdateBodiesVelocity(dt)
  for _, body in pairs(BodyList) do
    body.vx = body.vx + body.ax * dt
    body.vy = body.vy + body.ay * dt
  end
end

function UpdateBodiesPosition(dt)
  for _, body in pairs(BodyList) do
    body.x = body.x + body.vx * dt
    body.y = body.y + body.vy * dt
  end
end