Catching object in orbit with variable catcher force

physics.rb

#!/usr/bin/env ruby

require 'matrix'

module Drawing
  ZOOM  = 0.5
  SCALE = 40

  def clear
    @@clear ||= %x{clear}
    $>.write @@clear
  end

  def field
    vertial    = " " * SCALE << "|" << " " * SCALE << "\n"
    horizontal = "-" * SCALE << "x" << "-" * SCALE
    $>.write vertial * (SCALE / 2)
    puts horizontal
    $>.write vertial * (SCALE / 2)
  end

  def putc
    object = @object.to_a
    object = object.each_with_index.map do |f, index|
      f = f * SCALE * ZOOM + SCALE
      f /= 2 if index == 0
      f.to_i
    end

    $>.write "\e[#{ object[0] + 2 };#{ object[1] + 1 }Ho"
  end
end

class Simulation
  FPS    = 30
  DETAIL = 5

  include Drawing

  def initialize
    @object   = Vector[  0, 2]
    @velocity = Vector[0.6, 0]
  end

  # Acceleration vector from coil at (0, 0) with strenght 1.
  def coil_accel
    @object / -@object.r
  end

  def run
    loop do
      clear
      puts "Object is at %.2f x %.2f; velocity: %.2f\n" % [@object[0], @object[1], @velocity.r]
      field
      putc

      slowness = 1.0 / DETAIL
      strenght = @velocity.r
      @velocity += coil_accel * strenght * slowness
      @object += @velocity * slowness
      sleep 1.0 / FPS
    end
  end
end

Simulation.new.run

Object is on 2, 0 on a 2d plane. There's a coil in the middle that's pulling the object towards it.

a_anti_object = v_object / - |v_object|
a_coil = a_anti_object * |v_object|
F_coil = |a_coil|

Each second, v_object = v_object + a_coil. Soon it reaches force equilibrium and the object is orbiting the coil.