4.3 Hubble's Laws and the expansion of the universe

• Kepler's Laws

  1. Law of orbits: all planets travel in elliptical orbits with the sun at one focus
  2. Law of areas: a line from sun to planet sweeps out equal areas in equal times
  3. Law of periods: the square of the period of any planet is proportional to the cube of the semi-major axis of one orbit
• Binary Systems

  two objects in mutual orbit will orbit their common centre of mass

  both objects will have the same angular velocity, ω
• Orbits of 2 massive objects

  e.g. binary star system or massive planet and a star

  in this case, centripetal force is provided by the gravitational force of attraction

  the centripetal force of body 1 orbiting about the centre of mass is provided by the gravitational force of body 2
• The Doppler Effect

  if a wave source is moving away from an observer, the observed frequency of the waves is lowered (each peak has further to travel to reach the observer) so the wavelength increases (red-shift)

  if the source is moving towards the observer, the observed frequency increases so the wavelength decreases (blue-shift)
• Hubble's Law

  the velocity of recession of galaxies away from us is proportional to the distance away from us
• if actual density > critical density: expansion of the universe slows to zero, then contracts
• if actual density = critical density: expansion slows to zero at infinite size
• if actual density < critical density: expansion of the universe will continue forever