Understanding Moon Phases

Pat Thompson

January 12, 2021

My grandson, Quino, wondered why the moon "changes shape". I made this animation (using PacificTech Graphing Calculator) as a didactic object. Our discussions had a number of interesting aspects -- interpreting a 2-D display of 3-D phenomena, Piaget's decentering (adopting perspectives other than your own), and frames of reference to name a few. I'd be delighted to see others probe students' or teachers' thinking in regard to this animation (or something of your own design).

NB1: I simplified the simulation in a number of ways: Distances are not to scale, Moon orbits Earth four times per year, Earth rotates 5 times per Moon orbit, and the inclination of Moon's orbit to Earth's equator is 30 degrees instead of 5.1 degrees.

NB2: You can download the videos by right-clicking on them, or click the download link at the end.

This first video shows the moon orbiting Earth as Earth orbits Sun.

This second video shows the same as above, with how Moon looks from Earth's dark side during Moon's orbit.

Here is an augmented reality view of the animation recorded off the screen of my iPad Pro. I recommend you play it at full screen, then scroll through it with the play bar.

Here are five files.

• The 1-view video file.
  
  
• The 2-view video file.
  
  
• The augmented reality video file.
  
  
• The Graphing Calculator file (GC is by PacificTech) that generates this video. It has sliders to vary several parameters, including the number of Moon orbits per year and the number of Earth days per year. You can also rotate the axes to change your position relative to the Sun-Earth-Moon system. .
  
  If you don't have PacificTech's Graphing Calculator you can download a player at their site.
  
  
• A PDF file with the mathematics behind this animation in case you want to implement it in Geogebra or Mathematica.