Activity 1 - Measuring lunar phase angle and percentage illumination

In this activity, students estimate the illuminated lunar surface area during different phases, calculate phase angles, and explore the Moon's changing appearance throughout a lunar cycle. They use graph paper to measure and analyse these aspects, connecting maths and lunar phases.

Required resources

• Graph paper

• Calculator

• Print-out of Moon phases

Step by step guide

Step 1: Familiarise with Stellarium application

See Activity card What is Stellarium? if not familiar with this application.

Step 2: Supporting students through a mathematical problem

Give students a print-out of the Moon at seven different phases, along with a sheet of graph paper. Teachers can use images online or they can use a zoomed-in screenshot from the Stellarium software (www.stellarium.org).

Suggested phases are:

• three days before First Quarter

• three days after First Quarter

• Full Moon

• three days before Third Quarter

• Third Quarter

• four days after Third Quarter.

In the following image, use days 6, 8, 11, 15, 18, 21, and 25. Teachers should keep in mind (and perhaps ask students if they realise) that the phases in this image are taken from the Northern Hemisphere. They are upside down when viewed from the Southern hemisphere. 

Have students undertake the following:

• label each Moon phase with their Meriam Mir names. 

• place clear graph laminate over the Moon phase image, marking out the illuminated area.

• count the lit boxes to estimate the surface area of the Moon lit during each of these phases. (The smaller the boxes, the more accurate the measurements). 

• calculate the ratio of the lit area of the Moon to the total area of the Moon. 

• answer the question, What is the percentage change from the previous phase calculated? 

• calculate the phase-angle based on the Moon phase, using the data they calculated before. This can be plotted as a Sine graph, where 0 and 180 degrees are the x-axis, and the y-axis shows +90 to -90 degrees, where +90 degrees is First Quarter and -90 degrees is the Third Quarter. 

If the teacher uses screenshots from Stellarium (from a given place and time), the students’ work can be checked by clicking on the Moon during that phase. A drop down list of information is provided. One of them gives the percentage of Moon illuminated. 

Fig. 1 : (Left) Relationship between lunar orbital phase angle (angle between the Moon and Sun) and lunar phase as seen from Earth. (Right) Determining % illumination of the Moon as seen from Earth. This image is courtesy of Nick Strobel at www.astronomynotes.com. Used with permission.