# Forces of Nature: Using Earth and Planetary Science for Teaching Physical Science

## Gravity: A Relatively Heavy Subject

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## Lesson 2. Writing an equation to predict the moon phase

### Objective

Students will use data to derive an equation to determine moon phase as the percentage of the moon illuminated on any given day.

### Procedure

Using data from the U.S. Naval Observatory students will use a graphing calculator such as a TI-83 to make tables of data. Students will plot the data in a graph. From the data students will run a regression to write a sinusoidal equation.

Go to http://aa.usno.navy.mil/cgi-bin/aa_moonill2.pl to obtain data. Assign a different month of data for each student to input. Have the students put in data for every other day, such as first, third, fifth day of each month. L1 should contain the day and L2 should contain the percentage illumination of the moon.

Have students use STAT PLOT to plot a graph of their data. Have students run a TRIG regression of the data. Have students insert the regression equation into the “
*
y
*
equals” screen in order to graph the equation. Have students graph the equation.

As students are moving through each of the preceding steps a student, or the instructor, should also be using the TI-presenter. Once the graphs are successfully displayed there should be a discussion centered on the following questions:

- What is different about the graphs and their equations?
- What is the same about the graphs and their equations?
- What is the amplitude of each equation?
- What is the frequency of each equation?
- Why is there a phase shift?