Moon Dance III

  1. Place lamp in center of room on stool, to represent the sun.
  2. Have students form a circle around the lamp
  3. Have students rotate (spin) in place to model the earth rotating daily
  4. Have them face the lamp to represent noon
  5. Have them face away from the lamp to represent midnight. Ask them what can each see at midnight? (call on each student to state what seeing…wall clock, white board, door, other whiteboard)
  6. Have students walk around the lamp to model the earth orbiting the sun, Have them spin while orbiting

-Do they see different things at “midnight” from different positions in the orbit?
-Do we see different stars at midnight during different times of year? (some may know about summer stars and winter stars)
-Seeing different stars at midnight at different times of year is evidence supporting the claim that the earth is REVOLVING around the sun (while ROTATING on its axis)

  1. Now form pairs: one acts as the earth; other as the moon, Start in positions for new moon
  2. Have “earth” spin 7 times AND revolve around the “sun” while moon “moves” to first quarter position. NOTE: The moon at first quarter is located in the orbit of the earth around the sun.
  3. When we look at first quarter moon, we are looking at the ‘place’ in space where we just have been in our orbit around the sun.
  4. How long ago were we ‘there’?

Pose the question, then have partners switch roles and repeat the dance:

  1. “Earth” moves slowly counter clockwise around the sun while also rotating.
  2. The “moon” starts at new moon position (earth: moon: sun: in a line)
  3. As the “earth” spins 7 times while revolving (not too far, 1/52 of way around lamp)
  4. “moon” moves from new to first quarter position.
  5. “earth” looks back to see the “moon” in the “place in space” that the earth just left.

Repeat the question: When you see a first quarter moon in the sky, how long ago were all of us on earth in that “place” in space?
That’s the intriguing question that we are going to answer by using our explanatory model of the phases of the moon and mathematics.
First make a guess: an hour? Several hours? A day? Several days? A week?

  1. What we are trying to find out: How much time, t, it takes for earth to move the distance, d, between the earth & moon
  2. What we need to know: How far the moon is from the earth: about 250,000 miles = d

There are several ways to do this:

Assume circular orbit: How to calculate the circumference of a circle: 2πR
How far the earth is from the sun: about 100,000,000 miles = R
How long it takes the earth to go around the sun: T = one year
Speed of earth = 2πR/T so t = (d)/( 2πR/T) = (d)(T)/2πR
* Another way to think about this:

Time to go part way around a circle = distance part way around the circle
Time to go all the way around a circle distance all the way around the circle

Time to go part way = (distance part way around the circle) (Time to go all around)
around a circle (distance all the way around the circle)

                                    =     (dT)/(2πR)\\
                         =  about  (250000 miles)(one year)     =   (one year)\\
			    2 π (100,000,000 miles)                         2π 400\\

to make the math easy let one year = about 400 days

= about 400 days = about 1 day = about 24 hours = about 4 hours!

      2 π 400                    2 π                      6\\

When seeing a first quarter moon, you are looking where you and everyone else on earth used to “be” in space about 4 hours ago. LOOK ON SUNDAY? WHEN IS A FIRST QUARTER MOON VISIBLE (IF NO CLOUDS)?

( If use 93,000,000 miles and 365 days get about 3 ½ hours)