Build
and Operate an Analog Moon Computer
designed
by Nancy Whitman (Creswell
Middle School),
from
Moon lessons by Rick Kang (Friends of Pine Mountain Observatory)
Explanation of terms: Computer:
has input, process, output
Analog:
I/O in continuous increments (not discrete steps)
OBJECTIVE: Relate Moon Phase, Location of Moon in Sky,
Time of Observation to gain better
understanding of Moon’s motion and why we view phases.
GRAPHICS: We'll try to scan in and post an image of our prototype. Meanwhile, check out the digital version of the concept at the Nebraska Astronomy Applets Project (NAAP) site, this will give you an idea of what the cardboard device looks like. We found the NAAP version AFTER we had designed and built ours, hats off to NAAP, we like their additional 3D features, but we still really like our gadget as it seems to give the students more of a tangible connection to the Sun-Earth-Moon system as it's literally in-hand. MATERIALS:
White, orange, blue, and yellow cardboard, small brass “brads” (folding tabs),
gluestick, ruler, scissors, compass.
ASSEMBLY STEPS: 1.
Cut out the white cardstock baseplate, 8.5x11 inches (can be slightly narrower
and shorter).
2.
Cut out a yellow disk for Sun, approximately size of tracing around a penny.
3.
Cut out an orange disk for Time, approximately 3 inches wide, (use a compass to
trace circle on the cardstock.)
4.
Cut out a blue disk for the Earth, approximately 1.5 inches wide, (use a
compass to trace circle on the cardstock.)
Leave a small “nub” along the edge, this will represent “Mount Nose”,
as a pointer to reference the time. If
you draw several Earths so that their circles touch, you’ll have 4 nubs
automatically generated by the space between the circles.
5.
Glue the Sun disk at top of baseplate, about a half inch down from top edge,
and midway between the vertical 11-inch long sides. Write SUN on the disk.
6.
Use compass to draw a large circle for the Moon’s ORBIT, at the opposite end of
the baseplate from Sun, leaving a .5-inch border at sides and bottom of
baseplate. DON’T cut out!
7.
Glue TIME disk centered within this drawn circle.
8.
Carefully make small hole in center of Earth disk with the brass brad, so that
Earth disk can be rotated around the brad tabs snugly without snagging the
brad.
9.
Carefully make small slit in middle of
TIME disk, through baseplate, so that brad tabs can be pushed through
and then opened on opposite side of baseplate, securing EARTH to other two
layers, yet leaving EARTH disk free to be rotated. (Don’t glue EARTH down!)
Couple
of construction hints from experience:
After
cutting out the rectangular baseboard, if students can use compass to draw
large circle at one end to represent orbit of Moon (leaving about 1/4 inch
border on the three sides near edge of cardboard and clearly marking
centerpoint where pin of compass was, this will speed construction of the
"sandwich" (adding Clock circle and Earth circle). They also need to mark centerpoints on the
clock and the Earth circles (these marks will facilitate proper alignment of
the circles when brad is pushed through).
Please try to have students leave a small "nub" on perimeter
of Earth disk to represent "Mount
Nose" observation
location. If a student accidentally cuts
this off and only has a circle, that's OK, they can draw the peak location
toward edge of disk.
10.
Now we'll draw in the Moon in a variety of orbital positions: Draw half-inch diameter small circles along Moon orbit circle in eight
locations: Top, bottom, both sides (quarter of the way around), and then
exactly halfway between each of these “quarter points” along the orbit circle. These will show the orientation of Moon's sunlit portion from a vantage point way above Earth's north pole: Divide each Moon circle in half across each circle with respect to the SUN, and
since the actual Sun is so distant, draw the dividing line (the Terminator)
parallel to bottom of baseplate and in same crosswise orientation for each of
the eight small Moons. Shade in the
shadow half of each Moon, the side away from Sun.
Note how the Moon appears identical from this viewpoint, no matter where the Moon is in its orbit. An additional factor must account for why we see phases from Earth:
11.
Now draw a second corresponding set of half-inch diameter Moon circles just to the inside side of each of
the original Moons, separated by about ¼ inch from original Moons, and lined up
radially with center of Earth. These duplicate
Moons will be shaded to show APPEARANCE of that “phase” FROM EARTH, as you'd actually view the Moon from your location on Mount Nose on Earth. Because of this shift of perspective, these Moons will look different than the top-down views of their associated Moon with two exceptions, the Quarter phases. Example:
Full Moon at very bottom position of baseplate, opposite Sun, will
remain as just the outline, NO shading.
New or Dark Moon at middle of baseplate will be completely shaded, as is
between Sun and Earth. Quarter phases at
outside positions will be exactly same orientation as their associated Moons
show to outside of each of these circles.
Crescent
Moons at two positions between Dark and Quarter, will be shaded except for
crescent sliver that’s illuminated toward side of Moon closest to Sun, right
side on left Moon, and left side on right Moon.
The two Gibbous Moons between Quarter and Full, will have slim crescent
shaded shadows on sides facing “inward” toward orbit. LABEL each phase adjacent to pairs of Moons,
add terms Waxing to the two midway phases on left side with Sun at top and
Earth at bottom orientation of baseplate (Waxing Cresent, First Quarter, Waxing
Gibbous), and Waning on right side, Waning Gibbous, Last Quarter, and Waning
Crescent just before New (Dark) Moon.
Label the big circle, Moon’s Orbit. Draw a few arrows along orbit circle indicating direction Moon orbits Earth as viewed from this perspective above North Pole (counterclockwise!).
(We know this orbital pattern and phases from nightly sequence of
observations that show the changes of position in sky and phase, and the
cyclical (repeating) nature. Having
students do a “Moon Log”, sketching the Moon nightly/daily from when the Waxing Crescent first shows through Full
Moon, even tracking Moon through Waning
Crescent, will provide data and potentially a
richer learning experience.)
12.
Mark an Observer on the Earth disk: If you have a nub on your Earth circle, this is the observation place, Mount Nose. If not, draw
and shade in a wedge pointing outward to rim of Earth anywhere along disk, each leg of wedge about ¼ inch long. This is “Mount Nose”,
where you’ll be observing the sky from!
In either case, between the slopes (sides) of Mount Nose, draw
a tiny circle, this is the top of your head tipped way back looking skyward, so add a pair of eyes,
you can add brows and orbs so that the observer appears to be looking outward
from Earth, and add a smiling mouth below the base of Mount Nose, inside the
face circle. Complete the Stick Figure
drawing on the Earth disk: draw the body extending down to the brass fastener,
legs and feet extended below fastener.
The figure faces AWAY from you, you're looking at the observer's back side as he/she stands atop Mount Nose gazing skyward. Use a straight edge to draw a line crossways across the Earth disk
through top of brad, perpendicular to torso of figure, to represent the
Observer’s outstretched arms, perhaps detail in the fingers at the outside
edges near rim of Earth. LABEL left hand
EAST and right hand WEST as you view upright back side of figure, these represent the
observer’s HORIZONS. Add the word,
“Rise” near EAST, and “Set” near WEST. These
keys are very IMPORTANT when we use device to determine position of Moon in
sky, high overhead above Mount
Nose, or lower toward
eastern or western horizons, or perhaps below horizons, not visible at all! Add a curved arrow BELOW your stick figure's feet, on opposite side of brad from head, to
remind you which way the Earth rotates (can you figure this out? W to E)
Work through Sunrise, Noon, Sunset.
13.
Put clock times on Time Disk (larger cutout circle that's glued to baseboard, but under the Earth circle): Use Mount
Nose nub or wedge to orient Earth at appropriate clock times at Mount Nose
(relative to SUN). When Observer at Mount Nose
sees Sun highest in the sky (pointing directly at Sun), draw tick mark on Time Disk and write Noon on baseboard just beyond tick. Spin Earth halfway around.
With
your Mount Nose observation point now opposite the
Sun, make a tick mark on the Time disk, and label that tick Midnight. Then make tick marks on Time disk to both
sides, halfway between Noon and Midnight ticks, these new marks will be 6 AM
and 6 PM, label CORRECTLY, considering sequence relating to Earth’s rotational
direction that you’ve already marked on your Earth.
Doing a kinesthetic model as you work through this helps.
YOUR
COMPUTER IS COMPLETED!
You
can now relate Moon’s position in sky to it’s phase, to the time you’ll see it
there. Know two factors and you can
determine the third!
TEST
DRIVE: 1.a.
What time does the Full Moon rise?
Solution:
Locate Full Moon on Moon orbit circle, objects rise in East, so line up
Observer’s East (left) hand pointing toward Full Moon. Read the Time above Observer’s head, 6 PM.
b.
What time does the Full Moon “culminate” (get highest in sky)? Rotate your
Earth until Full Moon is directly over Mount Nose,
read the Time, 12 midnight.
c.
What time does the Full Moon set? Sets
in the west, so rotate Earth so West (right) hand and horizon of observer
points directly at Full Moon, read time overhead, 6 AM. So, Full Moon is technically the only phase
that’s up all night, rising at sunset and setting opposite the Sun at sunrise!
2.
You’re out at 3 AM and see the Moon high in the sky, what phase would the Moon
be?
Solution: Dial 3 AM over Mount Nose
(halfway between midnight and 6 AM.)
High in the sky is directly above Mount Nose,
what phase is closest to that position?
Waning Gibbous.
3.
You’re out at 7 PM and are looking for a Crescent Moon. Where do you look in the sky?
Solution: Dial 7 PM over Mount Nose
(a sixth of the way beyond 6 PM toward midnight.) Is there a Crescent Phase anywhere on the
Moon orbit circle, between the eastern and western horizons of your Mount Nose
location? The Waxing Crescent is over toward the
West.
Notice
that earlier in the afternoon, prior to 6 PM, you might also be able to view a Waning Crescent
very low in the West, “leading” the Sun, setting before sunset. (be careful trying to view thin Crescents
close to Sun as accidentally viewing Sun particularly in optical devices can
easily damage the device and cause instant blindness to you!)
------------------------------------------------------------- Here
are some additional tips for a complete lesson on Moon Phases:
One key step is to
project Sun-Earth-Moon software (see link for this free download under our
Online Resources) and place us in back of the Earth at small angle above, so we
could view Moon's orbit circle from perspective fairly similar to what students
would draw onto the baseplate around Earth, with Sun at distance. Had them glue Sun on, then draw Moon Orbit
circle at opposite end of baseplate, then glue on Time disk and affix Earth
disk with the brad. I then walked them
through the Sun-Earth-Moon scale model visualization so they wouldn't have any
misconceptions about the relative sizes and distances since their models are
not to scale. (Mini Basketball Earth, Tennis Ball Moon 25 feet away, 120 foot
diameter Sun 2 actual miles away from Earth/Moon!)
Next, we did the
ping pong ball manipulative, so that students had opportunity to visualize
phase changes better. (ping pong balls
that have ½ side painted black with poster paint to simulate shadowed side of
Moon, small hole drilled in bottom of ball for students to insert pencel to
hold their “Moon on a stick” out at arms’ length, their head is Earth…Use a
real or symbolic Sun in middle of classroom…You will need to EMPHASIZE that
sunlit side of Moon always needs to point directly toward Sun as Moon is moved
around Earth, students need to slightly twirl their Moons to do this! This is the most common error/problem when
doing this activity…Using smooth unpainted white Styrofoam spheres outdoors
with real Sun is much more dramatic!
We were then ready
to draw the eight Moon pair circles (orientation to Sun matched with
perspective from Earth). We again used
SEM software to show the dynamic phase changes (view from above North Pole of
Earth, which matches our analog device, and also gave me great opportunity to
demonstrate in 3D using a ping pong ball literally held up to projected orbit
of Moon on screen on wall. I answered a
number of questions from students about why various phases appeared the way
they did, and how the phase appearance related to the actual condition of
Moon's illumination at that location. We
started to have "aha" moments here.
Students were next
asked to shade in and label the eight Moon pairs. The reaction of many of the students was
significant, they readily began to see the correlation of Moon position to
phase displayed, and although were at first very baffled, soon had a lot more
"aha" moments. Almost all of
the students were very engaged and successfully completed their computers. This combination of Stellarium, then SEM plus
manipulatives plus scale model, culminating in the analog computer may be the
way to cement the Moon concepts, I'd really like to see an assessment of this
group shortly.
I've done this project with about 12 different classes since last Spring, from grades 3 through 12, mostly Middle and High School. Most lessons have gone very smoothly, having parts precut and large Moon orbit circle predrawn on baseplate is useful.
One major misconception that can surface is that some students think the Moon goes around it's entire orbit each night, they need to realize that the Moon's orbit takes a "Moonth", so each day/night, the Moon moves only a small fraction of the way around, although Earth HAS ROTATED one complete rotation within the Moon circle, thus bringing Mount Nose back to the Moon each day/night to observe the incremental shift of the Moon. A suggestion was made by a teacher to provide a circular mask shaped like a pie with a small slice cut out, to overlay the whole Earth and Moon area, thus displaying only the sector where the Moon would be for the night or day of interest. If you try this, I'd recommend to do it as a separate piece, not part of the sandwich, as the overview of the entire system is part of the strength of the model.
Track
the Moon through an entire cycle starting at New Moon, viewing actual Moon and
comparing to your Moon computer.
