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Paper Plate Education
"Serving the Universe on a Paper Plate"

Activity: Plate-a-tarium

Ultimo_plate_2.jpg (22802 bytes) Ultimo_inner_plate.jpg (12507 bytes)

The Plate-a-tarium is the ultimate plate model that shows the sun and planets in the solar plane relative to a fixed earth.  The Plate-a-tarium depicts features of the celestial sphere such as the celestial equator and ecliptic; indicates real time positions of the planets and the zodiac in both azimuth and altitude; and illustrates rising and setting position of the sun and planets for any given date.

Intersect Two Trays

Dsc00005.jpg (529310 bytes) In the sample Plate-a-tarium constructed here, an outer black plastic tray represents the celestial equator and an inner black plastic tray represents the solar plane.  The edge of the solar plane defines the ecliptic.   Cut out the central portion of the large tray so the smaller tray wedges snugly inside the opening.  Punch a small hole through the center of the inner tray.
The plastic trays provide rigidity.  As an alternative, you can simply cut a circle out of a cardboard cake tray, leaving the two hinge points uncut and reinforcing them with tape.  The cake tray model, however, will not hold up as well with all of the handling you can expect for your Plate-a-tarium.
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To reinforce the intersecting hinge points on the black plastic trays, you will soon tape a rigid wire to the backsides of the large tray.  You will run the wire through holes on the edge of the small tray so the wire rests across the top at the smaller tray's diameter.
Dsc00009.jpg (544638 bytes) But first, midway on the wire affix a sphere to represent the earth.  In this example the wire goes through the center of a blue bead, wraps around and up to suggest a north pole axis of the earth, and then goes back through the hole in the bead.  The earth should be centered over the small hole on the inner tray.
Dsc00008.jpg (542055 bytes)  Secure the trays so that the inner tray (solar plane) is inclined 23 degrees to the outer tray (celestial equator).  The backbone wire can help keep the trays separated.  Bend the wire around the bead so the north pole axis is perpendicular to the large outer tray (celestial equator). 
Dsc00007.jpg (574067 bytes) The wire representing the north pole will then appear inclined 23 degrees to the inner plate.  The earth should be floating above the hole in the inner tray.

Make a Solar System Plate

Dsc00011.jpg (606518 bytes) On a separate smaller plate or tray, draw the visible planets in orbit around the sun for their current positions.  This can be done several ways.  For example, you can plot the planet directions using Right Ascension data, or you can draw the familiar orbits around the sun and copy their respective positions from a current source. 

The following excerpt from the Planet Pointer II activity describes how to construct an accurate plate with the earth at the center of the plate (a requirement of that activity).  For simplicity you may prefer to have the sun at the center of the plate.  Either way works for this activity, though a hole will go through the earth, not the sun, in all of these heliocentric drawings.

Excerpt from Planet Pointer II:

 Planet_Pointer_RA_label_2.jpg (11357 bytes) Planet_Pointer_RA_label.jpg (9952 bytes) Around the perimeter of a plate, mark 24 hours of right ascension counterclockwise.  The center of the plate represents earth.

Planet_pointer_arrowed.jpg (13448 bytes) Planet_pointer_arrowed_zoom.jpg (13373 bytes) Plot the positions of the planets and the sun by extending lines outward from the central earth to the right ascension value.  The R.A. values can be found under "Planet Summary Data" and at "Sun and Moon data for today" at http://www.heavens-above.com...Label the lines with planet names or symbols.  Extend the sun line to the edge of the plate...

Planet_Pointer_orbits_and_sun_plate.jpg (13323 bytes) Planet_Pointer_orbits_and_sun.jpg (15455 bytes) An alternative method is to draw the earth at the center of the plate in orbit around the sun...  From the earth, extend lines outward through the planets (in their current orbital positions) toward the perimeter of the plate.  Notice that the inferior planets can be in two different positions in their orbit and still yield the same line of sight.  Label the lines with planet names or symbols.  Again extend the sun line to the edge of the plate... The resulting lines should be identical to the first method that uses right ascension.

Dsc00012.jpg (618282 bytes) The solar system plate shown at left shows a simple version.  From the earth, draw a bright yellow sun line outward through the sun to the edge of the plate.  As shown above, you may choose to draw lines from the earth through the planets as well.
Dsc00013.jpg (483980 bytes) Punch a hole through the earth.
Dsc00014.jpg (613597 bytes) Slide the solar system plate under the wire and align the hole in the inner tray with the hole in the earth.  Secure the planet plate to the inner tray with a paper fastener.  If you drew your orbits with the sun centered on the plate, when you spin the solar system plate it will rotate off-centered (and that is okay).  The blue earth should be floating directly above the paper fastener (not visible here).


Label the Ecliptic 

Vernal sunset 2.jpg (17267 bytes) Hold the outer tray as you would a steering wheel so that the top of the inner tray is above the plane of the outer tray, and the bottom of the inner tray is below the plane of the outer tray, as shown at left.    Rotate the solar system plate so the sun line is pointing to the right hinge.  That is, the sun line is along the wire on the right side.  You may label the edge of the inner tray "Vernal Equinox," for the sun coincides with the celestial equator on the vernal equinox.
Still holding the outer tray as in the previous step, rotate the solar system plate counterclockwise so the sun line points to the top of the inner tray.  You may label this point "June solstice."   The sun has moved 90 degrees left, or east, on the ecliptic to a point 23 degrees above the celestial equator (outer tray).
Now rotate the solar system plate counterclockwise 90 degrees so the sun line is pointing to the left hinge.  That is, the sun line is along the wire on the left side.  You may label the left edge of the inner tray "September  Equinox," for the descending sun coincides with the celestial equator on the September equinox.
Lastly rotate the solar system plate counterclockwise 90 degrees so the sun line points to the bottom of the inner tray.  You may label this point "December solstice."   The sun has moved on the ecliptic to a point 23 degrees below the celestial equator (outer tray).
Another benefit of using the rigid black tray is that the decorative scallops along the perimeter of the inner tray is conveniently divided into 24 sections.  Therefore each scallop represents one hour of right ascension, or 15 degrees. You may easily label the boundaries of the zodiacal constellations on the edge of the inner tray with the vernal equinox being the 0/24 hour point or the zero degrees point.  The sun line will then point to the zodiacal constellation through which the sun is traversing.

The table from the Defining the Zodiac activity lists the boundaries of the zodiac along the ecliptic:

Degrees            R. A.                         Sun moves into Constellation

000o  00'       00:00:00                  Vernal Equinox in Pisces, 1st of Spring!  
028o  42'       01:46:40                  Aries  
053
o  21'       03:24:05                  Taurus  
090o  09'       06:00:35                  Gemini  
118o  00'       08:00:15                  Cancer  
138o  03'       09:22:00                  Leo  
173
o  51'       11:37:30                  Virgo  
180
o  00'       12:00:00                  1st of Autumn!  
217
o  48'       14:21:45                  Libra  
241o  00'       15:55:30                  Scorpius  
247o  45'       16:23:30                  Ophiuchus (OFF ih YOU cuss)  
266o  12'       17:43:35                  Sagittarius  
299
o  39'       20:07:20                  Capricornus  
327
o  30'       21:58:40                  Aquarius  
351o  37'       23:29:00                  Pisces

 

Use Your Plate-a-tarium

The Plate-a-tarium will indicate where to look for the sun and planets for any given date or time, provided your planets plate is up to date.  

First set the date by rotating the sun line into the proper constellation or date along the ecliptic (inner plate).

While facing south, hold the outer tray as you would a steering wheel so that it is aligned with your celestial equator.  The angle of the celestial equator from the horizon is equal to 90 degrees minus your latitude.  For example, if you are at 40 degrees of latitude, the outer tray should be inclined 60 degrees.  

As you face south, the wire indicating the earth's axis should remain pointing toward the north pole or Polaris, even as you "turn the wheel."

The sun is your timepiece.  Set the time by rotating the outer tray so that the sun corresponds to its appropriate position.  A trick to bring the observer down to earth is to imagine that the Plate-a-tarium is submerged half way into a tub of water.  The portion above the water is the observers view; the portion below the water is obscured just as the ground blocks out our view of the other half of the sky.  As you rotate the outer tray, the sun line points to the position of the sun through the hours.

Set the Plate-a-tarium and rotate it through a day for the solstices and equinoxes and its utility suddenly becomes very clear!  Notice how the sun line points southeast at sunrise (for northern mid-latitudes) and southwest at sunset at the June solstice.  Witness how the sun rises due east (to the left) and sets due west (to the right) at the equinoxes.  

Vernal equinox sunset June solstice sunset September equinox sunset December solstice sunset
Vernal sunset.jpg (28734 bytes) June solstice sunset.jpg (31809 bytes) Dsc00031.jpg (490456 bytes) December_solstice_sunset.jpg (19273 bytes)
Vernal sunset 2.jpg (17267 bytes) June sunset 2.jpg (19203 bytes) Sept sunset 2.jpg (17912 bytes) Dec sunset 2.jpg (18041 bytes)
vernal sunset zoom.jpg (20927 bytes) June solstice sunset zoom.jpg (19272 bytes) Sept equinox sunset.jpg (76759 bytes) December solstice sunset zoom.jpg (17245 bytes)

To find out what planets are visible in the evening sky, set the sun below the horizon (rotate the "steering wheel" below the "bathtub's waterline").  The earth-to-planet lines should point directly to those planets, and be fairly accurate in both altitude and azimuth.  A small error is introduced because the planet orbits do not coincide directly with the solar plane.

Compare the altitude of the noon sun in December to the altitude of the noon sun in June.

You've heard of the Land of the Midnight Sun?  Set the solar system plate so the sun line points to the June solstice.  To travel to the north pole, hold the "steering wheel" so it is horizontal and rotate it.  The sun appears to make a circle overhead.

Try visiting the equator.  As you hold the outer tray vertically, notice how the sun never strays more than 23 degrees  from the zenith at noon.

Below are some more circumstances that show the sun's position through the seasons.

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Vernal equinox sunrise June solstice midnight September equinox sunset December solstice noon
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Contributed by Chuck Bueter.

 

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