Scaling Galileos Solar System

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Module 2-2
Scaling Galileos Solar System 2 - Size of the
Globes
Empty upon Empty Thats why they call it
space. Stern and Mitton, Pluto and
Charon, John Wiley and Sons, Inc., 1999, p. 27
Quantitative Concepts and Skills Scale Direct
proportions Unit conversions Arithmetic vs.
logarithmic scales Sort function Logic function
Do you have a feel for how far we are from other
planets? And how tiny our globe is?
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PREVIEW
The alumni want a fully scaled model of Galileos
solar system. Not only do the orbits need to be
correctly scaled relative to each other, but also
the little globes representing the planets,
moons, and sun need to be scaled correctly
relative to each other and to the orbits. We
found in Module 2.1, that, if we represented the
Earth as a globe one foot in diameter, the orbit
of Saturn would have to be more than 40 miles in
diameter. Scaling Saturns orbit down to the
allowable one mile means that the globe
representing Earth would have to be about a
quarter inch in diameter. Thats quite small.
What about the other bodies in Galileos solar
system. What size would they be? Slides 4 and 5
answer the question directly. The spreadsheet
with a 0.5-mi radius for Saturns orbit produces
the diameters for all of the globes. Slides 6-11
use the results of Slide 5 to compare the sizes
of the globes to the sizes of sedimentary
particles (boulders, cobbles, pebbles, and so
on). Slides 6-7 use the sorting feature. Slides
8-11 use logic functions. Slides 12-14 call
for charts plotting the size of the planets,
moons and sun relative to each other.
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Retrieve this spreadsheet from Module 2-1
Side Exercise -- How many moons are larger than
the smallest planet? Use the sort feature.
Sort function Block out the entire area on the
spreadsheet that you want to rearrange (B10G36).
Click on Tools, click on Sort, click on the
column you want to sort by (C).
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Retreive this spreadsheet from Module 2-1
(Slide 10)
Fill out all the sizes in Columns D and E using
the Scale in Cell C24. Change Cell D14 to 1/21.2,
as before. Delete Columns F through I. Insert a
new column (F) giving all of the model diameters
in mm.
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The rest of this module concerns these diameters.
How do they compare with the sizes of
sedimentary particles? How many of the little
globes in this scale model that extends across
campus are the size of sand grains?
Background -- The Wentworth Classification of
Sedimentary Particles minimum
diameter (mm) Boulder 256 Cobble
64 Pebble 4 Granule 2 Sand
1/16 Silt 1/256 Clay-sized particles are
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Comparing the little globes of the model to sizes
of sedimentary particles, 1

• Merge Rows 7-19 with
• Rows 22-27 as follows
• Create Block B2C19 by deleting Columns C-E in
  the spreadsheet of Slide 5. Before you delete
  those columns, preserve the values in Col F
  (block out the cells Copy Paste Special under
  Edit select Values).
• Type out Rows 21-27.
• 3. Rearrange Block B7C27 by sorting Col C
  (descending order) and delete inappropriate rows.

How do these sizes compare to these sizes?
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Comparing the little globes of the model to sizes
of sedimentary particles, 2
So in this model in which the orbit of Saturn is
a mile in diameter, Earth and Venus are the size
of small pebbles our Moon and one of Jupiters
moons are the size of large sand grains Mercury
and Mars are granules and Saturn and Jupiter are
cobbles. The Sun is a boulder.
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Comparing the little globes of the model to
sedimentary particles using Logic Functions (LF)
with Yes or No answers.
You can simply ask your spreadsheet Is this
value in the range of sand sizes?

• Retrieve your spreadsheet from Slide 6.
• Insert Col D. For each of the cells in D, use a
  LF to ask Is the corresponding value in Col C
  less than 2?
• Insert Col E. For each of the cells in E, use a
  compound LF to ask Is the corresponding value in
  Col C less than 2 AND greater/equal than 1/16?
• Insert Col F for cells that answer whether the
  corresponding size is in the pebble range?

Examples Formula for Cell D7
IF(C7IF(AND(C71/6),YES,no)
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Comparing the little globes of the model to
sedimentary particles using Logic Functions (LF)
with Yes or No answers, 2.
In this case, option 1 and option 2 produce the
same result for the sand-sized particles, but
option 1 would produce an incorrect result for
the pebble-sized globes. Why? Which of the two
options is the preferable strategy?
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Comparing the little globes of the model to
sedimentary particles using Logic Functions (LF)
to classify.
You can use your spreadsheet and a compound logic
function to classify the size of each globe.

• Retrieve your spreadsheet from Slide 8.
• 2. Insert Col D. For each of the cells in D,
  use a LF that responds boulder if the C-value
  is greater/equal to 256, cobble if the C-value
  is less than 256 AND greater/equal to 64, and
  pebble or smaller if neither of above.

Example Formula for Cell D7 IF(C7256,
boulder, IF(AND(C764), cobble,
pebble or smaller))
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Comparing the little globes of the model to
sedimentary particles using Logic Functions (LF)
to classify, 2.
Now modify your spreadsheet from Slide 10 to
respond boulder if the corresponding C-value is
greater/equal to 256 cobble if it is less than
256 AND greater/equal to 64 pebble if it is
less than 64 AND greater/equal to 4 granule if
it is less than 4 AND greater/equal to 2 sand
grain if it is less than 2 AND greater/equal to
1/6 and silt or clay if none of the above.
Example cell equation None provided this time.
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Comparing the sizes of the little globes to each
other
Recreate this spreadsheet and graphs starting
with a copy of the spreadsheet in Slide 11. The
layout of graph is like those of Slides 13 and 14
of Module 2.1.
The arithmetic scale does not differentiate the
globes at all well. The logarithmic scale is
better, but still it is tough to see all of the
globes. Try changing the x-values for the
planets to 2, and the x-values for moons to 7.
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Comparing the sizes of the little globes to each
other, 2
There are 12 points on each of the graphs.
Without looking at the values in the table, can
you count 12 points, even on the graph with the
logarithmic scale?
To resolve all the points, you can disperse the
x-values. For example, use x 2.0 to x 3.5
with an increments of 0.5 for the planets, and x
7.0 to x 9.0 with an increment of 0.5 for the
moons.
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Comparing the sizes of the little globes to each
other, 3
The graph with the logarithmic scale shows at a
glance that Jupiter and Saturn are an order of
magnitude larger than the next two largest
planets (Earth and Venus), which are nearly
identical in size. The sun is an order of
magnitude larger than Jupiter and Saturn. The
moons are of the same order as the smaller
planets, Mars and Mercury.
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End of Module Assignments

• Do the side exercise (Slide 3).
• Empty upon empty thats why they call it
  space. Comment.
• Add Uranus, Neptune, Pluto and their moons to the
  spreadsheet in Slide 5. Make use of data from
  Slide 3.
• Add Uranus, Neptune, Pluto and their moons to the
  spreadsheet in Slide 7.
• Add Uranus, Neptune, Pluto and their moons to the
  spreadsheet in Slide 11.
• Add Uranus, Neptune, Pluto and their moons to the
  spreadsheet in Slide 14.
• In Slide 14, we say that Jupiter and Saturn are
  an order of magnitude larger than Earth and
  Venus, and an order of magnitude smaller than the
  Sun. That statement pertains to diameter, not to
  surface area or volume. What are the
  order-of-magnitude relationships for area and
  volume.
• 8. Modify your spreadsheet and graphs in Slide
  14 to give areas and volumes of the prototype
  planets, moons and sun. Remember scientific
  notation.