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Week 12 Β· Design a Solar System Model

Tuesday

Choose a scale from real data
// Criteria, constraints, build, measure, improve
⏱ about 20 min

Tuesday: Choose a Scale from Real Data

Raven lays the NASA fact sheet on the hallway floor. "Neptune: 4,515 million kilometers. Mercury: 57.9 million."

"Our hall is nine meters," Rocket says. "So Neptune at nine meters. Then I just shrink everything the same amount."

"What do you notice about the inner planets?" Raven asks. "Mercury would be twelve centimeters from the Sun. Earth thirty."

Nova projects a line of glowing dots down the hall. "The first four crowd together," she says. "The giants spread out."

Rocket tries Earth's size at that scale and frowns. "Earth would be smaller than a grain of sand."

"One scale cannot do both," Raven says. Nova hums. "Now you know the trade-off. Choose."

The data from NASA

NASA's Planetary Fact Sheet lists each planet's average distance from the Sun in millions of kilometers, and its diameter in kilometers.

NASA says our solar system has eight planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus and Neptune. Pluto is a dwarf planet.

The first four are terrestrial planets with solid surfaces. The giant planets have swirling gases above a core. Jupiter and Saturn are gas giants, Uranus and Neptune ice giants.

PlanetDistance from the Sun (million km)Diameter (km)Model distance at 1 cm for 5 million km
Mercury57.94,87912 cm
Venus108.212,10422 cm
Earth149.612,75630 cm
Mars228.06,79246 cm
Jupiter778.5142,984156 cm
Saturn1,432.0120,536286 cm
Uranus2,867.051,118573 cm
Neptune4,515.049,528903 cm

Making a scale

A scale is a rule: so many real kilometers for each centimeter of model. The last column uses 1 centimeter for every 5 million kilometers.

To find a model distance, divide the real distance in millions of kilometers by 5. Neptune: 4,515 divided by 5 is 903 centimeters, about 9 meters.

If your space is shorter, pick a bigger number of kilometers per centimeter. Divide every planet by the same number so the scale stays true.

OpenStax Astronomy describes a model that shrinks everything by one billion. Earth becomes a 1.3 centimeter ball and sits 150 meters from a Sun 1.5 meters across.

At the hallway scale, Earth's 12,756 kilometers shrink to about three hundredths of a millimeter. That is the scientific limit from Monday.

USE THE TABLE
  • Read the question.
  • Tap your answer.
Which planet is farthest from the Sun in the table?
At 1 centimeter for 5 million kilometers, where does Jupiter go?
Which planet has the largest diameter?
At 1 cm for 5 million km, Earth's marker goes ____ cm from the Sun.
NASA counts ____ planets in our solar system.
PLANETS FROM THE SUN OUTWARD
  • ?Venus
  • ?Earth
  • ?Neptune
  • ?Uranus
  • ?Mars
  • ?Jupiter
  • ?Saturn
  • ?Mercury
WHY THIS EXERCISECorrect order is your first criterion. The data decide it, not memory.
StatementTrue or false?
The four inner planets crowd close to the Sun at any one scale.?
At a hallway scale, Earth would be about the size of a basketball.?
Dividing every distance by the same number keeps the scale true.?
Uranus and Neptune are ice giants.?
WHY THIS EXERCISEThe trade-off between distances and sizes is the heart of this design problem.
Try it
Decide your scale: how many million kilometers per centimeter so Neptune fits your space? Divide 4,515 by your space in centimeters.
Make your own version of the table with your scale. Round each model distance to the nearest centimeter.
Draw your hallway as a line. Mark the Sun at one end and all eight planet positions to your scale, with names.

Your plan has numbers now. Tomorrow is Sky Deck Lab: build it, then test it with a tape measure.

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