Lesson 6 of 6 · Estimates and the limits of scale models
Build a model and label its compromises
8 minute lesson · 3 checks along the way
Your goal for this lessonCalculate a shared size-and-distance scale, estimate uncertainty, and explain which relationships a model preserves or changes.
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Choose a scale before choosing the props
A scale model preserves selected relationships by multiplying real lengths by the same factor. If every length is reduced by a billion, both a planet’s diameter and its distance from another object must shrink by a billion to share one scale. A display that enlarges planets for visibility can still teach orbital order, but its caption must explain that object sizes and separations use different scales.
Begin with rounded Earth–Moon values: Earth’s diameter is about 12,800 kilometers, the Moon’s diameter about 3,500 kilometers, and their about 384,000 kilometers. These are supplied classroom estimates rather than one exact orbital snapshot. Ratios will tell us how much room the model needs. A photograph of the Moon’s surface can guide its appearance, but its published screen width does not set the model scale.
Apollo 8 photographed this nearly full Moon on December 22, 1968. This historical spacecraft view is useful for the model’s surface appearance. Its displayed diameter does not set a common scale with separately published Earth photographs.
Look closely
If this Moon picture and an Earth picture are printed at the same width, have you made a correct size model?
See what to notice
No. Equal print widths do not preserve the physical diameter ratio. With the lesson’s rounded values, a 10 cm Earth needs a Moon about 2.7 cm wide and a center separation near 3 m.
Make every length use the same ruler
Choose a model Earth 10 centimeters in diameter. The separation-to-Earth-diameter ratio is 384,000 ÷ 12,800 = 30, so the model centers belong about 300 centimeters, or three meters, apart. The model Moon’s diameter is 10 × 3,500 ÷ 12,800 centimeters, about 2.7 centimeters. The Moon belongs several dozen Earth diameters away, not pressed against the model Earth’s surface.
Center-to-center separation is not the empty gap between surfaces. In this model, subtract the Earth’s five-centimeter radius and the Moon’s roughly 1.35-centimeter radius from the 300-centimeter separation. The surface gap is about 294 centimeters. That distinction is small here but conceptually important: a measurement has endpoints, and changing those endpoints changes the question even when the same two objects are named.
Check 1 of 3
10 pointsUse the reading above. You can try again without losing points.
Work through a decision
Test whether the display fits
A museum offers a shelf only two meters long and proposes keeping the 10-centimeter Earth with the Moon just beside it. That would misrepresent separation if labeled a common-scale model. Instead, halve every model length: use a five-centimeter Earth, a roughly 1.4-centimeter Moon, and a 1.5-meter center separation. The pair now fits, with room for their radii, while preserving the same geometric ratios.
The designers also want the Sun on the shelf. At the original 10-centimeter Earth scale, a rounded Earth–Sun distance of 150 million kilometers becomes about 1,170 meters. Even after halving the model, it remains roughly 586 meters. The evidence favors a clearly labeled separate panel or a distance-only map. Squeezing the Sun onto the shelf without disclosing a scale change would erase the very relationship the model is meant to explain.
Check 2 of 3
10 pointsUse the reading above. You can try again without losing points.
Estimate honestly and preserve the lesson
Rounding a starting distance changes the result, but not every conclusion is equally sensitive to that change. Increasing the assumed Earth–Moon distance by ten percent increases the model separation by ten percent if Earth’s model size stays fixed. It does not change either body’s scaled diameter. A good estimate identifies which inputs control the answer and checks whether their plausible variation could reverse the decision about available space.
A geometric model does not automatically reproduce orbital periods, gravity, illumination, or the passage of light at a matching time scale. A logarithmic distance diagram can fit enormous ranges by compressing large intervals, but equal steps then represent equal factors rather than equal added distances. Use each model for its stated purpose. Keep its unit, scale rule, reference points, and omissions beside it so that a memorable display remains an honest explanation.
Check 3 of 3
10 pointsUse the reading above. You can try again without losing points.
Put it together
Your lesson progress
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