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A Sense of Proportion: Saturn is about 60,000 km in radius, and its rings are only about 0.01 km thick with ripples 100 m high. Design a really big model with Saturn 60 inches in radius (10 feet in diameter). How thick must the rings be in your model and how high can the ripples be?

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AMB000

Answer:

[tex]t_M=0.00001 \ inches[/tex]

[tex]h_M=0.0001 \ inches[/tex]

Step-by-step explanation:

We need a scale factor to go from the real sizes to the model sizes. We will use r for radius, t for thickness and h for ripple height.

Our scale factor is a number S that must convert a real size (R) to a model size (M), for example with the radius:

[tex]r_M=S r_R[/tex]

But since we know both radius we can calculate it as:

[tex]S=\frac{r_M}{r_R}=\frac{60 inches}{60000Km}=0.001\ inches/Km[/tex]

And then we can calculate our final sizes for the model (writing 100m as 0.1Km).

[tex]t_M=St_R=(0.001\ inches/Km)(0.01Km)=0.00001 \ inches[/tex]

[tex]h_M=Sh_R=(0.001\ inches/Km)(0.1Km)=0.0001 \ inches[/tex]

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