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Determining the Radius of a Model Earth From Scale Data

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Using different scales, find the radius of earth.

Imagine a scale model of the Universe, where a model of Earth is in London and a model of a very distant galaxy is in Venice. In this scale model, the Earth would be represented by a tiny sphere. Use the information below to calculate the radius of the model Earth. Give your answer to two significant figures.

Distance from London to Venice 9.9 × 10^5 m
Actual distance from the Earth to the distant galaxy 1.2 × 10^26 m
Actual radius of the Earth 6.37 × 10^6 m

The radius of the model Earth would have to be ___________ m

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Solution Summary

From known model data modelling the distance between Earth and a distant galaxy the predicted Earth radius in such a model is estimated.

Solution Preview

First you need to determine the scaling factor (S) which can be found by

S = Distance London to Venice/Actual Distance from Earth to Galaxy = 9.9 x 10^5/1.2 x 10^26

S = {9.9/1.2}10^(5-26) ...

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