# Calculating the ratio of the radii of two planets

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The weight of a object is the same on two different planets. The mass of planet A is only sixty percent that of planet B. Find ra/rb, which is the ratio of the radii of the planets.

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#### Solution Preview

If g_a is the acceleration due to gravity on planet A, then its radius ra and g_a are related as,

g_a = G (M_a)/(ra)^2 ....(1) where M_a is the mass of the planet.

Similarly, g_b = G (M_b)/(rb)^2 ...

#### Solution Summary

We calculate the ratio of the radii of the two planets. If one of the radii is known, then the radius of the other planet can be calculated.

$2.49