The weight of an object is the same on two different planets. the mass of planet a is only sixty percent that of planet b. find the ratio of ra/rb of the radii of the planets.

0.775

Explanation:

The weight of an object on a planet is equal to the gravitational force exerted by the planet on the object:

where

G is the gravitational constant

M is the mass of the planet

m is the mass of the object

R is the radius of the planet

For planet A, the weight of the object is

For planet B,

We also know that the weight of the object on the two planets is the same, so

So we can write

We also know that the mass of planet A is only sixty percent that of planet B, so

Substituting,

Now we can elimanate G, MB and m from the equation, and we get

So the ratio between the radii of the two planets is

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