Calculating the Ratio of Planet Masses Using Newton's Law of Gravitation

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To calculate the mass ratio of Mars to Earth using Newton's Law of Gravitation, the weight of an object on each planet is considered. The weight on Mars is given as 4N for a 1kg mass, while on Earth it is 10N. The radius of Mars, being half that of Earth, influences gravitational force calculations. The correct formula shows that the mass of Mars is approximately 0.1 times the mass of Earth, factoring in both weight and radius. Understanding the relationship between gravitational force, mass, and radius is crucial for accurate estimations.
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Homework Statement



The weight of an object of mass 1kg at the surface of Mars is about 4N. The radius of Mars is about half the radius of Earth. Estimate the ratio:

mass of Mars/Mass of Earth


Homework Equations





The Attempt at a Solution




The answer is 0.1 but I don’t see where that comes from? 1kg would be 10N on Earth but 4/10 is 0.4 not 0.1? I’m assuming the radius is important but I don’t know how.
 
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Hi puzzled2, welcome to PF.

Can you write Newton's law of gravitation for the two cases?
 

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