How Are G and g Related in Gravity?

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G, the universal gravitational constant, quantifies the strength of gravitational attraction between two masses, while g represents the gravitational field strength experienced by an object near a celestial body. The relationship between G and g can be established through the equation g = G * (M/r²), where M is the mass of the celestial object and r is the distance from its center. To find G using g, one can rearrange the equation to G = g * (r²/M). Understanding this relationship is crucial for solving problems related to gravitational forces in physics. The discussion emphasizes the need for clarity in using these equations to connect the concepts of gravitational force and field strength.
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Relation between "G" and "g"?

Homework Statement


How are "G" and "g" related?


Homework Equations





The Attempt at a Solution


I can't find this anywhere! The teacher didn't give us anything to serve as a guideline, and the internet isn't quite helping. But I do know that G is the measure of strength of the force of gravity between 2 objecs anywhere in the universe, and I know that g is the gravitational field strength at a given distance from the centre of a celestial object. How are they related?
 
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Since you know what each means, how would you find "G" if you were given "g"? (Or "g", given "G"?) What properties do you need?

Start by giving the equations you would use to find the force for each, then assume those forces are equal (as in, you are looking for the force exerted between a celestial object and another mass, and you are finding it two different ways).
 
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