How Are G and g Related in Gravity?

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SUMMARY

The relationship between "G" and "g" is defined through the equations of gravitational force. "G" represents the universal gravitational constant, approximately 6.674 × 10-11 N(m/kg)2, which quantifies the strength of gravity between two masses. In contrast, "g" is the acceleration due to gravity at the surface of a celestial body, typically measured in m/s2. To derive "G" from "g", one can use the formula g = G * (M/r2), where M is the mass of the celestial object and r is the radius from its center. Understanding this relationship is crucial for solving problems related to gravitational forces in physics.

PREREQUISITES
  • Understanding of Newton's Law of Universal Gravitation
  • Familiarity with gravitational constant "G"
  • Knowledge of gravitational field strength "g"
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the derivation of gravitational force equations in classical mechanics
  • Learn about the implications of the universal gravitational constant "G" in astrophysics
  • Explore variations of gravitational field strength "g" on different celestial bodies
  • Investigate the effects of distance on gravitational forces using the inverse square law
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Students in physics, educators teaching gravitational concepts, and anyone interested in understanding the fundamental principles of gravity and its mathematical representations.

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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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