What Are the Correct SI Units for the Gravitational Constant G?

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SUMMARY

The discussion centers on determining the SI units for the gravitational constant G in Newton's law of universal gravitation, represented by the equation F = GMm/r². The participants clarify that the force F has SI units of kg·m/s², while G must be derived from the equation. By rearranging the equation, G can be expressed as G = F * (r² / (M * m)). This leads to the conclusion that the SI units for G are m³/(kg·s²).

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  • Familiarity with SI units and dimensional analysis
  • Basic algebra for rearranging equations
  • Knowledge of mass and force units in physics
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ramin86
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I'm stuck on the following question:

Newton's law of universal gravitation is represented by the following equation.
F = GMm/r2

Here F is the magnitude of the gravitational force exerted by one small object on another, M and m are the masses of the objects, and r is a distance. Force has the SI units kg · m/s2. What are the SI units of the proportionality constant G?

Not sure of what to do, please help
 
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ramin86 said:
I'm stuck on the following question:

Newton's law of universal gravitation is represented by the following equation.
F = GMm/r2

Here F is the magnitude of the gravitational force exerted by one small object on another, M and m are the masses of the objects, and r is a distance. Force has the SI units kg · m/s2. What are the SI units of the proportionality constant G?

Not sure of what to do, please help

Just solve for G:

kg*m/s^2 = G*kg*kg/m^2

What you can do with numbers can also be done with units...
 
I solved for G and I get (m/s^2 / kg/m^2) = G, however, its not correct.
 
ramin86 said:
I solved for G and I get (m/s^2 / kg/m^2) = G, however, its not correct.
uhh... you didn't even simplify it. so guess what you have to do...
 

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