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

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Homework Help Overview

The discussion revolves around determining the correct SI units for the gravitational constant G in the context of Newton's law of universal gravitation, represented by the equation F = GMm/r². Participants are exploring the relationships between force, mass, and distance in this equation.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are attempting to derive the units for G by manipulating the equation and expressing force in terms of its SI units. There are questions about the correctness of their simplifications and the steps taken in their reasoning.

Discussion Status

The discussion is ongoing, with participants sharing their attempts to solve for G and questioning the accuracy of their results. Some guidance is being offered regarding the simplification of units, but no consensus has been reached on the correct approach.

Contextual Notes

There appears to be confusion regarding the simplification of units, and participants are encouraged to clarify their understanding of unit manipulation in the context of the gravitational equation.

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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