What Are the SI Units of the Gravitational Constant in Newton's Law?

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The discussion focuses on determining the SI units of the gravitational constant (G) in Newton's Law of Universal Gravitation, expressed as Fg = G(M1)(M2) / D^2. To ensure dimensional validity, G must have units that, when combined with the mass units (kilograms) and distance units (meters), result in Newtons (N). The participants seek clarification on the dimensional analysis required to derive the units for G. Ultimately, understanding the relationship between mass, distance, and force is essential for solving the problem. The conversation emphasizes the importance of dimensional consistency in physics equations.
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Newton's Law of Universal Gravitation states that the magnitude of the force of gravity (Fg) between any two objects in the universe depends on the mass of each object (M1 and M2) as well as the distance (D) between them. The equation to describe this functional relationship is given by:

Fg = G(M1)(M2) / D^2

where G is a constant called the "constant of universal gravitation"

Use dimensional analysis to determine what SI units the constant of universal gravitation must carry for Newton's equation to be dimensionally valid.


In the case of this question, would anyone be able to show me what they are looking for? Much appreciated!
 
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Welcome to physics forums.

The problem is asking you for the units of G. What do the units of G need to be so that the units of G\frac{M_1M_2}{D^2} are Newtons? (because the SI unit of force is the Newton)
 
Nathanael said:
Welcome to physics forums.

The problem is asking you for the units of G. What do the units of G need to be so that the units of G\frac{M_1M_2}{D^2} are Newtons? (because the SI unit of force is the Newton)

Would you mind explaining the steps on how to reach the answer? I'm still a bit unsure how you determine this given the variables.
 
M is mass. What are the units of mass? Can you take it from there?
 
Figured it out, thanks.
 

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