The discussion revolves around the gravitational constant (G) and its application within the context of Newton's Law of Universal Gravitation. Participants seek clarification on the units associated with G and how to apply this constant in calculations, with a focus on understanding the relationships between mass, force, and distance.
Participants do not reach a consensus on the correct interpretation of the units of G, and there is confusion regarding the notation used in the equations. The discussion remains unresolved with differing views on the clarity of the explanations.
There are limitations in the clarity of the explanations provided, particularly regarding the notation and the relationships between the variables in the gravitational equation. Some assumptions about the participants' background knowledge may not hold true.
Vagn said:Assuming you don't want General Relativity, then G comes from the Newtonian Law of Universal Gravitation, which is
F=GmM/r^2
Where F is the gravitational force, m is the mass of one object, M is the mass of the other usually larger object, and r is the distance between the centre of masses of the two objects.
We know F has units of Newtons, which can be written as kg m/s^2
We know the units of m, M and r, so we can write G's units as N m^2/kg^2 by rearranging the above equation for G.
HallsofIvy said:It's had to understand what you are asking. The "m" and "M" are the masses of the two objects. It doesn't matter which you call the "first object" and which the second. Where VAgn writes "N m^2/Kg^2" is neither the "m" nor the "M" in the original equation- it stands for "meters". And I hope that "=" in "N= m^2/kg^2" was a typo. What he wrote was "N m^3/kg^2. That is, that the units of G are "Newton-meters squared per kilogram squared".