What does the "m3 kg-1 s-2" mean in the gravitational constant?

Question

Not just what it stands for. I can't seem to understand it.

ps Explaining what the constant actually is might help me.

Answer 1

The gravitational constant comes about from the fact that the force of gravity is Proportional, but not Equal, to the terms on the right side: the mass of object one times the mass of object two and that divided by the distance between them.

Since it is only proportional, this relationship is not as useful as one might like. For instance, when using the relationship to get a value to use in a further equation, knowing that your value is only a proportionality is frustrating because you cannot "fit" it into the other equation, but have to leave an unknown variable in the other equation so you don't really advance your solution much. An example of this might be: you need to solve an equation, 7x - b = something you REALLY need to know, and you know what x is (let's say 4) but that b is really trouble. You only know that b is proportional to a couple values you know (let's say 7 and 3: 7/3). So either you change the equation to be: 28 - k*7/3 = something (and now you still don't know because k is unknown — lotta good it did you to get "b" out of there!) OR you can use the proportionality and say the something you need to know minus a constant (the 4*7 or 28) is proportional to b. Again, fat lot of good that did! You can't even be sure k is positive rather than negative. If positive, you at least know the "something" is less than the 4*7 or 28. But if it's negative, then the "something" is more than the 28... You're still in the dark. But what if someone good at such things had already measure that "k" and had a pretty good value for it? Now THAT would really be handy!

So... it had to be measured. "It" being the constant you could multiply the other three factors by to have an equation instead of a proportionality. A man named Cavendish did the first worthwhile measurement. Since then, it's been improved but not as much as you'd figure after 200 years. Man did good work. So, after all the pure math that Newton did and other since, we come down to measuring the final value to make the relationship truly useful.

Then it is converted to the various measuring systems like you'd convert meters to inches. The units change to match the system and you see the numerical part change as well. Kind of like changing an hour to minutes: 1 hour becomes 60 minutes. The units and the numerical part both change.

Answer 2

Consider how the gravitational constant is used. Newton's law of universal gravitation states F = GMm/r^2, or to simplify a bit by using F=ma, a = GM/r^2. Assuming you have measured all the variables, you can find the gravitational constant G: G = ar^2/M. The units of the constant G must match the units of the variable quantities. If we measure a in meters per second per second (m/s^2), r in meters, and M in kilograms, we wind up with the units of G being m^3/kg·s^2. You have cited it in a slightly different but equivalent format, using kg^-1 to indicate 1/kg and s^-2 for 1/s^2.

Answer 3

It's the units dude the result from the other terms that are directly measurable and have real units.

Answer 4

Meters Cubed, per Kilogram, per second squared. You may have seen it previously as
m3/kg/s2
or m^3/kg/s^2
It's the volume per unit weight per second squared.