Is the Gravitational Constant G Dependent on Unit Definitions?

[polaris12]

I learned about G (the gravitational constant) a while ago, but ever since then it was bugging me. I did not like how a seemingly random, irrational number whose existence could not be explained existed. Then I started thinking about this: if we arbitrarily changed the definition of a meter to, for example, slightly more than what a meter currently is, then wouldn't G have to change as well? So now I started thinking that if we changed the definitions of kilograms and meters, then eventually G would be 1N meter squared per kilogram squared, and its existence would be explained by the need to change the units into Newtons. Is there a flaw in my logic?

 

[polaris12]

hopefully my post wasn't too vague.

 

[Dale]

That is a good way to look at it. In relativity we often use units where G and c both equal 1. It then becomes clear that the value of these constants only tells us about our choice of units and not about physics.

 

[TurtleMeister]

Here's another way of looking at it. Originally posted in this thread https://www.physicsforums.com/showthread.php?t=398900

In some sense, G is a measure of the strength of gravity. If G were larger, gravity would be stronger; if G were smaller, gravity would be weaker.

 

[Rasalhague]

You might be interested in this article on Planck units, a system which extends the idea to other quantities:

http://en.wikipedia.org/wiki/Planck_units

 

[russ_watters]

I learned about G (the gravitational constant) a while ago, but ever since then it was bugging me. I did not like how a seemingly random, irrational number whose existence could not be explained existed. Then I started thinking about this: if we arbitrarily changed the definition of a meter to, for example, slightly more than what a meter currently is, then wouldn't G have to change as well? So now I started thinking that if we changed the definitions of kilograms and meters, then eventually G would be 1N meter squared per kilogram squared, and its existence would be explained by the need to change the units into Newtons. Is there a flaw in my logic?

No, you seem to understand fine...

...but it seems to trouble you that a physical constant would be such a slave to its units. It shouldn't. Consider your own height: whether you measure it in meters or feet, it doesn't change how tall you are.