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Newtonian law of Gravity:

$$F_g = \frac{m_1 m_2}{l^2} G$$ $$G = 6.7 * 10^{-11} \frac{m^3}{kg * s^2}$$

A meter is defined as:

the length of the path traveled by light in a vacuum in $1/299792458$ second

Am I right that If I redefine a meter as:

the length of the path traveled by light in a vacuum in $\frac{\sqrt{G}}{299792458} = 1/2432$ second

The coefficient $G$ would become $1\frac{m^3}{kg * s^2}$?

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Yes, and that's not new. Just one thing: do not call it "meter", that's already in use and that's misleading. You can invent any other word.

It is typical for physicist to work in non SI units (yep, all you life is a lie haha). In fact I hate this, but most physicist work in "new units", which are not centimeters or inches or anything like that. We just say "set units such that the speed of light is $c=1$.

Doing that, as $E=mc^2$, we can use energy units to express masses.

So is typical to set units so that $\hbar=1$, and also such that $G=1$.

This is called Plank units (search for them), and they are widely used among physicist.

I honestly hate this, because it is very confusing. Everybody should agree that, when reading a paper from another "branch", a big part of the effort is due to understanding what they are doing with units haha.

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    $\begingroup$ What is even worse is when they are using unit conventions you are not used to incorrectly. I have had my fair share of having to explicitly write out the units for each variable in an equation to make sure everything lines up, and then when it doesn't line up make sure I am not going crazy before I realize something was reported incorrectly. Not fun haha $\endgroup$ – Aaron Stevens Nov 28 '18 at 16:26
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    $\begingroup$ Lol I totally agree. A wise teacher of mine used to say "you should only care about order of magnitude and unit match, then let calculations for mathematicians/fellows" haha. Well, that teacher also used Plank units... contradictory, yes. But when he commited a mistake, or not a mistake but just doing math fast, the mess was so huge that we could easily lose so many minutes. The SI was direct haha. $\endgroup$ – FGSUZ Nov 28 '18 at 17:13
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    $\begingroup$ What's more, I'll add, he recognised that he did all that for lazyness (others don't recognise that, but that's the truth haha). Continuously switching from MKS to CGS just to avoid writing $\frac{1}{4\pi\epsilon_0}$. I kept thinking: why not just use $K=\frac{1}{4\pi\epsilon_0}$, as in school? Writing K is not such an effort, and then everything is much clearer and cleaner. $\endgroup$ – FGSUZ Nov 28 '18 at 17:15

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