What is the significance of the constant G in Newton's gravitation formula?

[Imabuleva]

I'm beginning to think Bobie is trolling...

 

[bobie]

There's not much to it. You have $GM=4\pi^2$, and we've chosen units in which $M=1$, so $GM=G$ and we're left with $GM=G=4\pi^2$.

Thanks, Nugatory,
one more question, if imabuleva allows me,
I have read that escape velocity is:
$v=\sqrt\frac{2GM}{r}$. , I suppose this is tangential escape,
what is the formula if a rocket tries to escape radially?

 

[TumblingDice]

I suppose this is tangential escape,
what is the formula if a rocket tries to escape radially?

Direction is not a factor. Tangential to radial doesn't matter as long as the path doesn't intersect the object it's escaping from.

 

[Nugatory]

$v=\sqrt\frac{2GM}{r}$. , I suppose this is tangential escape,
what is the formula if a rocket tries to escape radially?

The same. If you look at the derivation of the formula (it's a good exercise to derive it yourself) it will be pretty clear why the direction doesn't matter.