as earth radius is about 6000km, versus 10^-5, the gravity constant should be more exact.

Paul> as earth radius is about 6000km, versus 10^-5, the gravity constant should be more exact.

You mean it should be known more exactly? Why? If you can come up with a way to lower the current relative uncertainty of 4.7x10-5, I am sure the world will want to learn about it.

well, Kare, I just asked. I have no other method to calculate it.

ps. about the other question (on RG): you was right, I wrote instead of

It is not a matter of calculation; it is a matter of measurement.

Although it would be nice to have a more accurate determination of GN, it may be of larger interest to know whether it as been unchanged over time. And, for comparison with extra-dimensional models, to check the short-distance behaviour of gravity.

dear Thierry, you are right: celestial bodies always Change their mass (even if negligible).

In a recent precise measurement using cold atoms, Rosi et al, Nature 510, 518 (2014)  gets an error of 150 parts per million.

dear Biswajoy, in other words 0,00015? the 5th decimal?

I think it means that if G denotes Newton's constant and the error is denoted by ΔG then, ΔG/G=1.5 x 10-4

@ Paul

Sadly true

Here is how the constant enters in orbital transfer and gravity assist

https://en.wikipedia.org/wiki/Hohmann_transfer_orbit

https://en.wikipedia.org/wiki/Orbital_mechanics

I really don`t know; maybe specialists could imagine new experiments to determine more than 5 decimals, if it were important...

dear Andrew, you ment 1,5/10^4? i thought it can be written as: 15/10^5

although this is a formal discussion but I could add some fun by approximate the G constant in 2018 ( 6.67430) by a simple math formula, pi / (3.25XXYY * (log(pi) - 1)) where XXYY is repeated 2255. Obviously as pointed out above GC is a function of measurement!

thanks! now one can see why real numbers are good for (infinite number of decimals...)