Precision of the values of gravitational constant G

[david22]

Homework Statement

What are the magnitud of G (gravitational constant) and the age of the solar system in CGS system of units and in seconds respectively? and what is the precision of these values and why?

Homework Equations

The Attempt at a Solution

I found that the value of G in CGS system is 6.674 X 10^-8 cm³g^-1s^-2(approximately) and the age of the solar system is 4600 million years and in secons is : 1.450656 X 10¹⁷ seconds (approximately)
So my question is: what is the precision of these values? and why? do I need to put the uncertainities? I also found that the gravitational constant has a precision of 1 over 10,000 but why? so I really would appreciate your help :)

 

[mfb]

I also found that the gravitational constant has a precision of 1 over 10,000 but why?

The uncertainty is like that as there is no more precise measurement yet. G is tricky to measure because gravitational forces between masses in a lab are weak, and you always have the massive Earth (where the mass is not known precisely) disturbing everything.

For the age of the solar system, there should be some uncertainty on the value. You just have to convert it to seconds, I think.

 

[BvU]

I comment on the age of the solar system, especially on the phrase

the age of the solar system is 4600 million years and in secons is : 1.450656 X 10¹⁷ seconds (approximately)

This link says 4.6 billion years, give or take a few million years. NASA has 4.5 so the give or take should be done generously. Wiki claims 4.568, but end 2009 it was (or became?) "more than 4.5672". By then I stopped searching.

Convention is to provide so many digits that the uncertainty is around 0.5 in the last digit. So 4.5672 is from 4.56715 to 4.56725. This is not a very strict convention: if I say that I am 2 meter long I have a different accuracy in mind. But that's daily use, not physics.

Good experimental results are accompanied by a thorough estimate of the accuracy (which is often a lot of work!). The 2009 link is from a popular article; I would expect the scientific orignal to mention 4.5672 +/- something bigger than 0.00005. More like 0.005 (5 million years!). A more recent article mentions 0.25 million years for some key ingredient (4.56337+/-0.00025 My).

Somewhat more casual handing of unit conversions has a rough guideline: don't change the number of digits unless the first was a 1 or becomes a 1. So 4.6 converted would go to 1.45 and 1.72 something would go to 6.8 something else for example. This is because when the first digit is a 1, a change in the last digit is relatively big.

If you convert 4.6 billion years to 1.450656 X 10¹⁷ seconds you go from about 1% "accuracy" (0.05) to 3 X 10^-5%. That is unfounded. However, converting 4.5672 and employing the "rough guideline" would allow a 1 plus five more digits (not 1.45066 though!).

There is an extra snag here: looking up how many seconds in a year already gives different results ! What did you use ?