Universal gravitational constant

[lntz]

hey,

so in Newtons equations for gravitational force etc, the constant 'G' is used.

where does that come from? how do we know it's value? how was it discovered?

thanks, Lntz

 

[Nabeshin]

Well, at a very basic level, like that which Newton was working at, you suppose that the gravitational force between two objects is proportional to each of their masses, and inversely proportional to the square of the distance between them. How you arrive at this ansatz is a different question, but this puts you in the form
$$F\propto \frac{m_1 m_2}{r_{12}^2}$$

G is simply the proportionality constant. Its value is determined experimentally, first determined by Cavendish: http://en.wikipedia.org/wiki/Cavendish_experiment . It's actually notoriously difficult to measure directly, and the numerical value has quite large errors compared with the other fundamental interactions (i.e. electromagnetism).

 

[rbj]

and the value of G is only a consequence of the units used to express it. unlike popular conception, it is not really a parameter of the Universe in the same manner that dimensionless constants (as in the fine-structure constant) are. as long as it's real, positive, and finite, G can be any number you want, just by the choice of units used to express it. in Planck units G = 1.

 

[Whovian]

And how we know its value in standard SI units? If I remember correctly, the original experiment was something like http://www.physicsclassroom.com/class/circles/u6l3d2.gif . The time for the balls to line up is dependent on G, and since we know the initial radius and masses, we can use this to approximate G.

 

[jtbell]

Here's a picture of an actual Cavendish-type apparatus, for use in undergraduate laboratories:

http://principles.ou.edu/earth_planet/cavendish_balance.jpg

 

[lntz]

that's great, thanks all.

my next question to post was what an experimental setup looks like for measuring the effects of gravity

 

[rbj]

here's a photo of a research-quality lab setup for measuring G:

http://asd.gsfc.nasa.gov/Stephen.Merkowitz/G/Big_G.html

 

[Emilyjoint]

I know that G was measured early on by measuring the deflection of a pendulum brought close to a special mountain in Scotland.

 

[Emilyjoint]

the mountain is Schieallion and the year was 1774...found this out by Google search

 

[ttakacs]

Where/how might be the universal constants "stored" in matter (if this question makes a sense at all..)? If the answer is positive how can we be sure that there will be no technology in the future to change them at least locally?
Thank you.

 

[rbj]

the only universal constant that you need be wondering about are the dimensionless constants. like $\frac{m_p}{m_e}$ or the fine-structure constant $\alpha = \frac{e^2}{(4 \pi \epsilon_0) \hbar c}$. the value of $G$ or $c$ or $\hbar$ or $\epsilon_0$ are nothing other than reflections of the anthropocentric units we've come up with to measure things.

as far as Nature is concerned, all these constant need to be are real, positive, and finite. otherwize they can be any values and the only consequence of the values they take is that of the units used to express those dimensionful constants. they can be easily changed by changing the unit definitions. if you change your unit definitions to Planck units, they're all 1. no big deel.