The universal gravitational constant (G)

AI Thread Summary
Dimensional analysis is a valuable engineering tool that helps derive relationships between physical quantities, such as the period of a pendulum, which depends on string length and gravity. When applying this method to planetary motion, it becomes evident that the universal gravitational constant (G) is essential for connecting time, mass, and distance. General relativity supports the idea that G links these dimensions, similar to how the speed of light (c) allows for time and length measurements in different units. Interestingly, the mass of the Sun is often measured more accurately in meters than in kilograms, highlighting the challenges in determining G's value. Overall, the discussion emphasizes the significance of G in understanding gravitational interactions and measurements in astrophysics.
Yoni
Messages
65
Reaction score
1
A most common tool in engineering is "Dimensional Analysis":
http://en.wikipedia.org/wiki/Dimensional_analysis

This tool can provide you with the dependence and scale. For example, using Dimensional analysis one can easily derive how the Period of a pendulum, T, is dependent on string length and acceleration of gravity thus: T \propto \sqrt{ \frac{l}{g} }
The problem of course is that you need to know apriori that the Period is only dependent on string length and gravity, and not anything else (For example, if you don't neglect air viscosity the answer will be different).

Now, I tried the method on planets and asked how is the Period of a planet circling the sun dependent on other parameters. I assumed that the Period is only dependent on distance from the sun and the sun's mass. Of course, no time unit can be derived from mass and distance. So I was stuck!

I realized that I was missing something, and that something was the universal gravitational constant (G). But then it got me thinking what is G??

Can I say that this constant connects TIME to MASS and DISTANCE?

I guess general relativity addresses this, so I post this here.
 
Physics news on Phys.org
Yes, the gravitational constant connects mass to distance and time. Just as by taking the speed of light (c) to be 1 we get ability to measure time in meters or length in seconds. By analogy, by taking G to be 1, we get the ability to measure mass in meters.

One funny thing is that we know better the mass of the Sun in meters than in kilograms. We are able to precisely measure the mass of the Sun in meters using various relativistic phenomena. Then we can derive the mass in kilograms knowing the value of G, but the accuracy of the measurements of G is lower than the accuracy of measurements of the Sun mass in meters.
 
You don't even need relativity. Newtonian mechanics does quite nicely. Solar system astronomers never use mass. They use an object's gravitational parameter. The object's mass is it's gravitational parameter divided by G. The gravitational parameter is highly observable for the Sun and those planets that have satellites. That one has to divide by G to obtain mass in mass units means mass is known to a significantly reduced precision. Another way of looking at it: We can measure masses of the moons, planets, and the Sun in units of length3/time2 to a much higher degree of precision than in units of mass.
 
So I know that electrons are fundamental, there's no 'material' that makes them up, it's like talking about a colour itself rather than a car or a flower. Now protons and neutrons and quarks and whatever other stuff is there fundamentally, I want someone to kind of teach me these, I have a lot of questions that books might not give the answer in the way I understand. Thanks

Similar threads

Back
Top