Constant of gravitation-what is that?

[xailer]

greetings

Since I'm a beginner I hope the following questions can be exaplined layman's terms

Newton's gravitational law says that

F = G*m1*m2/r^2

G is called constant of gravitation, but what does this constant represent
and what is its use in the above formula.
And how did we derive it?

thank you very much

 

[gnpatterson]

I think you would have to stop being a layman once you understood the gravitational constant and admit to bing a genius

 

[gnpatterson]

However in simple terms it a constant that scales how we find the force the of gravitational attraction between bodies.

It is a very small effect, if G was big then we would notice that lumps of lead would stick together, as we don't normally see this without very sensitive equipement then we know that G is small

 

[gnpatterson]

It is not derived, it is measured, it is a universal constant, it can be converted into what ever measurement system you are using but it just comes from the fact that if you set a mass a distance from another mass then there is a tiny measurable force. It is all alround you all the time and it applies to every mass everywhere in the universe

It is best detected with gold or lead spheres as they can be made small and massive (have high mass?) to maximise the force

 

[xailer]

A-I guess I'm missing the obvious here since I don't get why we need to put constant that shows tiny force inside

F = m1*m2/r^2

formula in order to calculate forces between planets?


B-I assume it was measured only recently (in the 20 century) , but still G was somehow derived from kepler's

F = 4*PI^2*K*m/r^2

even if its value was not known. How ?

 

[jtbell]

I don't get why we need to put constant that shows tiny force inside

F = m1*m2/r^2

formula in order to calculate forces between planets?

Because we don't get the correct force if we don't include that constant. Or are you really asking, "why does the constant G have the particular value that it has?" The answer to that question is, "Nobody knows." It's one of the fundamental constants of nature, like the speed of light in a vacuum, and Planck's constant. So far, there is no generally accepted theory that "explains" the value of any of these constants.

I assume it was measured only recently (in the 20 century)

Actually, G was first measured in the late 1700s, by Henry Cavendish. He measured the tiny force between two objects in his laboratory and calculated G from the known values of m1, m2, r and F. Some universities do a modern version of this experiment as an undergraduate lab exercise. A Google search for "Cavendish experiment" will give you some details.

 

[xailer]

interesting

But how was G derived from kepler's formula

F = 4*PI^2*K*m/r^2

by Newton?

 

[gnpatterson]

I see your confusion, history of science is not adiquately linked to science

firstly the equation you refer to as kepler's is not a discoverys made by him. It is derived his observations and law combined with Newton's laws of motion F=ma and a crude (but valid) analysis of circular motion (the motion of the planets not being circular is the fly in the ointment).

you need to read http://en.wikipedia.org/wiki/Torsion_bar_experiment

 

[xailer]

I will read it thanx

But I still am not shure how much of this stuff do I actually have to know ...meaning how deep must I go ( first year of high school ) ?

 

[gnpatterson]

cavendish's experiment is sometimes referred to as the experiment that weighed the earth

you need to understand the sequence of observations and laws

firstly kepler made an empirical law about the orbits and periods of planets (empirical means that he could say it was true but could not explain why)

then Newton devised some laws of motion that defined the concept of Forces causing acceleration and motion

then Newton looked at the planets and decided that motion of the planets could be explained by a law that had to have a form of F=GMm/r^2

BUT the problem was that he could not say what G was!

Why? because he did not have a planet he could take apart and measure the mass of, all he could say was that if he saw a planet with moons orbiting it then it had a mass relative to the sun's mass.

Try it out for your self, the solar system is keplarian with given constant, the Jupiter system is keplarian with a different constant. What Newton did was to say that it is the mass that sets the constant, however he couldn't give the mass in absolute terms, only in relation to the observed systems.

 

[gnpatterson]

probably not that deep

 

[gnpatterson]

there is a radio program you can listen to on the subject at

http://www.bbc.co.uk/radio4/science/further5.shtml

it is program 4 on the page

 

[hypermorphism]

In addition, most physical laws are like that in that the originator empirically observes that one variable is proportional to some function of other variables, and has to determine the constant of proportionality that fits the units he is using. It is common in theoretical physics to use units that correspond to key constants of proportionality being set to unity (1).