G

[ydoaPs]

how was G calculated?

 

on a side note:

i know it wasn't anywhere close to what i did, because i used the inverse-square law for gravity in a thought experiment. i didn't just solve for G, so i may have messed up in getting the equation.

 

the experiment is: you are on a rocket on a planet. you fire your rockets and leave the planet(forgetting the fact that they use curved trajectories and orbit. no, forget that. it goes straight enough in the beginning.). use you initial speed, final speed, acceleration, mass of planet, and gravitational acceleration of the planet to find G.

 

[math]F=ma[/math] [math]{V_f}^2={V_i}^2+2a{x}[/math] [math]F=\frac{G{m^1}{m^2}}{r^2}[/math]

 

i solved for x

 

[math]{x}=\frac{{V_f}^2-{V_i}^2}{2a}[/math]

 

then x^2

 

[math]{x}^2=\frac{{V_f}^4-2{V_f}^2{V_i}^2+{V_i}^4}{4a^2}[/math]

 

i used ma for F in the inverse-square law formula and used x^2 for r^2(mass of rocket cancels)

 

[math]g=\frac{{4Gm_{planet}}a^2}{{V_f}^4-2{V_f}^2{V_i}^2+{V_i}^4}[/math]

 

then solved for G

 

[math]G=\frac{g({V_f}^4-2{V_f}^2{V_i}^2+{V_i}^4)}{4m_{planet}a^2}[/math]

 

i haven't solved yet, because i still need to find mass of a planet(probably earth, so i already know g) and realistic final velocity for the rocket in m/s.

but, i don't think it will work because you could use any acceleration for any velocity. too bad i thought of that after i went through a whole 2 minutes doing that.

[Martin]

how was G calculated?

....

 

Henry cavendish 1798 or so

 

it is a nontrivial problem because one does not know the mass of the earth

 

one has to measure the attraction between objects of known mass like two lead balls

 

he may possibly be the greatest experimentalist that ever lived

 

he figured out a device sensitive enuff to measure attraction between two, like golfball size, or tennis ball size, lead balls

using twist on a quartz fiber to measure force

 

and it is called the Cavendish and there STILL IS NO BETTER WAY

in other words people STILL USE THE CAVENDISH DEVICE to determine G, even 200 years later

 

there is no comparable experiment or experimental device in human history that is still the method of choice to measure something after 200 years

 

that is why henry Cav. may be the greatest experimentalist ever

 

he also measured the Coulomb constant of electric force before Coulomb did, but Coulomb got the credit

 

look up Cavendish on the web

[Martin]

anybody reading, be sure you do not confuse Newtons grav. constant G with little g, which is simply the acceleration of things falling near the surface of the earth

 

little g is no problem to measure and is about 9.8 meters per sq second

 

u can measure little g by watching something fall or by timing a pendulum

 

=========

Big G is hard to measure and it is about 6.7 x 10^-11 cubic meter per square second per kilogram.

 

If you have a mass M of some kilograms then you multiply GM

and that gives a quantity in terms cubic meter/sq. second

which will tell the gravitational attractiveness for M that other objects experience. It tells the pull that M has for other objects.

 

for normal size objects this pull is very weak and so GM (for a known mass M) is very difficult to measure accurately.

 

Cavendish called his determination of G by the name "weighing the earth"

because it allowed him to find out the mass of the earth

 

we know the gravitational effect of the earth, that is little gee for example, so we know GM for the earth.

after cavendish found out G, he could divide by G and get M for the earth---the mass in kilograms.

[ydoaPs]

what equation did he use to find it? i can punch a few buttons on my calc and get it, but how did he figure it out?

[ecoli]

Measure g by using a pendulum. The period of a pendulum=2π*(Length of string/gravity)^(1/2). Solve for G and you've got it.

[ydoaPs]

not g, G. the 6.67x10^-11 one.

[ecoli]

Ohh... sorry

[Martin]

what equation did he use to find it? i can punch a few buttons on my calc and get it, but how did he figure it out?

 

first understand the torsion pendulum consisting of a horizontal dumbell suspended in the middle by a quartz fiber

 

that is the core of the cavendish device

 

the pendulum rotates oneway a little until the fiber is twisted enough and then it rotates the other way a little

it has a PERIOD of oscillation

 

there is a formula which relates the period the mass (inertia) of the two balls to the

twist-resistance or torsion strength of the fiber (the torque with which it resists being twisted by a given angle---the torque is proportional to the angle, the more you twist it the greater the torque with which it resists-----oh, and the lever arm length.

 

the elegance of the cavendish device is that by TIMING this horizontal torsion oscillator (analogous to a pendulum) Cavendish learned just the necessary information to use the torsion pendulum as a gravitational force gauge. he would be some other massive object up close to one end and see by what angle the dumbell turned because of attraction