Gravitational Constant Measurement ?

[Debo Industry]

How did we measure the gravitational constant G = 2.034 x 10 ^ 17 cm ^ 2 and the Earth average density (specific gravity) p = 3.45 g / cm ^ 2 s ^ 2.

 

[PhysicoRaj]

The gravitational constant was measured by Henry Cavendish, using a setup, like this:

When the lead spheres are moved the gravitational force acting on the other set of spheres induces a force on the wire which twists, and the restoring torque can be equated to the gravitational force as follows:
torque = force * length
τθ=GMm/r²]*l
(where l is the length of bar, τ is the torque per unit angle of twist, θ is the angle of twist caused by the force).
So,
G=τθr²/Mml
θ, angle of twist can be measured by many methods.( in the figure it is measured by laser, and hence u see a mirror).

 

[Debo Industry]

The gravitational constant was measured by Henry Cavendish, using a setup, like this:

When the lead spheres are moved the gravitational force acting on the other set of spheres induces a force on the wire which twists, and the restoring torque can be equated to the gravitational force as follows:
torque = force * length
τθ=GMm/r²]*l
(where l is the length of bar, τ is the torque per unit angle of twist, θ is the angle of twist caused by the force).
So,
G=τθr²/Mml
θ, angle of twist can be measured by many methods.( in the figure it is measured by laser, and hence u see a mirror).

PhysicoRaj,
After working out the gravitation formula and obtaining gravitational constant G there appeared a chance to check up the correctness of finding by the Cavendish the force of gravitation between the first ball with the mass of 1.0 g and the second ball with the mass of 1.0 g, located at the distance of Rball-ball = 1.0 cm, and equal to 6,6742 x 10 ^ - 8 gсm / s ^ 2. Due to the fact that Cavendish carrying out his calculations in grains used the units of weight with the dimension of mass, the mass of each ball was found first of all.
The mass of the ball Мball was found as the relation of the ball Рball = 1.0 gcm / s ^ 2 weight to the Earth gravity acceleration gear = 980.665 cm / s ^ 2 by the formula: Mball = 1 / 980.665 = 1.0197 x 10 ^ - 3g. The gravity acceleration of the ball gball was found as the product of the ball mass Мball by the gravity acceleration of 1g of the body g1-m = 2.5645 x 10 ^ - 22 cm / gs ^ 2 by the formula:

gball = 1.0197 x 10 ^ - 3 x 2.5645 x 10 ^ - 22 = 2.615 x 10 ^ - 25 cm / s ^ 2.

The force of gravitation between the first mass standard Мball = 1.0197 x 10 ^ - 3 g and the second mass standard Мball = 1.0197 x 10 ^ - 3 g, located at the distance Rball-ball = 1.0 сm:

Fball-ball = 2.034 x 10 ^ 17 x (1.0197 x 10 ^ - 3 x 2.615 x 10 ^ - 25 + 1.0197 x 10 ^ - 3 x 2.615 x 10 ^ - 25) / 1.0 ^ 2 = 1,0847 x 10 ^ - 10 gcm / s ^ 2.

Thus, the force of gravitation between two balls in the experiment of Sir H. Cavendish was Fball-ball = 1,0847 x 10 ^ - 10 gсm / s ^ 2 , and not 6,6742 x 10 ^ - 8 gcm / s ^ 2 that is appeared to be 615.3 less

http://tsiganok.cc.ua/files/laws_of_motion_of_bodies_draft_220911.pdf (p.114).

 

[PhysicoRaj]

The force between the balls is equal to the gravitational constant if the masses taken are equal to unity and are placed at unit distance apart. Since 1 g is itself unit mass, the need to convert 'weight' of 1 g to 'mass' by dividing by 980.6 cm s^-2 is the compulsion of -
F=G M1 g2+M2 g1/r^2

if you use
F=G M1*M2/r^2
Then you need not do that.
to get 6.67x10^-8 gcm/s^2 , unit 'mass' is necessary but not unit 'weight'.

 

[PJC01]

The measurement of the gravitational constant G and the Earth's average density p is a complex and ongoing process that involves various experiments and observations. One commonly used method is through the Cavendish experiment, which involves measuring the gravitational attraction between two masses and using that to calculate G.

In this experiment, two small masses are suspended from a fixed point and a larger mass is placed nearby. The gravitational force between the two small masses and the larger mass causes them to move slightly, and this motion can be measured to determine the strength of the gravitational force. By varying the distance between the masses and measuring the resulting motion, scientists can calculate G.

The Earth's average density can also be calculated using this method, as the gravitational force between the Earth and a known mass can be measured and used to determine the Earth's mass. By dividing the Earth's mass by its volume, we can calculate its average density.

Other methods for measuring G and the Earth's density include using satellites to measure the Earth's gravitational field and using data from planetary motion to calculate G.

Overall, the measurement of the gravitational constant and the Earth's average density is a complex and ongoing process that requires careful experimentation and analysis. The value of G and the Earth's density may vary slightly depending on the method used, but our current understanding is based on multiple measurements and observations.