Value of G

In 1686, Isaac Newton realised that his Law of Universal Gravitation, which states that any two objects attract each other with a force equal to the product of their masses divided by the square of their separation times a proportionality constant, could explain the motion of the planets and the moon, as well as the motion of a falling apple. This proportionality constant G was calculated by Newton. This constant G is extremely useful for us to understand the nature of objects in our universe and it holds great significance.

Value of G-

In this article we will read about what we mean by G, the value of G in the gravitational force formula and lastly will take a look at the value of G in cgs.

G-

It is a physical constant that can be used to calculate the attraction between two masses.

How the value of G was calculated-

The basic constant’s value G has piqued the curiosity of physicists for almost 300 years and it has the longest history of observations, apart from the speed of light. The torsion balancing method, initially utilised by Cavendish, has been used in most G measurements. A dumbbell hanging by a very thin fibre was used in torsion balancing studies to quantify G. The dumbbell pendulum would revolve by a very modest amount when two hefty attracting bodies were put on opposing sides near the masses, twisting the fibre.

The attracting bodies were then twisted in the opposite way on the other side of the dumbbell. G is determined by the size of these twists. The dumbbell was placed into an oscillating motion and the frequency of the oscillation was measured in a version of this procedure. 

When the attractors were relocated to a new location, the gravitational interaction between the dumbbell and the attracting bodies caused the oscillation frequency to vary slightly, and this frequency change was utilised to estimate G. Gabe Luther and William Towler of the National Bureau of Standards and the University of Virginia developed this frequency shift technique. It was first released in 1982.

The Committee on Data for Science and Technology (CODATA), which collects and critically evaluates data on basic constants, gave G an uncertainty of 0.0128 percent based on their measurements. Although this seems to be quite exact, the fractional uncertainty in G is hundreds of times greater than the fractional uncertainty in other key physical constants like Planck’s constant or the charge on the electron. 

Following the measurement in 1982, Measurements from reputable research teams in Germany, New Zealand, and Russia cast doubt on the utility of G. The new ideals were diametrically opposed. A group from the German Institute of Standards, for example, acquired a value for G that was 0.6 percent higher than the recognized value; a group from Wuppertal, Germany, discovered a value that was 0.06 percent lower; and a group from New Zealand measured a value that was 0.1 percent lower.

Value of G in gravitational force formula-

Firstly, we will see what is the gravitational force formula, Newton’s law of gravity is another name for the gravitational force formula. It also specifies the amount of the force that exists between two things. The gravitational force formula also contains the gravitational constant, which has the value of G.

Formula- 

Gravitational force =

{(Gravitational constant)*(mass of object 1)*(mass of object 2)}/(distance between objects)2

Fg = Gm1m2/r2 

Fg = The gravitational force between two objects.

G = The gravitational constant.

m1 = Refers to the first object’s mass in kilograms.

m2 = Refers to the second object’s mass in kilograms.

r = The distance between the objects is measured in metres.

Value of G in this formula is 6.67 × 10−11 N m2 kg−2

Value of G in cgs-

Firstly, we will take a look ar what do we mean by cgs unit- The centimetre–gram–second (abbreviated CGS or cgs) system of units is a variation of the metric system that uses the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are explicitly derived from these three foundation units, however the CGS system was expanded in a variety of ways to include electromagnetism.

The CGS system was substantially replaced by the MKS system, which was expanded and replaced by the International System of Units, which was based on the metre, kilogram, and second (SI). SI is the sole system of units used in many sectors of research and engineering, while CGS is still widely used in several subfields.

Value of G in cgs units = 6.67×10−8cm3g−1s−2

Conclusion- 

In this article we read about what do we mean by G, read about its history, how the experiments were conducted in order to find the value of G in the initial research and in the later years, also read about the value of G in gravitational force formula and lastly read what is cgs unit and value of G in this system. As we see from what we have read the gravitational constant has great significance in our life as lots and lots of things are dependent on it, like planetary, satellite motion etc.