[Physics Class Notes] on Value of Gravitational Constant Pdf for Exam

The Newtonian gravitational constant, G, is one of nature’s most fundamental constants, although scientists don’t know its exact value. Despite the fact that Isaac Newton proposed the gravitational constant in his popular work Philosophiae Naturalis Principia Mathematica in 1687, the constant was not observed in a practical experiment until 1798.

It’s normally like this in physics. In the majority of cases, mathematical predictions take place over experimental proofs. In any case, it was Henry Cavendish, an English physicist, who was the first to quantify it, using a highly sensitive torsion balance to measure the very tiny force between two lead masses. Although there have been more precise measurements after Cavendish, the advances in gravitational constant values (i.e., being able to attain values of gravitational constants closer to Newton’s G) have been minimal.

In this article, you will understand about gravitational constant, how to measure it, and more. So, let us start by understanding the gravitational constant in the coming section.

What is Gravitational Constant?

The physical constant symbolized by G, which appears in the equation of Newton’s law of gravitation, is known as the gravitational constant. The English mathematician Sir Isaac Newton calculated the behavior of the force of gravity. He observed that the gravitational force among two objects is proportional to the product of their mass and inversely proportional to the square of the distance between their centers.

 

As per the Newton’s law, any two objects having mass m1 and m2 (in kilograms), with their centers separated by a distance r (in meter), will have a gravitational force F (in Newton) to exist between them, This force is denoted by:

 

 [F =frac {Gm_1m_2}{r^2}]

Derivation – Gravitational Constant

In the traditional format, the gravitational constant can be derived from Planck Length, Planck time, and Planck mass. While in wave format, the constant is derived from the electric force formula that is a decrease in amplitude of each particle faintly losing energy when an in-wave transits to out-waves.

 

Now, the SI unit of gravitational constant is given here below: 

 

6.67 x 10^-11 Newton meters square per kilogram square (N x m² x kg^-2). Throughout our solar system and galaxy, also the galaxy within the vicinity, the value of the constant is uniform.

 

Gravitational force [F = frac {G(m_1m_2)}{r^2}]

 

Unit of F= Newton(N)

 

Unit of mass =Kg

 

Unit of R=m

 

Unit of G=Nm² Kg^-2

 

Some astronomers believe that, as per the popular Big Bang theory, if the universe expands, then the value of G will gradually decrease.

Explanation

The laws of gravity, the gravitational effects on the planet Earth, other planets and stars were first calculated by Isaac Newton. In Newton’s gravity equation, the gravitational constant (G) first appeared, and later, Albert Einstein included it in his general relativity equation. G remains constant in Newton’s force equation even though force is related to the distance between the objects and their mass.

 

An electric force is generated by the reduction in the wave amplitude equal to the gravitational coupling constant for the electron and proton. For two electrons, such as two particles, there is a slight decrease in energy measurement. The reduction of destructive diffusion can have an obvious effect on a large body of electrically neutral atoms (atoms with protons and dissolving electrons). The wave equations that make up the model are constants that result in the occurrence of complex G constant, as shown below.

How to Measure the Gravitational Constant?

One of the four fundamental forces of nature is gravity (the others are electromagnetism, weak and strong interaction). Despite hundreds of years with a joint effort by scientists around the world, there is still no explanation for how it works. Also, scientists have become frustrated that even after a hundred of years; they haven’t been capable of finding a way to calculate the actual force.

 

Researchers in modern times have come very close with their findings; however, for universal gravitation constant, the current known value is 6.67408 × 10^-11 m³ kg^-1 s^-2. The researchers working in China in their new concept have modified the traditional way of measuring gravitational constant through torsion pendulum experiment. Henry Cavendish devised this first method in 1798, and since then, it has been modified many times to make it more accurate.

 

In the first method, the researchers built a silica plate coated with metal hung in the air by the wire. The two steel balls provide the gravitational attraction. By determining how much the wire was twisted the force of gravity was measured.

 

The second method was similar to the first, except that the plate was hung from a spinning turntable which kept the wire in place. In this method, by noting the rotation of the turntable, the gravitational force was measured.

 

In both methods, the researchers included the features to prevent interference from nearby objects and disturbances by adding seismic.

Gravity Constant

The gravity is denoted by g for Earth; it is the net acceleration that is conveyed to objects due to the collective effect of gravitation (from mass distribution within Earth) and the centrifugal force (from Earth’s rotation)

 

The acceleration is measured in meters per second squared (m/s²) as per the SI unit or equally in Newtons per kilogram (N/kg or N.Kg^-1). The gravitational acceleration near Earth’s surface is approximately 9.81 m/s², which means ignoring the impacts of air resistance. The speed of an object free-falling will increase by 9.81 meters per second every time. Sometimes quantity is informally referred to as small little ‘g’. 

Difference between ‘g’ and ‘G’

The main difference between ‘g’ and ‘G’ is that g stands for gravitational acceleration and ‘G’ stands for gravitational constant. The gravitational acceleration ‘g’ varies with altitude, whereas the gravitational constant value of ‘G’ remains constant. Gravitational acceleration is a vector quantity, whereas the gravitational constant is a scalar number.

Applications:

• The Gravitational Constant was initially investigated by Sir Isaac Newton’s Universal Law of Gravity.

• Einstein expanded on this in his theory of relativity.

• In a range of disciplines, this empirical constant is primarily used in the study of gravitational impacts.
  

Conclusion: 

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