Explanation on the Measurement of Gravitational constant?
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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FAQs on Value of Gravitational Constant
1. What is the Universal Gravitational Constant, denoted by the symbol 'G'?
The Universal Gravitational Constant (G) is a fundamental physical constant that represents the proportionality factor in Newton's Law of Universal Gravitation. It quantifies the magnitude of gravitational force between two objects. According to Newton's law, the force (F) is given by the formula F = G(m₁m₂)/r², where m₁ and m₂ are the masses of the two objects and r is the distance between their centres.
2. What is the accepted value and SI unit of the gravitational constant G?
The experimentally determined value of the Universal Gravitational Constant (G) is approximately 6.674 × 10⁻¹¹. Its SI unit is Newton metre squared per kilogram squared (N m²/kg²). This unit is derived directly from the gravitational force formula, where G = Fr²/(m₁m₂).
3. Why is the gravitational constant (G) referred to as a 'universal' constant?
G is called the 'universal' constant because its value is believed to be the same everywhere in the universe. It does not depend on the chemical composition, physical state, size, or location of the interacting masses. Whether calculating the force between two planets or two small objects in a lab, the same value of G applies, making it a truly fundamental constant of nature.
4. What is the main difference between the Gravitational Constant (G) and acceleration due to gravity (g)?
While related, G and g are fundamentally different concepts:
- Nature: G is a universal constant of proportionality that is the same everywhere. In contrast, g is the acceleration experienced by an object due to the gravitational pull of a celestial body (like Earth) and its value varies with location.
- Value: The value of G is constant (6.674 × 10⁻¹¹ N m²/kg²). The value of g on Earth's surface is approximately 9.8 m/s², but it decreases with altitude and is different on other planets.
- Units: G is measured in N m²/kg², while g is measured in m/s².
- Type of Quantity: G is a scalar quantity, whereas g is a vector quantity, as it has both magnitude and direction (towards the centre of the body).
5. How was the value of the gravitational constant G first determined?
The value of G was first measured experimentally by Henry Cavendish in 1798, over a century after Newton formulated his law. He used a highly sensitive instrument called a torsion balance to measure the minuscule gravitational attraction between two pairs of lead spheres. By measuring this faint force, the masses, and the distance, he was able to calculate the value of G for the first time.
6. Does the value of G change if measured on the Moon or at the centre of the Earth?
No, the value of the Universal Gravitational Constant (G) does not change. It remains constant regardless of the location. In contrast, the acceleration due to gravity (g) would be different. On the Moon, 'g' is about 1/6th of its value on Earth. At the centre of the Earth, the net gravitational force is zero, so the value of 'g' is zero. However, G remains 6.674 × 10⁻¹¹ N m²/kg² in all these locations.
7. What are the dimensional formula and importance of the Universal Gravitational Constant (G)?
The dimensional formula for G is [M⁻¹L³T⁻²]. This is derived from its formula G = Fr²/m₁m₂. The importance of G is immense; it is a cornerstone of physics and cosmology. It allows us to calculate the gravitational force between any two objects with mass, which is crucial for:
- Understanding the orbits of planets, moons, and satellites.
- Calculating the mass of celestial bodies like the Earth, Sun, and other planets.
- Modelling the formation and structure of galaxies and the universe itself.
