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Value of Gravitational Constant - Unit, Application, FAQs

Value of Gravitational Constant - Unit, Application, FAQs

Vishal kumarUpdated on 02 Jul 2025, 04:40 PM IST

G, the Newtonian gravitational constant, is one of nature's most fundamental constants, yet scientists still don't know its exact value of gravitational constant. Although Isaac Newton introduced the gravitational constant in his popular work Philosophiae Naturalis Principia Mathematica in 1687, it was not until 1798 that the constant was observed in a real experiment. Don't be surprised if this happens. In physics, it's usually like this. In most cases, mathematical predictions come before experimental proofs. Anyway, Henry Cavendish, an English physicist, was the first to successfully quantify it, using an extremely sensitive torsion balance to measure the very small force between two lead masses. Although there have been more accurate measurements after Cavendish, the gains in value of gravitational constants (i.e., being able to achieve value of gravitational constants closer to Newton's G).

This Story also Contains

  1. What is the Gravitational constant?
  2. SI unit of gravitational constant:
  3. Applications:
Value of Gravitational Constant - Unit, Application, FAQs
Value of Gravitational Constant

It is the proportionality constant in Newton's law, which connects the gravitational force value between two bodies to the product of their masses and the inverse square of their distance. It quantifies the relationship between the geometry of space-time and the energy-momentum tensor in the Einstein field equations.

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What is the Gravitational constant?

The gravitational constant is the physical constant denoted by G, which appears in Newton's law of gravitation's equation. Sir Isaac Newton, an English mathematician, calculated the behaviour of gravity. He discovered that the gravitational force value between two objects is proportional to the product of their masses and inversely proportional to the square of their separation.

According to Newton's law, any two objects with mass m1 and m2 (in kilogrammes) and a distance r (in metre) between their centres would have a gravitational force value F (in Newton) acting on them. The following is a description of gravitational force value:

Fm1m2

F1/r2

Fm1m2r2

F=Gm1m2r2

The approximate value of the gravitational constant is, G = 6.67408 × 10-11 N m2 Kg-2

The value of the gravitational constant of the gravitational constant remains unchanged on the moon, Mars, or anywhere else in the universe, making it an invariant entity.

How to Measure the Gravitational constant?

. Hundreds of years and a global collaboration of scientists later, there is still no explanation for how it works. Scientists are also frustrated because they haven't been able to compute the exact force despite working on it for almost a century.

Researchers in modern times have come extremely near with their findings; however, the current known value of gravitational constant for the universal gravitation constant is 6.67408 10^{-11}m^3 kg^-1 s^-2. In their innovative concept, Chinese researchers have updated the old method of determining gravitational constant using a torsion pendulum experiment. This original approach was created by Henry Cavendish in 1798, and it has been changed numerous times since then to improve accuracy.

In the first way, the researchers created a metal-coated silica plate that was suspended in the air by a wire. The gravitational attraction is provided by the two steel balls. The force of gravity was calculated by determining how much the wire was twisted.

The second method was similar to the first, but the plate was suspended from a spinning turntable, which held the wire in place. The gravitational force value was measured using this method by observing the spin of the turntable.

By include seismic properties in both approaches; the researchers were able to avoid influence from adjacent objects and disturbances.

Gravity Constant:

Metres per second squared (m/s2) or Newtons per kilogramme (N/kg or N.Kg-1) are the SI units for acceleration. The gravitational acceleration near the Earth's surface is about 9.81 m/s2, which means that air resistance isn't a factor. Every time an object free-falls, its speed increases by 9.81 metres per second.

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Commonly Asked Questions

Q: What is the gravitational constant and why is it important?
A:
The gravitational constant, denoted as G, is a fundamental physical constant that quantifies the strength of the gravitational force between two objects. It's important because it allows us to calculate the gravitational force between any two masses in the universe, from apples falling on Earth to the orbits of planets around stars.
Q: How does the gravitational constant relate to Newton's law of universal gravitation?
A:
The gravitational constant G appears in Newton's law of universal gravitation: F = G(m1m2/r^2). It acts as a proportionality factor, determining the strength of the gravitational force between two masses (m1 and m2) separated by a distance r.
Q: Is the gravitational constant truly constant throughout the universe?
A:
Current scientific understanding suggests that the gravitational constant is indeed constant throughout space and time. However, some theories propose that it might vary over extremely long timescales or in different parts of the universe, though no conclusive evidence has been found for this.
Q: Why is the gravitational constant so difficult to measure precisely?
A:
The gravitational constant is challenging to measure because gravity is the weakest fundamental force, and experiments must be extremely sensitive. Factors like nearby mass distributions, vibrations, and electromagnetic interference can affect measurements, leading to ongoing refinements in its value.
Q: How was the gravitational constant first measured?
A:
The gravitational constant was first measured by Henry Cavendish in 1798 using a torsion balance experiment. He measured the tiny gravitational attraction between lead spheres, which allowed him to calculate the density of the Earth and, indirectly, the value of G.

SI unit of gravitational constant:

Per kilogramme square, 6.67 x 10 -11newton metres square (N x m 2 x kg -2). The value of quantity g in the law of gravitation of the constant is constant throughout our solar system and galaxy, as well as in nearby galaxies.

F=G ( m1.m2)/ R2 is the gravitational force value.

Newton is the unit of force (N)

Kg is a unit of mass.

R is in meters in the unit of measurement.

Unit of G:

G=Nm2Kg-2

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Commonly Asked Questions

Q: What is the numerical value of the gravitational constant?
A:
The gravitational constant G is approximately 6.674 × 10^-11 N(m/kg)^2. This extremely small value explains why gravity is the weakest of the four fundamental forces and why we only notice its effects on large scales.
Q: What are the units of the gravitational constant?
A:
The units of the gravitational constant are N(m/kg)^2 or m^3 kg^-1 s^-2. These units ensure that when multiplied by masses and divided by distance squared, the result is a force in Newtons.
Q: Why isn't the value of G simply 1?
A:
The value of G isn't 1 because it depends on our choice of units for mass, length, and time. If we used different units, G could be 1, but we use SI units (kg, m, s) for consistency across all areas of physics, resulting in G's small numerical value.
Q: Can the gravitational constant be derived from other physical constants?
A:
Currently, the gravitational constant cannot be derived from other physical constants. It is considered a fundamental constant of nature, meaning its value must be determined experimentally rather than calculated from theory.
Q: Is the gravitational constant the same for all types of matter?
A:
Yes, the gravitational constant is the same for all types of matter. This universality is a fundamental aspect of gravity and is part of Einstein's equivalence principle, which states that gravitational and inertial masses are equivalent.

Applications:

1. Sir Isaac Newton's Universal Law of Gravity was the first to investigate the Gravitational constant.

2. In this theory of relativity, Einstein expanded on this.

3. This empirical constant is solely used in the research of gravitational impacts in a variety of disciplines.

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NCERT Physics Notes:

Commonly Asked Questions

Q: How does the gravitational constant relate to black holes?
A:
The gravitational constant plays a crucial role in black hole physics. It appears in the equations that determine a black hole's Schwarzschild radius (event horizon) and is essential for calculating the gravitational effects of black holes on surrounding space and matter.
Q: What would happen if the gravitational constant were slightly different?
A:
If the gravitational constant were slightly different, it would profoundly affect the universe. A stronger G would lead to faster star formation and shorter stellar lifetimes, while a weaker G might prevent stars and galaxies from forming. Even small changes could make the universe uninhabitable.
Q: How does the gravitational constant affect the orbits of planets?
A:
The gravitational constant determines the strength of the gravitational force between planets and their stars. It appears in Kepler's laws of planetary motion and influences orbital periods, shapes of orbits, and the stability of planetary systems.
Q: How does the gravitational constant affect the weight of objects on Earth?
A:
The gravitational constant doesn't directly affect an object's weight on Earth. Weight is determined by the mass of the object and the Earth's gravitational field strength (g ≈ 9.8 m/s^2). However, G is used in calculating g based on the Earth's mass and radius.
Q: How does the gravitational constant relate to Einstein's theory of general relativity?
A:
In Einstein's theory of general relativity, the gravitational constant G appears in the Einstein field equations. It relates the curvature of spacetime to the distribution of matter and energy, playing a crucial role in describing how mass and energy warp the fabric of spacetime.

Frequently Asked Questions (FAQs)

Q: How does the gravitational constant affect the concept of gravitational cooling in white dwarfs?
A:
The gravitational constant is essential in understanding gravitational cooling in white dwarfs. G appears in equations describing the star's structure and energy loss, influencing the cooling rate and thus the use of white dwarfs as cosmic chronometers.
Q: Why is the gravitational constant important in understanding the cosmic microwave background?
A:
The gravitational constant plays a crucial role in understanding the cosmic microwave background (CMB). G influences the growth of primordial density fluctuations, the acoustic oscillations in the early universe, and the overall expansion history, all of which affect the observed CMB patterns.
Q: How does the gravitational constant affect the concept of gravitational slingshot maneuvers?
A:
The gravitational constant influences gravitational slingshot maneuvers used in space exploration. While G doesn't appear directly in the equations, it determines the strength of a planet's gravity, which is crucial for calculating the speed boost a spacecraft can achieve during a flyby.
Q: What role does the gravitational constant play in the study of exoplanets?
A:
The gravitational constant is crucial in exoplanet research. It's used in calculations involving orbital periods, planet masses, and the habitable zones around stars. G also affects our understanding of planetary system formation and stability in different stellar environments.
Q: How does the gravitational constant relate to the concept of gravitational waves?
A:
The gravitational constant is fundamental to gravitational waves, ripples in spacetime caused by accelerating masses. G appears in equations describing the generation and propagation of these waves, influencing their strength and the types of events we can detect with current technology.
Q: Why is the gravitational constant important in understanding the early universe?
A:
The gravitational constant plays a crucial role in models of the early universe. It affects the rate of expansion, the formation of primordial black holes, and the development of large-scale structures. Any variation in G over cosmic time would have profound implications for cosmology.
Q: How does the gravitational constant affect the concept of gravitational redshift?
A:
The gravitational constant is essential in understanding gravitational redshift, where light loses energy as it escapes a gravitational field. G appears in equations describing this effect, which is observed in phenomena from solar spectral lines to light escaping neutron stars.
Q: What role does the gravitational constant play in determining the Roche limit?
A:
The gravitational constant is crucial in calculating the Roche limit, the distance within which a celestial body held together only by gravity will disintegrate due to tidal forces. G appears in the equations balancing self-gravity against tidal forces, affecting phenomena like ring formation around planets.
Q: How does the gravitational constant relate to the concept of gravitational collapse?
A:
The gravitational constant is fundamental to gravitational collapse, the process by which an object contracts under its own gravity. G determines the critical mass and density required for collapse, influencing star formation, the evolution of massive stars, and the formation of black holes.
Q: Why is the gravitational constant important in calculating the Schwarzschild radius?
A:
The gravitational constant is crucial in calculating the Schwarzschild radius, which defines the event horizon of a black hole. G appears directly in the equation Rs = 2GM/c^2, determining the size of the event horizon for a given mass and thus the observable properties of black holes.
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