# Gravitational constant

**GNewton's gravitational constantuniversal gravitational constantconstant of gravitationNewton's constantacceleration due to gravityNewtonian constant of gravitationNewtonian gravitational constantuniversal constant of gravitationdensity**

[[File:NewtonsLawOfUniversalGravitation.svg|thumb|right|300px|The gravitational constantwikipedia

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### Physical constant

**constantconstantsuniversal constant**

, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

There are many physical constants in science, some of the most widely recognized being the speed of light in vacuum c, the gravitational constant G, the Planck constant h, the electric constant ε 0, and the elementary charge e.

### Mass

**inertial massgravitational massweight**

with the product of their masses and the inverse square of their distance.

If a first body of mass m A is placed at a distance r (center of mass to center of mass) from a second body of mass m B, each body is subject to an attractive force F g = Gm A m B /r 2, where G = 6.67 N kg −2 m 2 is the "universal gravitational constant".

### Newton's law of universal gravitation

**law of universal gravitationuniversal gravitationNewton's law of gravitation**

, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity. is a key quantity in Newton's law of universal gravitation.]] According to Newton's law of universal gravitation, the attractive force (

where F is the gravitational force acting between two objects, m 1 and m 2 are the masses of the objects, r is the distance between the centers of their masses, and G is the gravitational constant.

### Cavendish experiment

**1798 experimentCavendish pendulumCavendish type experiments**

The first implicit measurement with an accuracy within about 1% is attributed to Henry Cavendish in a 1798 experiment.

The Cavendish experiment, performed in 1797–1798 by British scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory and the first to yield accurate values for the gravitational constant.

### Gravity

**gravitationgravitationalgravitational force**

, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

Where F is the force, m 1 and m 2 are the masses of the objects interacting, r is the distance between the centers of the masses and G is the gravitational constant.

### General relativity

**general theory of relativityrelativitygeneral relativity theory**

, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity.

Matching the theory's prediction to observational results for planetary orbits or, equivalently, assuring that the weak-gravity, low-speed limit is Newtonian mechanics, the proportionality constant can be fixed as κ = 8πG/c 4, with G the gravitational constant and c the speed of light.

### Einstein field equations

**field equationsEinstein's field equationsEinstein equations**

In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor.

where is the Ricci curvature tensor, is the scalar curvature, is the metric tensor, is the cosmological constant, is Newton's gravitational constant, is the speed of light in vacuum, and is the stress–energy tensor.

### Earth radius

**Earth radiiradius of the EarthEarth**

is the radius of the Earth, the two quantities are related by:

where is the angular frequency, is the gravitational constant, and is the mass of the planet.

### C. V. Boys

**Charles Vernon BoysCharles V BoysCharles Boys**

was introduced in the 1890s by C. V. Boys.

In 1895 he published a measurement of the gravitational constant G that improved upon the accuracy achieved by Cavendish.

### Planck units

**PlanckPlanck energy density5 seconds**

The gravitational constant is taken as the basis of the Planck units: it is equal to the cube of the Planck length divided by the product of the Planck mass and the square of Planck time:

the gravitational constant, G,

### Dimensionless physical constant

**fundamental physical constantfundamental physical constantsfundamental constants**

Depending on the choice of units, variation in a physical constant in one system of units shows up as variation of another constant in another system of units; variation in dimensionless physical constants is preserved independently of the choice of units; in the case of the gravitational constant, such a dimensionless value is the gravitational coupling constant,

The term fundamental physical constant is often used to refer to the dimensionless constants, but has also been used (primarily by NIST and CODATA ) to refer to certain universal dimensioned physical constants, such as the speed of light c, vacuum permittivity ε 0, Planck constant h, and the gravitational constant G, that appear in the most basic theories of physics.

### Time-variation of fundamental constants

**constancy of fundamental constantsmust be unvarying constantsvariation in a physical constant**

Depending on the choice of units, variation in a physical constant in one system of units shows up as variation of another constant in another system of units; variation in dimensionless physical constants is preserved independently of the choice of units; in the case of the gravitational constant, such a dimensionless value is the gravitational coupling constant,

Paul Dirac in 1937 speculated that physical constants such as the gravitational constant or the fine-structure constant might be subject to change over time in proportion of the age of the universe.

### Gravitational coupling constant

**strength of gravity**

Depending on the choice of units, variation in a physical constant in one system of units shows up as variation of another constant in another system of units; variation in dimensionless physical constants is preserved independently of the choice of units; in the case of the gravitational constant, such a dimensionless value is the gravitational coupling constant,

* is the gravitational constant;

### Einstein's constant

**Einstein's constant of gravitation**

The scaled gravitational constant, or Einstein's constant, is:

Einstein used Newton's law of universal gravitation in his field equations, and the constant of κ is directly proportional to Newton's gravitational constant :

### Planck length

**length1.61.616 × 10 −26 nm**

The gravitational constant is taken as the basis of the Planck units: it is equal to the cube of the Planck length divided by the product of the Planck mass and the square of Planck time:

The Planck length can be defined from three fundamental physical constants: the speed of light in a vacuum, the Planck constant, and the gravitational constant.

### Force

**forcesattractiveforce vector**

According to Newton's law of universal gravitation, the attractive force (

This constant has come to be known as Newton's Universal Gravitation Constant, though its value was unknown in Newton's lifetime.

### Planck mass

**Planck scalemassPlanck-scale**

The gravitational constant is taken as the basis of the Planck units: it is equal to the cube of the Planck length divided by the product of the Planck mass and the square of Planck time:

where c is the speed of light in a vacuum, G is the gravitational constant, and ħ is the reduced Planck constant.

### Henry Cavendish

**CavendishCavendish, HenryH. Cavendish**

The first implicit measurement with an accuracy within about 1% is attributed to Henry Cavendish in a 1798 experiment.

Cavendish's work led others to accurate values for the gravitational constant (G) and Earth's mass. Based on his results, one can calculate a value for G of 6.754 × 10 −11 N-m 2 /kg 2, which compares favourably with the modern value of 6.67428 × 10 −11 N-m 2 /kg 2.

### Escape velocity

**escapeEarth's escape velocityescape velocities**

appears as above in Newton's law of universal gravitation, as well as in formulas for the deflection of light caused by gravitational lensing, in Kepler's laws of planetary motion, and in the formula for escape velocity.

where G is the universal gravitational constant (G ≈ 6.67×10 m·kg·s), M the mass of the body to be escaped from, and r the distance from the center of mass of the body to the object.

### Solar mass

**mass of the SunSun's masssolar masses**

In astrophysics, it is convenient to measure distances in parsecs (pc), velocities in kilometers per second (km/s) and masses in solar units

Because Earth follows an elliptical orbit around the Sun, the solar mass can be computed from the equation for the orbital period of a small body orbiting a central mass. Based upon the length of the year, the distance from Earth to the Sun (an astronomical unit or AU), and the gravitational constant (

### Planck time

**time5.391 s5.391 × 10 −44 s**

= gravitational constant

### Astronomical unit

**AUastronomical unitsAUs**

where distance is measured in terms of the semi-major axis of Earth's orbit (the astronomical unit, AU), time in years, and mass in the total mass of the orbiting system ( =

With the definitions used before 2012, the astronomical unit was dependent on the heliocentric gravitational constant, that is the product of the gravitational constant G and the solar mass.

### Stress–energy tensor

**energy–momentum tensorenergy-momentum tensorstress-energy tensor**

Newton's constant appears in the proportionality between the spacetime curvature and the energy density component of the stress–energy tensor.

where R_{\mu \nu} is the Ricci tensor, R is the Ricci scalar (the tensor contraction of the Ricci tensor), is the metric tensor, is the cosmological constant (negligible at the scale of a galaxy or smaller), and G is the universal gravitational constant.

### Orbital mechanics

**astrodynamicsastrodynamicistorbital dynamics**

In orbital mechanics, the period

where G is the gravitational constant, equal to

### Francesco Maria Grimaldi

**Francesco GrimaldiGrimaldiGrimaldi, Francesco Maria**

Between 1640 and 1650, Grimaldi and Riccioli had discovered that the distance covered by objects in free fall was proportional to the square of the time taken, which led them to attempt a calculation of the gravitational constant by recording the oscillations of a pendulum.

Grimaldi and Riccioli also made a calculation of the gravitational constant by recording the oscillations of an accurate pendulum.