In 1976 the International Astronomical Union ( IAU ) revised the definition of the AU for greater precision, defining it as that length for which the Gaussian gravitational constant ( k ) takes the value when the units of measurement are the astronomical units of length, mass and time.

An equivalent definition is the radius of an unperturbed circular Newtonian orbit about the Sun of a particle having infinitesimal mass, moving with an angular frequency of radians per day ; or that length such that, when used to describe the positions of the objects in the Solar System, the heliocentric gravitational constant ( the product GM < sub >☉</ sub >) is equal to ()< sup > 2 </ sup > AU < sup > 3 </ sup >/ d < sup > 2 </ sup >.

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 M < sub >☉</ sub >.

It introduced the Gaussian gravitational constant, and contained an influential treatment of the method of least squares, a procedure used in all sciences to this day to minimize the impact of measurement error.

* G is the gravitational constant

where denotes Newton's gravitational constant,

Since the rate of clocks and the gravitational potential have the same derivative, they are the same up to a constant.

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 < sup > 4 </ sup >, with G the gravitational constant and c the speed of light.

In the above, the size of the loop Λ acts as a coupling constant between the gravitational field and the electromagnetic field.

is the " universal gravitational constant ".

Some terms associated with gravitational mass and its effects are the Gaussian gravitational constant, the standard gravitational parameter and the Schwarzschild radius.

So for the gravitational force — or, more generally, for any inverse square force law — the right hand side of the equation becomes a constant and the equation is seen to be the harmonic equation ( up to a shift of origin of the dependent variable ).

The gravitational constant G has been calculated as:

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, Planck's constant h, the electric constant ε < sub > 0 </ sub >, and the elementary charge e. Physical constants can take many dimensional forms: the speed of light signifies a maximum speed limit of the Universe and is expressed dimensionally as length divided by time ; while the fine-structure constant α, which characterizes the strength of the electromagnetic interaction, is dimensionless.

For example, the National Institute of Standards and Technology uses the term to refer to any universal physical quantity believed to be constant, such as the speed of light, c, and the gravitational constant G.

Other theories of gravitation require gravitational redshift, although their detailed explanations for why it appears vary.

If it exists, the graviton is expected to be massless ( because the gravitational force appears to have unlimited range ) and must be a spin 2 boson.

A gravitational theory ( objects fall to the center ) existed at the time but Pytheas appears to have meant that the phases themselves were the causes ( αἰτίαι aitiai ).

The standard gravitational parameter GM 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.

From a local perspective, time registered by clocks that are at rest with respect to the local frame of reference ( and far from any gravitational mass ) always appears to pass at the same rate.

The general theory of relativity describes how, for both observers, the clock that is closer to the gravitational mass, i. e. deeper in its " gravity well ", appears to go slower than the clock that is more distant from the mass.

Thus for example it appears in the Einstein field equations, describing the properties of a gravitational field surrounding any given mass:

The gravitational weakening of light from high-gravity stars was predicted by John Michell in 1783 and Pierre-Simon Laplace in 1796, using Isaac Newton's concept of light corpuscles ( see: emission theory ) and who predicted that some stars would have a gravity so strong that light would not be able to escape.

For weak gravitational fields and slow speed relative to the speed of light, the theory's predictions converge on those of Newton's law of universal gravitation.

This equation is Newton's law of universal gravitation, expressed in differential form in terms of the gravitational potential φ ( t, x ) and the mass density ρ ( t, x ).

The gravitational constant G is a key quantity in Newton's law of universal gravitation.

It is also known as the universal gravitational constant, Newton's constant, and colloquially as Big G. It should not be confused with " little g " ( g ), which is the local gravitational field ( equivalent to the free-fall acceleration ), especially that at the Earth's surface.

Although Newton's theory has been superseded, most modern non-relativistic gravitational calculations are still made using Newton's theory because it is a much simpler theory to work with than general relativity, and gives sufficiently accurate results for most applications involving sufficiently small masses, speeds and energies.

Ultimately, it was Newton's friend, editor and publisher, Edmond Halley who, in his 1705 Synopsis of the Astronomy of Comets, used Newton's new laws to calculate the gravitational effects of Jupiter and Saturn on cometary orbits.

It shows how astronomical observations prove the inverse square law of gravitation ( to an accuracy that was high by the standards of Newton's time ); offers estimates of relative masses for the known giant planets and for the Earth and the Sun ; defines the very slow motion of the Sun relative to the solar-system barycenter ; shows how the theory of gravity can account for irregularities in the motion of the Moon ; identifies the oblateness of the figure of the Earth ; accounts approximately for marine tides including phenomena of spring and neap tides by the perturbing ( and varying ) gravitational attractions of the Sun and Moon on the Earth's waters ; explains the precession of the equinoxes as an effect of the gravitational attraction of the Moon on the Earth's equatorial bulge ; and gives theoretical basis for numerous phenomena about comets and their elongated, near-parabolic orbits.

) Newton's gravitational attraction, an invisible force able to act over vast distances, had led to criticism that he had introduced " occult agencies " into science.

However, Newton's laws ( combined with universal gravitation and classical electrodynamics ) are inappropriate for use in certain circumstances, most notably at very small scales, very high speeds ( in special relativity, the Lorentz factor must be included in the expression for momentum along with rest mass and velocity ) or very strong gravitational fields.

The gravitational pull on the mass towards the satellite with mass and radius can be expressed according to Newton's law of gravitation.

The heliocentric theory was successfully revived nearly 1800 years later by Copernicus, after which Johannes Kepler and Isaac Newton gave the theoretical explanation based on laws of physics, namely Kepler's laws for the motion of planets and Newton's laws on gravitational attraction and dynamics.

The experiments have put an upper limit on the change in Newton's gravitational constant G of less than 1 part in 10 < sup > 11 </ sup > since 1969.

This replaced Newton's vector gravitational force by the Riemann curvature tensor.

This includes Newton's law of gravitation, and the relation between gravitational potential and field acceleration.

Kepler's laws of planetary motion may be derived from Newton's laws, when it is assumed that the orbiting body is subject only to the gravitational force of the central attractor.

Similarly, the total mass inside a sphere containing a black hole can be found by using the gravitational analog of Gauss's law, the ADM mass, far away from the black hole.

File: Cavendish-walk. jpg | Henry Cavendish ( 1731-1810 ): greatest English chemist and physicist of his age, researched composition of the atmosphere, the properties of different gases, the synthesis of water, the law of electrical attraction and repulsion, a mechanical theory of heat, calculated the weight of the Earth in the Cavendish experiment, determined the universal gravitational constant

The gravitational force, spring force, magnetic force ( according to some definitions, see below ) and electric force ( at least in a time-independent magnetic field, see Faraday's law of induction for details ) are examples of conservative forces, while friction and air drag are classical examples of non-conservative forces.

On these two aspects, Hooke stated in 1674: " Now what these several degrees gravitational attraction are I have not yet experimentally verified " ( indicating that he did not yet know what law the gravitation might follow ); and as to his whole proposal: " This I only hint at present ", " having my self many other things in hand which I would first compleat, and therefore cannot so well attend it " ( i. e., " prosecuting this Inquiry ").

On these two aspects, Hooke stated in 1674: " Now what these several degrees gravitational attraction are I have not yet experimentally verified " ( indicating that he did not yet know what law the gravitation might follow ); and as to his whole proposal: " This I only hint at present ", " having my self many other things in hand which I would first compleat, and therefore cannot so well attend it " ( i. e. " prosecuting this Inquiry ").

* 1640 – Ismael Bullialdus suggests an inverse-square gravitational force law.

* 1640 — Ismael Bullialdus suggests an inverse-square gravitational force law

A gravity assist or slingshot maneuver around a planet changes a spacecraft's velocity relative to the Sun, though the spacecraft's speed relative to the planet on effectively entering and leaving its gravitational field, will remain the same ( as it must according to the law of conservation of energy ).

Measuring the exponent in the law of universal gravitation is more a test of whether space is Euclidean than a test of the properties of the gravitational field.

The conservation law can be used to express the speed of a body in a constant gravitational field as:

The MOG results were compared to MOND and were nearly indistinguishable right out to the edge of the rotation curve data, where MOND predicts a forever flat rotation curve, but MOG predicts an eventual return to the familiar inverse-square gravitational force law.

In the case of a gravitational field g due to an attracting massive object, of density ρ, Gauss ' law for gravity in differential form can be used to obtain the corresponding Poisson equation for gravity.

Ohm's law only applies to linear networks, Newton's law of universal gravitation only applies in weak gravitational fields, the early laws of aerodynamics such as Bernoulli's principle do not apply in case of compressible flow such as occurs in transonic and supersonic flight, Hooke's law only applies to strain below the elastic limit, etc.