what is meant by universal gravity?

Answer 1

Every object and all matter attracts other matter to it through the force of gravity.
The Universal Gravity Equation defines how much this force is as a function of the masses of the objects and the distance between them.
This equation can be used to verify the acceleration of gravity on Earth.

Two objects will attract each other proportional to their masses and inversely proportional to the square of distance between them. If the mass of one body is designated as M, the mass of the other as m, and the distance between them is r, then the force of attraction F between the two bodies is:

F = G*M*m/r2

where G is the universal gravitational constant.

G = 6.67*10-11 N-m2/kg2. The units of G can be stated as Newton meter-squared per kilogram-squared or Newton square meter per square kilogram.

Since force = mass times acceleration, the universal gravity equation implies that as objects are attracted and get closer together, the force increases and the acceleration between them also increases.

Answer 2

Newton propounded his law of universal gravitation.according to which any two bodies in universe attract each other with a force which is directly proportional to the product of their masses and inversely proportional to the square of distance between them.
(F=G m1m2/d^2 )where G is the universal Gravitation constant.
Units of "G" are mlT^-2*l^2/m*m
=T^-2*l^3/m=l^3/mT^2

Answer 3

Universal gravitational constant implies that the "form of the equation" of the gravitational constant is the same for all observers. So it doesn't matter whether you perform the experiment in alpha centauri or on earth to determine the nature/form of the equation, you will always get the same form.

Answer 4

the force is directly propotional to the product of their mases and inversely proportional to the square of the distance.

Answer 5

Isaac Newton's law of universal gravitation states the following:

Every point mass attracts every other point mass by a force directed along the line connecting the two. This force is proportional to the product of the masses and inversely proportional to the square of the distance between them:

F = -G \frac{m_1 m_2}{r^2}

where:

F is the magnitude of the (repulsive) gravitational force between the two point masses
G is the gravitational constant
m1 is the mass of the first point mass
m2 is the mass of the second point mass
r is the distance between the two point masses

Assuming SI units, F is measured in newtons (N), m1 and m2 in kilograms (kg), r in metres (m), and the constant G is approximately equal to 6.67 × 10−11 N m2 kg−2 (newtons times meters squared per kilogram squared).

It can be seen that the repulsive force F is always negative, which means that the net attractive force is positive. (This sign convention is adopted in order to be consistent with Coulomb's Law, where a positive force means repulsion between two charges.)
Acceleration due to gravity

Let a1 be the acceleration due to gravity experienced by the first point mass. Newton's second law states that F = m1 a1, meaning that a1 = F / m1. Substituting F from the earlier equation gives:

a_1 = G \frac{m_2}{r^2}

and similarly for a2.

Assuming SI units, gravitational acceleration (as acceleration in general) is measured in metres per second squared (m/s2 or m s−2). Non-SI units include galileos, gees (see later), and feet per second squared.

The force attracting a mass to the earth, also attracts the earth to the mass, so that their acceleration to each other is given by:

a_1 + a_2 = G \frac{m_1+m_2}{r^2}

If m1 is negligible compared to m2, small masses would have approximately the same acceleration. However, for appreciably large m1, the combined acceleration, should be considered.

If r changes proportionally very little during an object's travel – such as an object falling near the surface of the earth – then the acceleration due to gravity appears very nearly constant (see also The Earth's gravity). Across a large body, variations in r, and the consequent variation in gravitational strength, can create a significant tidal force.

Bodies with spatial extent

If the bodies in question have spatial extent (rather than being theoretical point masses), then the gravitational force between them is calculated by summing the contributions of the notional point masses which constitute the bodies. In the limit, as the component point masses become "infinitely small", this entails integrating the force (in vector form, see below) over the extents of the two bodies.

In this way it can be shown that an object with a spherically-symmetric distribution of mass exerts the same gravitational attraction on external bodies as if all the object's mass were concentrated at a point at its centrePrincipia. (This is not generally true for non-spherically-symmetrical bodies.


Newton's law of universal gravitation can be written as a vector equation to account for the direction of the gravitational force as well as its magnitude. In this formula, quantities in bold represent vectors.

\mathbf{F}_{12} = - G {m_1 m_2 \over r_{21}^2} \, \mathbf{\hat{r}}_{21} or \mathbf{F}_{12} = G {m_1 m_2 \over r_{21}^2} \, \mathbf{\hat{r}}_{12}

where

F12 is the force on object 2 due to object 1
G is the gravitational constant
m1 and m2 are respectively the masses of objects 1 and 2
r21 = | r2 − r1 | is the distance between objects 2 and 1
\mathbf{\hat{r}}_{21} \equiv \frac{\mathbf{r}_2 - \mathbf{r}_1}{\vert\mathbf{r}_2 - \mathbf{r}_1\vert} is the unit vector from object 1 to 2

It can be seen that the vector form of the equation is the same as the scalar form given earlier, except that F is now a vector quantity, and the right hand side is multiplied by the appropriate unit vector. Also, it can be seen that F12 = − F21.

The vector formula for gravitational acceleration is similarly analogous to the scalar formula:

\mathbf{a}_1 = G {m_2 \over r^2_{21}} \, \mathbf{\hat{r}}_{21}

Gravitational field

The gravitational field is a vector field that describes the gravitational force which would be applied on an object in any given point in space, per unit mass. It is actually equal to the gravitational acceleration at that point.

It is a generalization of the vector form, which becomes particularly useful if more than 2 objects are involved (such as a rocket between the Earth and the Moon). For 2 objects (e.g. object 1 is a rocket, object 2 the Earth), we simply write \mathbf r instead of \mathbf r_{21} and m instead of m1 and define the gravitational field \mathbf g(\mathbf r) as:

\mathbf g(\mathbf r) = -G {m_2 \over r^2} \, \mathbf{\hat{r}}

so that we can write:

\mathbf{F}( \mathbf r) = m \mathbf g(\mathbf r)

This formulation is independent of the objects causing the field. The field has units of force divided by mass; in SI, this is N·kg−1.

Problems with Newton's theory

Although Newton's description of gravity is sufficiently accurate for many practical purposes and is therefore widely used, it is limited to domains where gravitational potential is a small fraction of speed of light squared. The more accurate general relativity theory of gravity must be used in general cases. General relativity results in Newtonian gravity in the limit of small potential, so Newton's law of gravitation is often said to be low-gravity limit of general relativity.

Theoretical concerns

* There is no prospect of identifying the mediator of gravity. Newton himself felt the inexplicable action at a distance to be unsatisfactory (see "Newton's reservations" below).
* Newton's theory requires that gravitational force is transmitted instantaneously. Given classical assumptions of the nature of space and time, this is necessary to preserve the conservation of angular momentum observed by Johannes Kepler. However, it is in direct conflict with Einstein's theory of special relativity which places an upper limit—the speed of light in vacuum—on the velocity at which signals can be transmitted.


Disagreement with observation

* Newton's theory does not fully explain the precession of the perihelion of the orbit of the planets, especially of planet MercuryPrecession. There is a 43 arcsecond per century discrepancy between the Newtonian prediction (resulting from the gravitational tugs of the other planets) and the observed precession.
* The predicted deflection of light by gravity using Newton's theory is only half the deflection actually observed. General relativity is in closer agreement with the observations.
* The observed fact that gravitational and inertial masses are the same for all bodies is unexplained within Newton's system. General relativity takes this as a postulate. See equivalence principle.


Newton's reservations

While Newton was able to formulate his law of gravity in his monumental work, he was deeply uncomfortable with the notion of "action at a distance" which his equations implied. He never, in his words, "assigned the cause of this power". In all other cases, he used the phenomenon of motion to explain the origin of various forces acting on bodies, but in the case of gravity, he was unable to experimentally identify the motion that produces the force of gravity. Moreover, he refused to even offer a hypothesis as to the cause of this force on grounds that to do so was contrary to sound science.

He lamented the fact that "philosophers have hitherto attempted the search of nature in vain" for the source of the gravitational force, as he was convinced "by many reasons" that there were "causes hitherto unknown" that were fundamental to all the "phenomena of nature". These fundamental phenomena are still under investigation and, though hypotheses abound, the definitive answer is yet to be found. While it is true that Einstein's hypotheses are successful in explaining the effects of gravitational forces more precisely than Newton's in certain cases, he too never assigned the cause of this power in his theories. It is said that in Einstein's equations, "matter tells space how to curve, and space tells matter how to move", but this new idea, completely foreign to the world of Newton, did not enable Einstein to assign the "cause of this power" to curved space any more than the Law of Universal Gravitation enabled Newton to assign its cause. In Newton's own words:

I have not yet been able to discover the cause of these properties of gravity from phenomena and I feign no hypotheses... It is enough that gravity does really exist and acts according to the laws I have explained, and that it abundantly serves to account for all the motions of celestial bodies. That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one another, is to me so great an absurdity that, I believe, no man who has in philosophic matters a competent faculty of thinking could ever fall into it.[citation needed]

If science is eventually able to discover the cause of the gravitational force, Newton's wish could eventually be fulfilled as well.

It should be noted that the word "cause" here is not being used in the same sense as "cause and effect" or "the defendant caused the victim to die". Rather, when Newton uses the word "cause," he (apparently) is referring to an "explanation". In other words, a phrase like "Newtonian gravity is the cause of planetary motion" means simply that Newtonian gravity explains the motion of the planets. See Causality and Causality (physics).

source wikipedia