Is the Gravitation equation G m1m2/r2 defined at r=0?

Question

The gravitaional equation of Gm1m2/r2 tells that the gravitational force is inversely proportional to the square of distance between the objects so what will happen to the gravitation when the two objects collide or merge into each other i.e. when r=0. Will it become infinite? Can an object be imagined as of built of small particles bound by infinite gravitation?

Answer 1

In the gravitation equation, r is the separation of the centers of mass of the gravitationally bound objects. Two discrete macroscopic objects never meet this condition.

Answer 2

This equation (F=G m_1 m_2 / r^2) is generally considered to be an approximation to a deeper theory of gravity. This is Newton's equation for gravity and seems to indicate that two "point particles" would have an infinite amount of energy available if you could get them close enough. Of course, real objects are not point particles, and we don't see this happen.



In General Relativity, which is Einstein's theory of gravity, there is a size below which you can't concentrate matter without it forming a "black hole", which helps to solve the "infinite energy problem". A collection of objects with a total mass M will form a black hole when (roughly speaking) they are confined within a radius R = 2 G M / c^2, where G is Newton's constant, and c is the speed of light. This means you can only get M c^2 worth of energy out of a system of collapsing objects of mass M.



This is a very profound question, as it is quite difficult to reconcile Einstein's theory of gravity with the theory of quantum mechanics. The two theories seem to contradict at very short distance scales, and most physicists believe that a new theory of quantum gravity is needed to understand the Universe at this very small scale, called the Planck scale, after Max Planck.



> Can an object be imagined as of built of small particles bound by infinite gravitation?



Physicists try to avoid theories with unnecessary infinities in them. In fact there is a process of mostly-cancelling some positive and negative infinities called "renormalization", but we don't generally think of objects being bound by infinite gravitation.





You are asking the right kind of questions - if you are interested in reading further, there are many good books on this subject. My favorite at the moment is Lee Smolin's "Three Roads to Quantum Gravity". If you want a longer book list, ask. There are also many good web sites available, some for beginners, others much more technical. Try Googling on "gravity small scales".

Answer 3

Quantum mechanics stops two particles with mass occupying the same space, so the condition r=0 cannot be met. However, r can be very small as in the case of a neutron star, where the gravitational force is sufficient to stop a neutron from decaying to a proton and electron. What goes on inside a black hole is unknown, this may be what happens when r=0. It is not clear that the laws of physics as we know them still hold, so maybe the quantum exclusion doesn't apply.

Answer 4

In classical mechanics all objects have size, no object can be expressed as a point in space. due t this r cannot equal zero as we must take into consideration the radius of the object. Also as you proceed to the centre of an object the force decreases linearly so the equation is always defined classically. (in any classical mechanics when something is represented as a point it isonly an approximation and not part of the theory)

Only in quantum mechanics are objects sometimes expressed as a single point in a continuum of space. However as a previous answer said the union of QM and general relativity, our best understanding of gravity, has not yet been fruitful but not due to the above problem. There are far deeper problems one of which it may be impossible to forma consistent quantum field theory on curved space time.

Answer 5

The Newtonian gravitational equation: -



F = -GMm/r^2



Assumes that all of the mass is a point-mass and does not allow for a distribution of mass. However, using a different Newtonian analysis it possible to show that for a uniform gravitating sphere of radius 'R', that inside the body: -



F = -GMmr/R^3



Where 'r' is the distance from the centre. Thus, when r=0 the Newtonian gravitational force towards the centre also has zero value.

Answer 6

Value of r in the equation G= m1*m2/r^2

can never become zero , as no two particles (masses) can ever occupy the same place in the universe i.e. have the same co-ordinates pointing their location in the universe. So there will always be some distance between the particles- it might be infinitely large or infinitesimal .



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