Gravitation is centripetal force, like electric force in the atom. The source of gravity is mass. The source of electricity is charge. Difference is only in strength and trend of force. Charges with opposite signs attracts and with equal signs repels. According gravity: The masses with opposite signs are repulsive and with equal attracts.

For rotation there must be additional force normal to axis between both masses.

thx.. u just assumed or considered that gravity assert centripetal force.

my question is more fundamental.. if a mass is exerting gravity towards its centre then it is linear. how could linear force produce centripetal force. can u help me with the formula derivation.

secondly, for rotation.. are you referring to the great attractor.

An exhaustive explanation with the formulas is here: https://en.wikipedia.org/wiki/Centripetal_force

Usually one considers two reference frames, fixed frame and rotating frame. If an acceleration in rotating frame is ar and in fixed frame is ai then, one can derive an useful relation between two types of acceleration (See: Goldstein's Classical Mechanics) as,

ar=ai -2 ω x vr - ωxωxr - dω/dt x r

Second term in the r.h.s is coriolis term, third term is centrifugal term, fourth term is Euler term. The last term is absent if it is a uniform rotation.

This comment would be deeply unpopular, but it must be made, since there is a question raised!

Gravity in the celestial bodies involves matter and motion (hence force); both of which involve dialectical contradiction. But neither causality based universal gravitation of Newton, nor geometry based GR of Einstein even recognize any contradiction, much less explain or resolve it. So; matter and motion are mysteries for both Newton and Einstein; these mysteries keep on piling up as they proceed with their deliberations.

Newton gets matter from God and motion as a “first impulse” from the same deity. Einstein’s geometry based theory does not even know matter and motion. Please recall Zeno’s paradox on the impossibility of motion. In Einstein’s own words, “Since the theory of general relativity (GR) implies the representation of physical reality by a continuous field, the concept of particles and material points cannot play a fundamental part and neither can the concept of motion. The particle can only appear as a limited region in space in which the field strength or energy density is particularly high”. Einstein, A. On the General Theory of Relativity, in David Levy (Ed.). The Scientific American Book of the Cosmos, N.Y., 2000, pp. 13.

But Einstein does indeed mysteriously bring in both matter and motion through the backdoor!

Both of these two theories of gravity start with a mystery, so is there any wonder that they both harvest only mysteries and beyond certain limit these mysteries turn into Myths, Fairy Tales, Singularities and so on that we see in modern cosmology?

Please consider the following humble article:

Article THE CONCEPTUAL DEFECT OF THE LAW OF UNIVERSAL GRAVITATION OR...

Gravity can produce centripetal force, but this gravity is not Newtonian. Fr example, gravitational force F^1 in the de Sitter bubble with positive cosmological constant 3/a^2, where a is horizon of events, is F^1 = c^2r/a^ = H^2r, where r is the distance from observer to horizon events, H is the Hubble constant. So, H is the angular velocity of 3-space. It is necessary to not that 3-space does not rotate relative to time, as in the de Sitter space all g_0i = 0. (If not all g_0i equal zero, the 3-space rotates relative time, i.e. is non-holonomic). The rotation of the non-holonomic Sitter 3-space is purely spatial. Thus the Hubble constant in the de Sitter bubble is the angular velocity of 3-space.

May be Yes or No!

No , according to the classical physics where it first comes up, it's a "fictitious force".

Yes, according to the Equivalence principle it has exactly the same physical effects as gravity.

According to Leibniz's ideas, gravity is the result of the sum of a radial acceleration (proportional to r^2) plus a transversal acceleration (proportional to r^3) that is r'' = M/r^2 + J^2/r^3. Check more in centrifugal forces in Wikipédia or in my SUMMARY. But Leibniz cannot prove it for both Kepler's laws of Areas and Harmonic and general conics. On the other hand, I have proved the identity r^3 r'' = Mr + J^2 (where M is called MACCEL and J is the angular momentum) which holds for any movement. Thus, Leibniz's concept of gravity differ from Newton's concept (as centrifugal opposite gravity). Eventually I can send to you the mathematical proof of the cited identity (which is one of the corner-stone of my approach to explain THE NATURE AND MECHANISM of Gravity). Thanks in advance.

The mathematical deduction of the above cited equation r" = M/r^2 + J^2/r^3 can be found in my paper KEPLER'S EQUATION - A Kinematical Deduction here available, within the section 3, equation number 14. Its solutions leads to the general conics and Kepler's Equations using only kinematical variables, while Newton used dynamical variables (such as mass and forces). Thanks in advance for your replies.

Raul Nunes I'm completly ignorant, but it catch my curiosity. Can we say that Gravity is only a force reproduced from centripetal movement? And maybe that's why nobody could detect gravitational particles (gravitons) ? What do today's best physicists say about this? Do I really need a lot of mass to generate gravity or if I subject an object to high centripetal speeds do I generate that same "gravity" for small masses?

To reinforce my comment of December 12, 2018, the following is a link to a new publication:

Article KEPLER -NEWTON -LEIBNIZ -HEGEL Portentous and Conflicting Le...

In the special case of circular orbits only, gravity is a centripetal force. Otherwise more generally, gravity is what is called a "central force".

It should be remembered that a centripetal force is a special kind of force that acts at right angles to the direction of motion of a moving object. One example is the electromagnetic force F = qvxB. Other examples occur where a constraint, such as a wall, or a piece of string, thwarts the action of a centrifugal force, where that object would otherwise have been undergoing straight line motion. Hence the remaining inertial force, which is a centripetal force, causes the object's path of motion to curve. See "The Centrifugal Force Argument" at Article The Centrifugal Force Argument

So further to what I said in the previous note, gravity is never technically a centripetal force by definition. Gravity is a central force, which in the special case of circular orbits is equal and opposite to the centrifugal force, and does act like a centripetal force. It should be noted though that in general, gravity is not equal and opposite to the centrifugal force, and even where it is, as in circular orbits, it does not form an action-reaction pair with centrifugal force as per Newton's third law of motion.

I suppose any force could act momentarily as a centripetal force, but the term is generally applied to the examples stated above where the force is enduring and only ever causes a change in the direction of motion, and not the speed.