Yes, it does apply to gravitation, just like it does to any field theory. The statements of the final view are wrong; Newton's third law doesn't require instantaneous interactions.

It just expresses the fact that the center of mass of an isolated system defines an inertial reference frame-that's what it's all about. 

Think about the purpose of the third law. Why did Newton or anybody else need it?

@ Valentin, But what  about the case when Sun is taken out of the solar system, earth still follows its regular trajectory for next 8 and half minutes as if the Sun was still there.

Dear Vikash,

You are right. Newton’s Third law (To every action there is an equal and opposite reaction) does not apply for Universal Gravitation or “Free Fall” ; because there is no opposite reaction in this case; if that was not so, gravity could not be an universal attractive force as assumed by official physics.  The whole framework of modern cosmology is defective and this is the very reason why more and more dark/black cosmic monsters and processes have to be invoked in more or less regular basis. Newton’s Third Law is indispensable in terrestrial mechanics; yet it has no role is the mechanics of the cosmic bodies! This violates the fundamental principle that the laws of physics are the same in all reference frames.

 The reason for this gross misunderstanding (and the necessity to manufacture more and more  mysteries) of the dynamics of the cosmic bodies lies in the causality based world outlook of official physics, philosophy and theology. In the terrestrial realm the cause and effect of motion, force, momentum etc. can be accounted for even quantitatively. But this is not the case at the cosmic (or quantum) level. Physics has no understanding of the origin of “motion” of all kinds. Newton ascribes cosmic motion to an “impulse” from God and He must always be on hand to “cause” motion and keep things going at all levels of existence! Einstein solves this nagging problem in GR by wishing off and eliminating any role of matter and motion; as if it is so easy to do!

Only a materialist dialectics based world outlook that posits contradictions (and their resolution mediated by chance and necessity) as its basis of its enquiry; takes into account Newton’s Third Law; can rescue modern physics and cosmology (and also quantum dynamics) from this mess and the crisis. Please see my article in RG; my numerous comments (including few made today in the RG forum by Dr. Engelhardt; as well as my numerous books and articles on this issue. Only the links to my recent article and the forum by Dr. Engelhardt are given below; the others are available from my RG profile:

1. https://www.researchgate.net/publication/317040165_THE_CONCEPTUAL_DEFECT_OF_THE_LAW_OF_UNIVERSAL_GRAVITATION_OR_%27FREE_FALL%27_A_DIALECTICAL_REASSESSMENT_OF_KEPLER%27S_LAWS

2.  https://www.researchgate.net/publication/312118218_Free_Fall_in_Gravitational_Theory?feedback/

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

Article Free Fall in Gravitational Theory

Of course there is an opposite reaction in gravity-it's just negligible in many cases. How to take it into account is described by Einstein's equations, when the RHS can't be neglected. 

The two forces are equal when each contains a component of acceleration force. In general the gravitational components are not equal forces, as can be shown by introducing a small third mass to the system.. When masses are not equal the smaller mass must accelerate more than the larger mass to maintain the equality. Strictly speaking all the masses in a gravity system will accelerate, although the larger masses accelerate less than the smaller masses. 

Usually there is angular momentum in which motion occurs around the combined center of gravity. So the definitions of force are not exactly correct, although they are sufficient in many cases. In this question there can be two different values of r, depending on which mass is being measured from the common center of gravity.

As I understand now, "Newton's" third law was proposed initially for contact forces and so action-reaction emerged instantaneously. However, provided the transmission of forces are bound by the speed of light, then the third law is still applicable for action at a distance.

"Newton’s third law states that when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction." -Encyclopedia Britannica.

Here of-course the term "interaction" is a general term. When we specialize to gravitational interaction it still holds as expected. Consider the case of a book resting on a table. Here the book is applying a force on the table in the downward direction and the table is applying the same amount of force in the upward direction to achieve a condition of static equilibrium. In the case of astronomical systems we can consider the example of sun and earth system. Both are moving around the center of mass, and the CM is moving as a free particle. Here also; when we factor out overall motion of the center of mass, then in the center of mass frame, force applied by sun on earth is same in magnitude with the force applied by the earth on the sun. Direction of two forces (action and reaction) are however opposite.

"However, provided the transmission of forces are bound by the speed of light, then the third law is still applicable for action at a distance."

Newton's Third Law specifically mentions "ACTION" and an equal and "OPPOSITE REACTION"! All the Ph.D. holding physicists in this forum explain gravity in terms of "action at a distance" , instnataneous or non-instantneous and explain away the "equal and opposite" part of the Third Law. So, gravity as an universal attractive force necessarily leads to the cosmic monsters like the "Back Holes" and all other ever new cosmic "mysteries" and monsters!

Now comes centre of mass (CM) "moving as a free particle" theory! Is CM a physical, tangible, material body existing independently of the earth and the Sun that can influence the gravitational force between them?

This lasting confusion about gravity (as an unidirectional and an universal attractive force) in Causality based physics existed since Newton - the very reason Albert Einstein tried to solve this problem by eliminating the term "Force", "Matter" and "Motion" altogether; by incorporating even more fantastic bending of "Spacetime"! “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 universal attractive force still survives, because Einstein had to import matter and motion from the backdoor (and like Newton) as an "impulse" from the creator!

Dialectics in the persons of Hegel and Marx gave a rational explanation of the assembly of the heavenly bodies (like the solar system for example) in terms of a contradiction of the "inherent free motion" of the cosmic bodies and their temporary confinement in various cosmic assemblies due to a gravitational attractive force between them. For dialectics, motion is an inherent attribute of matter; there can be no matter without motion and no motion without matter.

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

https://www.amazon.com/Philosophy-Space-Time-Whence-Cometh-Matter/dp/984041884X

On the other hand quantum gravity is an unknown theory. Therefore whether it satisfies Newton's third law or not is not less unknown, I guess.

One way we could view it is from your kind of perception but I have different kind of regards on this issue;

"Experiment on non equivalency of rest and uniform motion:

Next, let us suppose that we have a solid rectangular box placed on a smooth surface such that the frictional effect between two surfaces may be negligible. Let the two adjacent sides of that rectangular box, is pushed by any means in the two ways procedures. By means of which, it will be in the state of rest i.e. ‘x’ position at both t=o and t=T cases, in one stage. It is not the matter of talk as anyone will be satisfied with the answer for this stationary position i.e. the box is pushed equally from the two adjacent sides. Similarly, let it be in the state of motion, shifting to the position ‘x’ by uniform displacement at t=T from ‘x’ at t=0. This uniformly displaced position relative to the time gives the measure of uniform velocity ‘v’. It matters that whether this kind of displacement is occurred because, of greater amplitude of pushing from one side, in comparative to the other or not. This emphasizes the real cross-check of Newton’s law of inertia of motion, which in general sense usually simplifies the problem by noting that there is equal amplitude of pushing in either case because, at both cases it fulfills the condition of first law. Let us view it in specific sense. To say that these both cases are equivalent, they must stand on common footage. Over-viewing the first case, there is no doubt two sides have equal magnitudes, thus one side cancels the other side and the box remains stationary. If so, in second case, anyone of the two sides must be of greater magnitude to breakout the stage of stationary or rest because, the occurrence of movement from the rest stage entirely depicts different condition to one another. If rest and uniform motion are equivalent, the resting body sometime needs to be in uniform motion and vice-versa. Practically, there must always be one side magnitude greater to give the displacement as a form of resultant. Let us define these pushing amplitudes as forces F1 and F2 from the left hand side and right hand side respectively, as shown in figure below (attached).

In first case, F1=F2 but in second case F1>F2, such that the resultant displacement is because of magnitude of F1-F2 pushing force. ‘University Physics’ states the third law paradox which arises because, the block slides while stonemason remains stationary. It states that the sliding is because of Newton’s first law, as net force on moving body is zero, after the block starts to move [36]. This and above phenomenon is exactly same as the ‘terminal velocity’ explained above where, F1 acts as total weight of falling mass and F2 acts as upthrust force. The difference is that ‘University Physics’ neglects the sense of upthrust while I do not. Here, we may habitually think that if F1 is really greater, then there must be increasing order of velocity rather than a uniform, but it is not so what is happening. If it is so, there will be no existence of viscous force aroused due to ‘terminal velocity[1]’. We have already described above what is the real cause of terminal velocity. This is the example of action-reaction pair acting on same body which reflects that the dynamic equilibrium isn’t possible in same body. So, Newton’s third law of motion is not applicable in this kind of motion. In chapter five, we will explain how and where this law is applicable."___________from my book "Unique Perceptions on Physics".

But after preparing my article " A simple course of relative acceleration in Physics", I came to conclude that Newton's third law is never incorrect. The thing which is incorrect is our interpretation to link it causally how it is inappropriate to use. For your kind of interpretation, regardless how and what way the gravitational effect get loosed, the third law will permit its influence until as long as there is simply attraction is held. Your question is not new in literature, but it is linked to other phenomenon like Mach's principle and inertia. What is wrong, is application of Newton's first two laws of motions how they are actually should not be used.