The gravitation has been for a long time treated by people as a mysterious force attracting massive objects, one to another, from a distance, acting through empty space, approximately according to Newton's law for Newtonian force F_N = GMmr/r³, where G is Newtonian gravitational constant and r is distance between centers of gravity of masses M and m. Newton didn't believe in existence of such force because of this empty space between the masses. The same as Einstein, who didn't believe in "spooky action at a distance".

Derivation of Einsteinian (static) gravitational force

(1) ... E(x) = γmc²(x),

where E(x) is the total energy of a particle, γ is ratio of relativistic energy of a particle to its invariant energy which in static case reduces to γ = 1, m is its invariant mass, and c(x) is gravitational speed of light, and c(x)|_(x=0)=c (invariant speed of light). In static case (when position of m is not changing) equation (1) reduces to E(x) = mc²(x). It turns out that the mysterious "gravitational force" shows up as a derivative of the above equation with respect to the displacement of the particle dx in its own reference frame and coming from the fact that the time slows down in the vicinity of any external mass M. With this slowing down of time in vicinity of mass M, the energy of any particle in vicinity of mass M diminishes, since all movements of the particle are slower, so all of them have less energy represented by E(x) in equation (1). So necessarily there is a certain "apparent force" acting on mass m equal

(2) ... F = - dE(x)/dx,

where dx is displacement of particle in relation to the center of gravity of mass M, the source that is the reason of slower running time acting on mass m directed towards mass M taken previously for an attractive force of "gravitational attraction" while it is only an apparent inertial force coming from particle m pressing towards the most probable position of this particle in vicinity of mass M, possition of minimum of its energy, which the particle has without any external prompting force. It is a subtle quantum effect of gravitation making the Einsteinian gravitation a quantum theory automatically assuring that increments or decrements of gravitational energy have to be quanta

(3) ... ΔE = hν,

where h is Planck constant, and ν is the frequency of a carrier delivering this gravitational energy (frequency of gravitational wave of Einsteinian theory). The apparent force of this effect is the inertial force of the particle pushing against the external mass M with force
F of equation (2). Since the energy of any particle is controlled by Einstein's equation (1) then when time runs slower in vicinity of mass M, the energy E(x) is diminshed according to its derivative

(4) ... dE(x)/dx = 2mc(x)dc/dx,

where c(x) is the speed of light determined by the spacetime metric at position x. Equation (4) because later equation (6) implies that

(5) ... dc/dx = - a/c/2,

where a is acceleration with which a rocket ship has to move to produce the acceleration producing the inertial force F of equation (2) on the principle of equivalence of acceleration and gravitational force. Equation (5) may be derived from a rocket ship moving with acceleration a which according to the principle of equivalence of gravitation and acceleration is the same as acceleration causing the same "gravitational force" as equation (2) and remembering that the same gravitational effect is bending the light ray in the accelerating rocket ship twice as much as the observed in flat space of Newtonian math since the second half of light ray bending comes from the invisible in Newtonian math curvature of space. Finally the Einsteinian gravitational force is

(6) ... F = - dE(x)/dx = 2mcdc/dx = - 2mca/c/2 = ma,

and appeares more accurate than the Newtonian force F_N given in the preamble. The small difference between those two forces (Newtonian F_N and Einsteinian F) that astronomical observations of movement of planet Mercury show, come from the difference between flat space of Newtonian math and the curved physical space of Einstein's physics that is responsible for equation (5).

This is the whole mystery of "gravitational force" demystified by the Einsteinian time dilation and the curvature of space, and turning out to be a regular inertial force, pushing the body m of Einstein's equation (1) towards external mass M, that allegedly "attracts it", but its presence only modifies the spacetime making it such that the time runs in it slower and there is more space by the same amont that time runs slower (the space is curved). The science has managed to send one more myth (of "attractive gravitational force", down the drain, discovering in the process the quantum properties of gravitation: tendency of matter to occupy the lowest energy levels at the expense of creating an inertial force of equation (3) pressing against other matter(M). In free fall in there are no gravitational forces and therefore no pushing against other matter.

Gravitation demystified

The math and physics of the way Einstein demystified gravitation is described for astronomers in [http://www.fuw.edu.pl/~wjast/163.htm this paper]. For anybody else, below, in this summary:

Summary: The apparent gravitational force ("at rest") F is caused by the curvature of space and the time dilation that together (acting 50/50 since each shares with another half of their common action) cause the effects of diminishing energy of objects immobilized in curved space. When the objects are not immobilized (left in a free fall), they follow their natural positions of the greatest probability of being there in spacetime without producing any forces. E.g. the Moon folowing its natural path around the Earth moving at each point of its travel with appropriate acceleration a compensating changes of its total energy E regardless of its mass m, moving around the "apparently attracting mass" M. In this way no additional energy is created or destroyed and the law of conservation of energy is satisfied automatically for all the moving bodies of the universe. This is the Einsteinian gravitation. No "attractive gravitational forces" in free fall and no "potential gravitational energy" beyond energy contained already in the mass m of mases of bodies of equation (1) that for this reason may be called also "potential energy", since its derivative with respect to dx, the same as in the Newtonian math, equals the "gravitational force"F = - dE/dx. So the mass m is now a counterpart of the old Newtonian "potential energy" responsible for maintaining the balance of energies in universe while lifting a weight were increasing the amount of potential energy in the universe and dropping it was using this accumulated "potential energy" to do the work. Now the Newtonian mathematical tricks related to "potential energy" are not needed since Einsteinian physics does all the work automatically conserving energy within invariant masses m. There is no other potential energy in the universe beyond this conteined in invariant masses m of equation (1). Especially there is no "negative potential energy" exploding in the Big Bang event at the alleged beginning of the universe since the Einsteinian universe, being eternal, neither have (nor needs) any beginning, time itself being relative.