My answer: the gravitational force between two bodies/planets attracts towards its centers of planets.
I think, the answer depends on the kind of the space-time, where you do calculations. I considered the Schwarzshield metric in the empty space-time. It was shown that the acceleration of a free falling body on the Earth's surface is g = GM/R^2, where M, R are the radius and the mass of the Earth. This result was obtained from the condition r = r_g, where r_g is the Schwarzshield ravitational radius. As is known, by the condition r_g = 0 we have: 1) g_00 = 0; 2) g_11 incrieses infinitely. Thus we obtain by r = r_g that 1) the time component is g_00 = 0 (the observed time is stopped); 2) g_11 increases infinitelly. So, we have obtained 1) the stoped time (g_00 = 0); 2) the spatial distances incrise infinitelly. The curvature was not considered there. The gravitational inertial force is determined by Zelmanov in his theory of physical observed values. The 3-dimensional gravitaional inertilal force in the non-rotating Shwarzshield space (all components g_0i = 0) is: F_1 = [(c^2/(c^2 - w)] dw/dr = - GM/r^2. where r = R + h, R --- the radius of the Earth, M is its mass, h is the distance from the centre of the Earth. If h
Dear Chinnaraji Annamalai,
curvature is a mathematical "trick" to avoid handling all the different gravitational forces around a mass-sphere (-> Tensor Mathematics).
Thus, both is true:
the gravitational force between two objects attracts towards their (bary-)centers ... AND acts as curvature.
Usually, applying curvature mathematics, deals with a problem:
the object (typically a sphere with mass) seems to have a lower limit for distances from its bary-center, the Schwarzschild-Radius, which is dependent on the total mass of the planet.
It seems, seen from the outside, as if everything gets slower and slower the shorter the distance is to this Radius, until no more time is ticking, as Larissa Borissova explained...
But: The actually effective mass is only that enclosed within the sphere's surface where the measurement takes place.
The closer you measure to the bary-center, the less mass is enclosed - thus, the related Schwarzschild-Radius also decreases towards zero, and time is ticking normally.
Consequently, exactly at the bary-center, you are weightless: all masses around you "tear" into all directions contemporaneously with the same strength.