''Now replace the bowling ball with the sun and the marble with Earth. By analogy, gravity does not pull the Earth around the sun. Rather, the sun bends space around it, and curved space pushes Earth so that it moves around the sun.''
''Gravity does not pull you into a chair; space pushes on you creating the feeling of weight.''
You have to remember that this rubber sheet, bowling ball, and marble analogy is used by Einstein as a new model for describing a more general description of Gravitational Interaction.
In Newton's description of Gravitational Interaction any two mass bodies interact with mutual attraction and that mutual attraction causes each mass body to accelerate towards a common center of that two body system. The mutual attraction is measured with a gradient field strength that is inversely proportional to the square of the distance from the center of the system ($$ \frac{1}{d^2}$$). And finally, the gravitational interaction can act over infinitesimal distances (across very small distances), and across infinite space (across very large distances). Newton's Theory of Gravity predicts that over very large cosmological distances the force of interaction is communicated instantaneously. The Einstein Model describes that the interaction is communicated at the speed of light.
Newtonian Gravitational Force
$$F = \frac{m_{test}m_{Net}G}{d^2}= \frac{m_{1}m_{2}G}{d^2} -> \frac{kg m}{s^2} $$.
In Einstein's description of Gravitational Interaction any two mass bodies interact with mutual attraction, and that mass can be either: inertial mass or spacetime mass. Although this spacetime mass is not clearly defined in the Einstein Field Equation, the Higgs Boson is a very good candidate for this spacetime mass.
The essence of Einstein's Gravitational Interaction is that when a first mass body exerts a force on a second mass body, the second body exerts an equal and opposite force on the first body; in accordance with Newton's Second and Third Law of Motion, theory; however that speed of interaction is the speed of light $${c^2}$$.
Likewise, in the vacuum of space, an inertial net mass body exerts an equal an opposite force on the space and time or "spacetime" in that local vicinity of the net mass body. The net Inertial Mass body immersed in the three dimensional space and time around the body is modeled by a spacetime continuum, Stress Energy Tensor (Ideal Gas energy) and curvature, so that is can be said that matter warps the space and time around any Net inertial mass body ($$m_{Net}$$) given by the following equation.
Einstein Mass-Energy Field Equation
$$R_{ab} - \frac{1}{2}R g_{ab} + \Lambda g_{ab} = 2 \pi (\frac{T_{ab}} {\frac{1}{4} \frac{c^4}{G}}) = G_{ab} -> m$$.
Source of Curvature - Closed Geodesic - Stress Energy Tensor
$$T_{ab} = \ (Pressure_{ab})(g_{ab}) = (\frac{1}{4} \frac{c^4}{G})(\frac{G_{ab}}{2 \pi}) = \frac{1}{2}\ m_{Net}{c^2}$$
$$T_{ab} = (\frac{1}{2 \pi})(\frac{1}{4} \frac{c^4}{G})(R_{ab} - \frac{1}{2}R g_{ab} + \Lambda g_{ab}) -> \frac{kg m^2}{s^2}$$.
What Einstein does here is reintroduce the Aether that he discarded. Because of this modeling of curvature and the warping of space and time it requires that spacetime be modeled as a ideal gaseous material.
However the Einstein Mass-Energy Field Equation above only predicts where mass curves spacetime and pushes on other objects. For example imagine the Roman Coliseum/Stadium floor to be a giant rubber sheet or carpet. If you were standing at one end of the coliseum on the rubber sheet, and someone else was at the other end of the Coliseum standing on the rubber sheet; although we would both see and experience the sheet bend and curve in our local vicinity. However, our individual curvatures will have no effect on either person standing on the opposite end of the stadium.
Einstein's equation predicts only how a net inertial mass curving or warping spacetime affects objects in its near gradient field, beyond the influence of curvature another equation is used. This normally where the Schwarzschild Metric comes in.
$${(s_{S})^2} = (1 - (\frac{r_{S}}{d})){\ (ct)^2} - s^2 = (1 - (\frac{r_{S}}{d})){\ (ct)^2} - \(\frac{d^2} {1 - (\frac{r_{S}}{d})}\) - \ d^2\({a}^2 + \ b^2 \sin^2(a_0))-> \ {m^2} $$
or infinitesimal change
$${d(s_{S})^2} = (1 - (\frac{r_{S}}{d})){\ (cdt)^2} - \(\frac{d(d^2)} {1 - (\frac{r_{S}}{d})}\) - \ d^2\(d({a}^2) + \ d(b^2) \sin^2(a_0)) -> \ {m^2} $$.
Similar to Newton's mutual attraction where the strength of the gradient field inversely proportional to the square of the distance from the center of the system ($$ \frac{1}{d^2} -> \frac{1}{m^2}$$); Einstein's mutual attraction is measured with a gradient field strength that is inversely proportional to the square of the distance from the center of the system given by the following ($$\frac{1}{2}R - \Lambda -> \frac{1}{m^2}$$).
So when it is said that space is pushing or exerting a force on you, that means that you also exert an equal and opposite force on the vacuum of spacetime. It can be said that, in accordance with Newton’s “Third Law of Motion;” every Net Inertial Mass ($$m_{Net}$$) body exerts an equal and opposite force on the Spacetime Mass ($$m_{ab}$$) associated with the surrounding medium of Spacetime of which it is evolved and immersed in the universe. In essence, spacetime interacts gravitationally with the inertial mass and mass interacts gravitationally with spacetime.
Qs: Is space pushing the Earth in a preferred direction? How does space decide in which direction a planet is going to be ''pushed.''
The nature of gravity is that every gravitational interaction system is a four (4) dimensional vortex motion, having accelerations or pushing in tangential, radial, and orthogonal directions on any body imersed in the Net Inertial Mass gravitational field.
$$g_{Gravity} = \frac{F}{m_{test}} = \frac{m_{Net}G}{d^2} -> \frac{m}{s^2}$$.
