question: How gravity bending space causes other objects to move
comment: For #2 you are correct. I think part of your question comes from why/how do things have the energy to speed up towards each other so I'll answer that part Gravity as we describe it is a force. This force is dependent on the gravitational constant in the universe and masses of the system/bodies in question. Forces such as gravity and magnetism have potential energies associated with them. When you pull 2 magnets apart you use your kinetic energy to 'give' potential energy to the magnets and if they get close enough to overcome drag/friction/other forces they will release that potential energy and snap together. When you "magically" place your two bodies in the scenario you are actually giving that asteroid a large amount of gravitational potential energy because it is no longer on a flat sheet it is now on the valley created by the star. The sheet is really a visualization of potential energy. Objects want to decrease their potential energy (converting it to kinetic energy) so they will roll down the potential energy sheet to more favorable spots.
passages: Mach's question regarding the bulging of rotating bodies is resolved because local space-time geometry is informing a rotating body about the rest of the universe. In Newton's theory of motion, space acts on objects, but is not acted upon. In Einstein's theory of motion, matter acts upon space-time geometry, deforming it; and space-time geometry acts upon matter, by affecting the behavior of geodesics.
   Since then, general relativity has been acknowledged as the theory that best explains gravity. In GR, gravitation is not viewed as a force, but rather, objects moving freely in gravitational fields travel under their own inertia in straight lines through curved space-time – defined as the shortest space-time path between two space-time events. From the perspective of the object, all motion occurs as if there were no gravitation whatsoever. It is only when observing the motion in a global sense that the curvature of space-time can be observed and the force is inferred from the object's curved path. Thus, the straight line path in space-time is seen as a curved line in space, and it is called the "ballistic trajectory" of the object. For example, a basketball thrown from the ground moves in a parabola, as it is in a uniform gravitational field. Its space-time trajectory is almost a straight line, slightly curved (with the radius of curvature of the order of few light-years). The time derivative of the changing momentum of the object is what we label as "gravitational force".
   Section::::Technology used to compensate for the negative effects.:Artificial gravity.
  
  Artificial gravity (AG) is the increase or decrease of gravitational force on an object or person by artificial means. Different types of forces, including linear acceleration and centripetal force, can be used to generate this artificial gravitational force.
   Linear acceleration, even at a low level, can provide sufficient g-force to provide useful benefits. A spacecraft under constant acceleration in a straight line would give the appearance of a gravitational pull in the direction opposite of the acceleration. This "pull" that would cause a loose object to "fall" towards the hull of the spacecraft is actually a manifestation of the inertia of the objects inside the spacecraft, in accordance with Newton's first law. 
   A related question, raised by Ernst Mach, was how rotating bodies know how much to bulge at the equator. This, it seems, requires an action-at-a-distance from distant matter, informing the rotating object about the state of the universe. Einstein coined the term Mach's principle for this question.
   In Einstein's theory of general relativity, gravitation is an attribute of curved spacetime instead of being due to a force propagated between bodies. In Einstein's theory, masses distort spacetime in their vicinity, and other particles move in trajectories determined by the geometry of spacetime. The gravitational force is a fictitious force. There is no gravitational acceleration, in that the proper acceleration and hence four-acceleration of objects in free fall are zero. Rather than undergoing an acceleration, objects in free fall travel along straight lines (geodesics) on the curved spacetime.
  
  Section::::See also.
  
  BULLET::::- Air track
  
  BULLET::::- Gravimetry
  
  BULLET::::- Gravity of Earth
   Compared with planets and other astronomical bodies, the objects of everyday life (people, cars, houses, even mountains) have little mass. Where such objects are concerned, the laws governing the behavior of test particles are sufficient to describe what happens. Notably, in order to deflect a test particle from its geodesic path, an external force must be applied. A chair someone is sitting on applies an external upwards force preventing the person from falling freely towards the center of the Earth and thus following a geodesic, which they would otherwise be doing without matter in between them and the center of the Earth. In this way, general relativity explains the daily experience of gravity on the surface of the Earth "not" as the downwards pull of a gravitational force, but as the upwards push of external forces. These forces deflect all bodies resting on the Earth's surface from the geodesics they would otherwise follow. For matter objects whose own gravitational influence cannot be neglected, the laws of motion are somewhat more complicated than for test particles, although it remains true that spacetime tells matter how to move.
   Since it is apparent that in the descent [along the arc] there is more impediment acquired, it is clear that gravity is diminished on this account. But because this comes about by reason of the position of heavy bodies, let it be called a positional gravity [i.e. "gravitas secundum situm"]
   Section::::History.
   Further, the "gravity" felt by an object pressed against the hull of the spacecraft is simply the reaction force of the object on the hull reacting to the acceleration force of the hull on the object, in accordance with Newton's Third Law and somewhat similar to the effect on an object pressed against the hull of a spacecraft rotating as outlined above. Unlike an artificial gravity based on rotation, linear acceleration gives the appearance of a gravity field which is both uniform throughout the spacecraft and without the disadvantage of additional fictitious forces.
   BULLET::::- 1589 - Galileo Galilei uses balls rolling on inclined planes to show that different weights fall with the same acceleration
  
  BULLET::::- 1638 - Galileo Galilei publishes "Dialogues Concerning Two New Sciences" (which were materials science and kinematics) where he develops, amongst other things, Galilean transformation
  
  BULLET::::- 1645 - Ismaël Bullialdus argues that "gravity" weakens as the inverse square of the distance
  
  BULLET::::- 1651 - Giovanni Battista Riccioli and Francesco Maria Grimaldi discover the Coriolis effect
   In any analysis of spacetime, evidence of gravitation requires that one observe the relative accelerations of "two" bodies or two separated particles. In Fig. 5‑1, two separated particles, free-falling in the gravitational field of the Earth, exhibit tidal accelerations due to local inhomogeneities in the gravitational field such that each particle follows a different path through spacetime. The tidal accelerations that these particles exhibit with respect to each other do not require forces for their explanation. Rather, Einstein described them in terms of the geometry of spacetime, i.e. the curvature of spacetime. These tidal accelerations are strictly local. It is the cumulative total effect of many local manifestations of curvature that result in the "appearance" of a gravitational force acting at a long range from Earth.
   In spacetime terms, the path of a satellite orbiting the Earth is not dictated by the distant influences of the Earth, Moon and Sun. Instead, the satellite moves through space only in response to local conditions. Since spacetime is everywhere locally flat when considered on a sufficiently small scale, the satellite is always following a straight line in its local inertial frame. We say that the satellite always follows along the path of a geodesic. No evidence of gravitation can be discovered following alongside the motions of a single particle.
   The weight of an object on Earth's surface is the downwards force on that object, given by Newton's second law of motion, or (). Gravitational acceleration contributes to the total gravity acceleration, but other factors, such as the rotation of Earth, also contribute, and, therefore, affect the weight of the object.
  
  Gravity does not normally include the gravitational pull of the Moon and Sun, which are accounted for in terms of tidal effects.
  
  It is a vector (physics) quantity, whose direction coincides with a plumb bob.
  
  Section::::Variation in magnitude.
   BULLET::::- For a moving gravity-source the gravitational field can be considered as an extension of the object, and carries inertia and momentum - since a direct collision with the moving object can impart momentum to an external particle, interaction with the object's gravitational field should allow "momentum exchange" too. Consequently, a moving gravitational field drags light and matter. This general effect is used by NASA to accelerate space probes, using the gravitational slingshot effect.
  
  Section::::Rotation-dragging effects.
   Section::::Gravity.
  
  Section::::Gravity.:Newton.
  
  Newton's classical theory of gravity offered no prospect of identifying any mediator of gravitational interaction. His theory assumed that gravitation acts instantaneously, regardless of distance. Kepler's observations gave strong evidence that in planetary motion angular momentum is conserved. (The mathematical proof is valid only in the case of a Euclidean geometry.) Gravity is also known as a force of attraction between two objects because of their mass.
   In the 4th century BC, the Greek philosopher Aristotle believed that there is no effect or motion without a cause. The cause of the downward motion of heavy bodies, such as the element earth, was related to their nature, which caused them to move downward toward the center of the universe, which was their natural place. Conversely, light bodies such as the element fire, move by their nature upward toward the inner surface of the sphere of the Moon. Thus in Aristotle's system heavy bodies are not attracted to the Earth by an external force of gravity, but tend toward the center of the universe because of an inner "gravitas" or heaviness.
   In general relativity, gravity has curvature effects on the four dimensions of the universe. A common analogy is placing a heavy object on a stretched out rubber sheet, causing the sheet to bend downward. This curves the coordinate system around the object, much like an object in the universe curves the coordinate system it sits in. The mathematics here are conceptually more complex than on Earth, as it results in four dimensions of curved coordinates instead of three as used to describe a curved 2D surface.
  
  Section::::Parallel transport.
  
  Section::::Parallel transport.:The interval in a high-dimensional space.
   Einstein proposed that spacetime is curved by matter, and that free-falling objects are moving along locally straight paths in curved spacetime. These straight paths are called geodesics. Like Newton's first law of motion, Einstein's theory states that if a force is applied on an object, it would deviate from a geodesic. For instance, we are no longer following geodesics while standing because the mechanical resistance of the Earth exerts an upward force on us, and we are non-inertial on the ground as a result. This explains why moving along the geodesics in spacetime is considered inertial.
   Action at a distance
  
  In physics, action at a distance is the concept that an object can be moved, changed, or otherwise affected without being physically touched (as in mechanical contact) by another object. That is, it is the nonlocal interaction of objects that are separated in space.
  
  This term was used most often in the context of early theories of gravity and electromagnetism to describe how an object responds to the influence of distant objects. For example, Coulomb's law and Newton's law of universal gravitation are such early theories. 
   Historically, geologists have used the terms "gravity spreading" and "gravity gliding" interchangeably, or with little distinction. This article follows the convention of "Excursus on gravity gliding and gravity spreading" by D.D. Schultz-Ela, which defines gravity spreading as a lateral extension and vertical contraction, which thus must be applied to a non-rigid body. Gravity gliding, however, is applied to a block that is not being deformed, and is therefore less common to observe. However, it can be difficult to distinguish between the two in real world scenarios, and often both occur simultaneously.
  
  Section::::Mechanism.
   Another equivalent way of thinking about this process is that as a large object moves through a cloud of smaller objects, the gravitational effect of the larger object pulls the smaller objects towards it. There then exists a concentration of smaller objects behind the larger body (a "gravitational wake"), as it has already moved past its previous position. This concentration of small objects behind the larger body exerts a collective gravitational force on the large object, slowing it down.
   Caution is required in describing structures on a cosmic scale because things are often different from how they appear. Gravitational lensing (bending of light by gravitation) can make an image appear to originate in a different direction from its real source. This is caused when foreground objects (such as galaxies) curve surrounding spacetime (as predicted by general relativity), and deflect passing light rays. Rather usefully, strong gravitational lensing can sometimes magnify distant galaxies, making them easier to detect. Weak lensing (gravitational shear) by the intervening universe in general also subtly changes the observed large-scale structure.
   In a field model, rather than two particles attracting each other, the particles distort spacetime via their mass, and this distortion is what is perceived and measured as a "force". In such a model one states that matter moves in certain ways in response to the curvature of spacetime, and that there is either "no gravitational force", or that gravity is a fictitious force.
  
  Section::::Classical mechanics.
   Section::::History.:Gravitational Models (1964-Current).
  