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The question came to mind after watching this video: http://www.youtube.com/watch?v=MTY1Kje0yLg

If the Earth and Moon can bend space-time, and if the Earth's gravity is strong enough to reach the Moon, then if an astronaut or any object is floating in space somewhere near the Earth at zero speed, should it get attracted to the Earth and eventually burn up in the Earth's atmosphere?

Similar to how the small spheres in the video roll down to the larger object? Could this be why space is so empty? Because even far-away objects that were not in motion were sucked into the Sun or some other planet because of gravity? Obviously then, the asteroids orbit the Sun.

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    $\begingroup$ Yes, if by zero speed you mean zero initial velocity relative to the Earth's surface (or let's say relative to Earth's center, since I don't want to include Earth's rotation in this - that's simply a distraction). One's position and velocity relative to a nonrotating frame wherein the Earth's center is stationary full define one's trajectory; this is true whether you're thinking about the problem from a Newtonian standpoint or whether you're calculating geodesics for the relevant solution to the Einstein field equations .... $\endgroup$ – WetSavannaAnimal May 22 '16 at 9:55
  • $\begingroup$ .... (i.e. the Schwarzschild nonrotating black hole with an Earth mass centered at Earth's center). You, like David Bowie, will simply fall to Earth. As for your comments on "why space is so empty", then yes you can take this as the reason: gravity makes stuff clump. Prof. Penrose has more to say about this clumping and its relationship with the Universe's thermodynamics in the later chapters of "Road To Reality". $\endgroup$ – WetSavannaAnimal May 22 '16 at 9:57
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Yes. All objects are gravitationally attracted to one another. Even people.

Therefore, the earth will draw you to itself no matter how far out you are.

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Gravity is an attractive force, and classical Newtonian theory is adequate to answer in the affirmative: starting from two objects in space at rest, the attractive potential is 1/r , r their distance, and they will fall on each other.

The reason planets and satellites have a stable orbit is due to the solutions of the kinematic equations when there exists momentum and angular momentum. The solutions in general are conic sections.

Conic sections are important in astronomy: the orbits of two massive objects that interact according to Newton's law of universal gravitation are conic sections if their common center of mass is considered to be at rest. If they are bound together, they will both trace out ellipses; if they are moving apart, they will both follow parabolas or hyperbolas.

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