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How much mass would an artificial mechanical planet need to have to curve spacetime enough so that a smaller artificial planet/moon would be attracted to it?

And let's say we put this artificial between the Earth and Mars, would it begin to orbit the Sun?

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    $\begingroup$ A mosquito will attract a sand grain at one million miles distance. This is currently a very poorly formulated question. $\endgroup$ – Floris Aug 27 '16 at 20:22
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    $\begingroup$ And BTW, you can figure this out with Newtonian, or classical gravity, no need for worrying about curving spacetime. For planetary or sun sized or lesser object classical Newtonian gravity is a good enough approximation-- all but one minor aspect of observed solar system orbits that we can measure are described within that accuracy by classical gravity. The one unique difference is the perihelion of mercury which shifts a tiny bit. You need bigger masses to really need the curvature description. So, this question does not need general relativity at all to be answered. $\endgroup$ – Bob Bee Aug 27 '16 at 20:57
  • $\begingroup$ @Floris comment noted for future questions. $\endgroup$ – jasmaar Aug 28 '16 at 1:04
  • $\begingroup$ @jasmaar, I'd suggest trying to clarify this one. $\endgroup$ – heather Aug 28 '16 at 12:46
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How much mass would an artificial mechanical planet need to have to curve spacetime enough so that a smaller artificial planet/moon would be attracted to it?

In theory any mass could do what you describe, some of the small asteroids have moons around them.

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Asteroid Ida, (about 32 km in diameter) with its moon Dactyl around it. Ida has a mass of around $4.2 ± 0.6 ×{10^16} $ kg Ida and Dactyl

And let's say we put this artificial system between the Earth and Mars, would it begin to orbit the Sun?

That depends on its orbital velocity, lots of asteroids orbit between Mars and Jupiter, and an artifical asteroid could orbit between Earth and Mars, but it must have the correct velocity to do so, and there are other factors that could affect a stable orbit.

Solar System Dynamics. has more information on planetary orbitals.

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