# Towing of asteroid

I recently studied that NASA has planned to tow and place it in the orbit of the moon. My doubt is when asteroid is placed in the orbit near moon.since the gravitational field of earth is very high.what will it revolve around the moon or the earth. Can anyone clarify my doubt ??

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The real threat is not the Earth's gravity, but the gravitational anomalies (mascons - for "mass concentrations") on the Moon. They have significant impact on the lifetime of Moon's satellites and the choice of orbits. –  Deer Hunter Apr 11 '13 at 10:21

There are stable orbits around the Moon, also Nasa, Esa, and many more have satellits orbiting the Moon, and they don't "decay" towards the Earth.

To look for the physics and no only examples search for Hill sphere:

Acording to the last link, the Moon's sphere of influence is 38 Moon radii or $66.1\cdot 10^{3}km$ plenty of space to host an asteroid.

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