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Asteroid capture can happen when an asteroid approaches a large planetary body.
Typically asteroids that approach close enough to a planet are thrown out into space or impact the body. In rarer instances, the asteroid is captured in orbit around the planet[1]. This is possible with any planetary body given the right conditions.
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Asteroid capture happens when an asteroid has enough velocity to keep "missing" the planet itself when it is falling towards it, but it does not have enough velocity to escape that planet's orbit. In other words, a asteroid is captured when the asteroid reaches a stable orbit around the planet that it was heading towards. Asteroids also have natural properties that may lend themselves toward being captured. The properties of an asteroid that are most significant to this process are its mass and its relative velocity toward the planet in question. The mass of the planet in question is also a key variable, as is the trajectory of the asteroid.
An asteroid with too much velocity will pass by the planet with a hyperbolic orbit, shooting it out into space. Asteroids that do not have enough velocity will fall into the planet in an impact event. Any trajectory which has a lower relative velocity compared to the escape velocity (which changes with distance) will result in either capture or impact.
The earth-moon system creates a particularly unstable situation whereby the orbit of the asteroid is destabilized. However, with the right orbital stabilization techniques, it may be possible to keep an asteroid in orbit above the earth.
The main reason one would want to capture asteroids is to gain convenient access to its resources. Even a relatively poor resourced asteroid has about 20% iron, a significant about of water, and other volatiles in the form of minerals that we could use (i.e. clay, and oxygen). Another reason as to why Earth would like to capture asteroid, other than it's resources, would be to keep said asteroid from colliding with Earth.
The asteroid Apophis (one of the poorly resourced asteroids) contains enough materials to construct about 150 five-gigawatt solar power satellites at 25,000 tons of steel and silicon each. It also contains enough material to construct Kalpana One style habitats for 100,000 people. All of the habitats would be shielded by the dross remaining after the iron is smelted out of the asteroid ore. The oxygen freed from iron ores during smelting would amount to well over a million tons more than what is needed for the habitats valuable fuel mass of ion thrusters. These would be used to move the habitats and solar power satellites into their chosen orbits, and also used to spin them up.
There are not yet technologies to move the asteroids ourselves and put it wherever we want. So we use gravitational slingshots. A gravitational slingshot, also known as a gravity assist, is a way to pick up speed using a moving planet’s gravity. When a spaceship or an asteroid passes close to a planet or large moon, its orbit is changed, sometimes dramatically. More importantly, small changes in the position or timing of an existing close approach are enormously magnified.
Spontaneous capture relates to a method whereby an asteroid's velocity is not changed and it is captured by the planet.[citation needed]
Aerocapture relates to a method of slowing down an object, which could theoretically be an asteroid. It involves slowing down the asteroid with the atmosphere of the planet.
The problems surrounding causing a man-made capture scenario are many. These stem from the fact that we do not have enough detailed information on the orbital elements of our solar system. Even the slightest variations in estimates for planetary velocity and mass can cause multiple earth radii of change in the asteroid deflection.[citation needed]
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