Asteroid capture can happen when an asteroid

Asteroid

Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...

 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. This is possible with any planetary body given the right conditions.

Detailed explanation

Asteroid capture happens when an asteroid has enough velocity to keep "missing" the planet it is falling towards but not enough velocity to escape orbit, in other words, when it reaches a stable orbit around it. Asteroids have natural properties that may lend themselves to be captured. The properties of an asteroid that are most significant to this process are its mass and relative velocity to the planet in question. The mass of the planet is also a key variable.

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

Impact event

An impact event is the collision of a large meteorite, asteroid, comet, or other celestial object with the Earth or another planet. Throughout recorded history, hundreds of minor impact events have been reported, with some occurrences causing deaths, injuries, property damage or other significant...

.

Asteroid capture by Earth

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.

Effecting capture

Spontaneous Capture relates to a method whereby an asteroid's velocity is not changed and it is captured by the planet.

Aerocapture

Aerocapture

Aerocapture is a technique used to reduce velocity of a spacecraft, arriving at a celestial body with a hyperbolic trajectory, in order to bring it in an orbit with an eccentricity of less than 1. It uses the drag created by the atmosphere of the celestial body to decelerate. Only one pass in the...

relates to a method of slowing down an object, which could theoretically be an asteroid. It would require slowing down the asteroid with the atmosphere of the nearby planet.

Problems

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.