The phrase "to capture an asteroid" means sending a spacecraft to approach and bring an asteroid into its orbit or control, usually for scientific study or possibly for mining resources. Full definition
A 2017 study suggests that Trojan asteroids near Mars are from the planet, and not captured asteroids from other regions in space. (space.com)
NASA has considered capturing an asteroid and placing it in orbit around the moon, close enough for us to extract resources without risking a collision with Earth. (newscientist.com)
The space agency's rush to capture an asteroid for its astronauts can only lead to no good, critics argue at workshop (sciencemag.org)