The next giant leap in space exploration may be a short hop on a small space rock.

This week, President Barack Obama will request $105 million in NASA's 2014 budget for a mission that would capture a small asteroid, tug it near the moon and later send astronauts to study and grab samples of it.

The asteroid-capturing robot could launch as soon as 2017, with astronauts flying to meet it near the moon by 2021, according to a NASA briefing presented to Congress last week.

Obama's request includes $78 million for NASA to develop technologies for the project and $27 million for beefing up its asteroid-detection work. The mission would fulfill a goal the president set three years ago to send astronauts to an asteroid.

The mission would marry ongoing NASA projects — including asteroid detection, robotic spacecraft development, the construction of a giant new rocket named the Space Launch System and the building of a deep-space human exploration capsule called Orion. An unmanned test launch of Orion is set for next year.

By this summer, NASA is to decide whether the project is feasible, according to agency documents.

The human portion of the mission would send people beyond Earth's orbit for the first time since the final Apollo moon landing in 1972. Crews visiting the captured asteroid could conduct experiments in extracting water, oxygen, metals and silicon, all valuable materials that would help future astronauts "live off the land" during long missions.