Hayabusa achieved the second and largest of four engine firings designed to guide the probe back home.
The probe visited the asteroid Itokawa in 2005, making close approaches designed to capture soil samples.
But the mission has been plagued by technical glitches affecting the engines and communications with Earth.
It remains unclear whether the probe managed to grab material from Itokawa; scientists will have to open the capsule to find out.
At the weekend, the Japanese Space Agency (Jaxa) announced that Hayabusa had successfully completed its second Trajectory Correction Manoeuvre (TCM), guiding the spacecraft to Earth's "outer rim".
The craft is now roughly 7,600,000km from our planet, according to Jaxa.
The spacecraft is scheduled to return to Earth on 13 June.
At a distance of 40,000km from Earth, the Hayabusa "mothership" will release its sample return capsule.
Shielding should protect the capsule from the high temperatures it will experience during re-entry. Parachutes will then deploy to slow the capsule's speed for its touchdown in the Australian outback.
It is due to land at the Woomera Test Facility in South Australia at around 1400 GMT.
Scientists will be on tenterhooks as they wait for the capsule to be opened.
Even if Hayabusa failed to grab large samples at Itokawa, the capsule may still contain some residues from the asteroid which could be analysed in laboratories.
Hayabusa probably failed to collect large samples from the asteroid
Researchers have already been able to study remote sensing data sent back to Earth by the spacecraft during its encounter with the asteroid.
Hayabusa - which means "Falcon" in Japanese - was launched from the Kagoshima Space Center in Japan on 9 May 2003.
It arrived at Itokawa in September 2005, returning astonishing images of the potato-shaped asteroid's jagged terrain.
Hayabusa made two "touchdowns" designed to collect rocks and soil for return to Earth. But it apparently failed to fire a metal bullet designed to gather the samples.
Asteroids contain primordial material left over from the formation of the Solar System billions of years ago.
A fuel leak in 2005 left Hayabusa's chemical propellant tanks empty, so engineers had to use the spacecraft's ion engines to guide the spacecraft home.
Ion thrusters are highly efficient but have a low acceleration. This means that each trajectory correction takes much longer to complete than it would with chemical engines.
Source : http://news.bbc.co.uk/2/hi/science_and_environment/10196807.stm
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