This is the first of three flights planned in total from the Arnhem Space Center (northern Australia).
The rocket, which carries a small space telescope described as a "mini Hubble", took off up to 350 km altitude in the starry night.
"It's a historic moment for us as a company in particular, but it's also historic for Australia," Equatorial Launch Australia CEO Michael Jones told AFP before takeoff.
His company owns and operates the launch site located in the far north of the island.
Mr Jones described Sunday's liftoff as the Australian space industry's "coming out" and hailed the chance to work with NASA.
After several delays due to rain and wind, the suborbital sounding rocket was able to leave to study the X-rays emanating from the stars Alpha Centauri A and B, which together form a binary star.
After reaching its peak, the rocket payload must record data on the binary system before descending back to earth using a parachute.
According to NASA, this launch offers a unique insight into other solar systems and offers new opportunities for scientists.
Mr Jones said the unique location had complicated preparations: the rockets have to be brought from Darwin to the site - a 28-hour drive - and it took years of work to get all the official clearances.
The next launch is scheduled for July 4, leaving little time for the team - time to "dusting ourselves off, taking a day off, and then getting back to it", according to Mr Jones.
It is the first NASA rocket to take off from Australia since 1995. Australian Prime Minister Anthony Albanese hailed the start of a "new era" for his country's space industry.
© 2022 AFP