The Suborbital Imaging Spectrograph for Transition region Irradiance from Nearby Exoplanet host stars, or SISTINE, mission launch was delayed on Tuesday night.
A new attempt has been set for Wednesday night, offering about a four-hour launch window.
Equatorial Launch Australia Executive Chairman Michael Jones said officials went through the countdown on Tuesday with every intent to launch.
"But the consistent winds were outside the parameters that we considered safe," he said in a statement.
"On that basis, we made the decision to delay."
A first successful launch occurred late last month from the Arnhem Space Centre on the Dhupuma Plateau, near Nhulunbuy.
Together with a third rocket to launch later this month, the SISTINE rocket will take measurements of ultraviolet light to help narrow the search for habitable planets.
The two missions will work together to get a full picture of the ultraviolet light coming from stars Alpha Centauri A and B.
Just how much ultraviolet radiation is emitted by different types of stars is poorly known.
Without accurate knowledge, astronomers can't accurately predict which planets might host life.
"We need to understand the stars so that we can understand any planets we find there," said Kevin France, astronomer at the University of Colorado, Boulder, and principal investigator for the SISTINE mission.
About 75 NASA personnel are in Arnhem Land for the missions, the agency's first in Australia in 27 years and first-ever from a commercial spaceport outside the US.
NASA last launched from Australia in 1995, when its rockets lifted off from the Royal Australian Air Force Woomera Range Complex in South Australia.
The local Yolngu helped build Arnhem Space Centre, which is owned by Equatorial Launch Australia, on their land.
They're also taking part in the upcoming launch, including retrieving rocket modules when they return to Earth.
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