Green was awarded a Doctorate of Philosophy (Ph.D.) by the University of Sydney in 1973, writing a thesis titled "Spiral structure of the galaxy from a radio continuum survey" under the supervision of Bernard Mills.
[2] Green rejoined the University of Sydney's School of Physics in 1991 and "went on to build a prolific career focussed on the ecology and structure of the Milky Way Galaxy".
[3] She served as director of the Molonglo Observatory Synthesis Telescope for over a decade and was appointed as the school's first female head in 2007.
She was also an inaugural co-chair of the Women in Astronomy Working Group of the International Astronomical Union.
[2] She was appointed Companion of the Order of Australia (AC) in the 2022 Queen's Birthday Honours, for "eminent service to science, particularly physics and astrophysics, as an educator and researcher, as a mentor to colleagues and students, and a role model to women".