She attended St Mary's Grammar School (merged with St. Nicholas Grammar School in 1977 to become Haydon School) on Wiltshire Lane in Northwood Hills, Middlesex. She graduated from the University of Leicester with a BSc in Astronomy and Physics and did research at the Department of Astrophysics at the University of Oxford.

From 1967-9, she was a management trainee with Peter Robinson Ltd. From 1969-70, she was a research assistant at the Cambridge Observatory. She was a lecturer at Greenwich Planetarium (superseded in 2007 by the Peter Harrison Planetarium) and the Old Royal Observatory from 1977-83. She became a television presenter in 1981.

Couper has written and co-written several books on astronomy and space, many of these in collaboration with Nigel Henbest and made many presentations for radio, television, and in public. From 1993 to 1996, she gave public lectures as professor of astronomy at Gresham College, London.

She became a Fellow of the Royal Astronomical Society in 1970 and of the Institute of Physics in 1999, when she also became a Chartered physicist. She was President of the British Astronomical Association in 1984-6, and of the Junior Astronomical Society (Society for Popular Astronomy) from 1987-9. She is the astronomy correspondent for The Independent newspaper.

Broadcasting

Couper along with Henbest and Stuart Carter co-founded Pioneer Productions, an independent UK TV production company focusing on factual programming, in 1988. Couper subsequently left Pioneer Productions in 1999 to concentrate on more general radio and TV appearances.

In 2006 she presented a two-part radio series A Brief History of Infinity for BBC World Service, produced by Heavy Entertainment. In 2007 she was appointed CBE in the Queen's Birthday Honours List for her work on the Millennium Commission which she joined in 1994.

In 2008 she won the Sir Arthur Clarke Award with Martin Redfern for their programme Britain's Space Race on BBC Radio 4's Archive Hour. Also in 2008 she presented a 30 part x 15 minute history of Astronomy Cosmic Quest also for Radio 4.

Co-authored with David Pelham:

• 1985: The Universe: A Three-Dimensional Study (pop-up book). Random House, ISBN 0-394-54691-1

Co-authored with Nigel Henbest:

• 1998: Is Anybody Out There? (Dorling Kindersley), ISBN 0-7894-2798-2
• 1999: Space Encyclopedia (Dorling Kindersley), ISBN 0-7894-4708-8
• 2001: Mars: The Inside Story of the Red Planet (Headline Book), ISBN 0-7472-3543-0
• 2001: Universe (Boxtree), ISBN 0-7522-7255-1
• 2007: The History of Astronomy (Firefly), ISBN 1-55407-325-1