He was born in Cockermouth in Cumbria in 1788 (not 1789 as claimed by many sources), the son of John Fallows, a weaver, and his wife Rebecca Fallas. Due in some part to the dedication of his father and the generosity of the townspeople, the scholarly Fearon was given the funds to attend St John's College, Cambridge, where he studied mathematics, coming third in his year when he graduated in 1813. He obtained his Master of Arts in 1816 and went on to teach mathematics at Corpus Christi College, Cambridge. He also became a Fellow of St John's College, Cambridge and an ordained priest in the Church of England. On 29 February 1820 he was elected a fellow of the Royal Astronomical Society and on 8 June 1820 he was granted a fellowship of the Royal Society. One of his proposers for his fellowship to the Royal Society was John Herschel (son of William Herschel) whom he met at St John's College, Cambridge. Later in that year he was appointed by the Admiralty to be the astronomer at the Cape of Good Hope, which would involve overseeing the building of an observatory in what was then a British colony. Before travelling to South Africa, he married Mary Anne Hervey, on 1 January 1821. Between 1821 and 1829 he worked to site, plan and develop the observatory, which was the first astronomical observatory in the southern hemisphere. He also served the Church of England in his time there. He, and all the observatory staff, caught scarlet fever in 1830 and, still Director of the observatory, he died of scarlet fever in Simon's Town, South Africa in 1831 at the age of forty-three.
He was the astronomer to King George IV, and catalogued over 300 stars from his observatory in South Africa. When he first arrived, he only had two portable instruments and a clock, perhaps a Harrison clock. The instruments were a Circle and a Transit Instrument. When the observatory was built, he used a Jones Mural Circle and a Dolland Transit Circle. The Royal Society published his 'Catalogue of 273 Stars' in 1824.
- Warner, Brian (1997). "The Age of Fallows". Monthly Notes of the Astron. Soc. Southern Africa 56: 107–8. Retrieved 2012-11-17.
- Hockey, Thomas (2009). The Biographical Encyclopedia of Astronomers. Springer Publishing. ISBN 978-0-387-31022-0. Retrieved August 22, 2012.
- "Fallows, Fearon (FLWS809F)". A Cambridge Alumni Database. University of Cambridge.
-  Royal Society Archives
-  VisitCumbria
-  Cockermouth History
- Stuart Atkinson's Article on Fallows
- Astronomical Society of South Africa biography
- Oxford Biography
- The Royal Society
- Royal Astronomical Society