John Francis (Frank) Skjellerup was the tenth of the thirteen children of Peder Jensen Skjellerup, a Danish immigrant farmer in Australia, and his wife Margaret, born Williamson. His father died when he was still a small boy, with the result that he left school at the age of 14 to work for the Victorian Post Office. He trained as a telegraph operator and early in 1900 was recruited by the government of the Cape Colony. In February that year he started working as an assistant in the Central Telegraph Office, Cape Town, and still held that post in 1914. He spent the rest of his working life in South Africa, but when he retired he returned to Australia in May 1923 and settled in Melbourne.
The appearance of a daylight comet in January 1910, and the return of Halley's Comet that same year, made him interested in astronomy. He bought a 76 mm refractor and began systematically searching for comets in 1911. He discovered his first comet on 11 September 1912, but it turned out to have been observed by W.F. Gale in Australia a few days earlier. He reported his find in 'Observations of Gale's Comet (1912a)' (Journal of the British Astronomical Association, 1913, Vol. 23, pp. 210-211). Finally, on 19 December 1919, he discovered a comet (C/1919 Y1) that was named after him. On 11 December 1920 he found the second comet for which he received credit (C/1920 X1). These two discoveries were reported in Circular No. 6 (1920) and No. 8 (1921) of the Cape Astronomical Association. His next comet, found on 16 May 1922, was later shown to be the same as that observed by J. Grigg in 1902 (26P/Grigg-Skjellerup). It has a period of only 5.1years, and was extensively studied by the Giotto space probe in 1992. This find was followed by comet C/1922 W1 on 26 November 1922. After his return to Australia in 1923 he independently discovered comets C/1927 X1 and C/1941 B2.
Skjellerup was also a dedicated variable star observer. He and A.W. Long* received permission in 1917 to use a 152mm refractor at the Royal Observatory in Cape Town for this work. He continued his observations in Australia. Between 1916 and 1927 he made over 6000 brightness estimates of some 120 variable stars, mainly Mira-type variables.
In 1912 Skjellerup became a foundation member of the Cape Astronomical Association and served as its first secretary-treasurer. When the association resumed its activities in 1916, following the outbreak of World War I (1914-1918) he was director of its Variable Star Section. By 1921 he was joint vice-president of the association. During 1921/2 he delivered a paper on 'Variation of the Moon's declination' at a meeting of the association. In 1922 the association amalgamated with its counterpart in Johannesburg to form the Astronomical Society of South Africa, with Skjellerup serving as its first treasurer and director of its Variable Star Section. He resigned from the latter position in December 1922. Later, in Australia, he was president of the Astronomical Society of Victoria for three years.
Skjellerup was married to Mary Peterson, but they had no children.