Edmund Goetz was educated in Alsace (part of Germany from 1871), Amiens (France), and Littlehampton, on the south coast of England. He became a novice at Roehampton, London, joining the Society of Jesus (Jesuits). In November 1885 he came to South Africa and by 1887 was teaching mathematics and physics at St Aidan's College, Grahamstown. In 1889 he was transferred to Jersey, United Kingdom, where he taught the same subjects at the French Naval School. He obtained his Licentiate in Science in Paris, listing his qualification as Master of Arts (MA). In 1902 he worked under Father Hagen (who later became Director of the Vatican Observatory) in Georgetown University, Washington, and collaborated in the compilation of Hagan's Atlas Stellarum Variabilium and in his publication of Heis's observations of variable stars.
The scientific studies Goetz undertook from 1901 were in preparation for his subsequent appointment in Rhodesia (now Zimbabwe). He arrived in the country in June 1903 to become the first director of the government-sponsored observatory in Bulawayo, which was run by the Jesuits. He was a Fellow of the Royal Astronomical Society and remained in charge of the observatory until 1926, when the Jesuits left Bulawayo and gave the observatory building back to the government. The observatory was well-equipped for meteorological and magnetic observations, and later also acquired a 127 mm equatorial telescope and an astronomical clock. In 1913 the telescope was housed in a new astronomical observatory with a rotating dome, funded by the British South Africa Company and leading mining companies and trading firms in Bulawayo in recognition of Goetz's work. The observatory was later named after him.
Goetz regularly supplied meteorological observations, including measurements of the rate of evaporation, from his second order meteorological station to the Meteorological Commission of the Cape of Good Hope from 1903 to 1907. He was an active member of the Rhodesia Scientific Association for 30 years, serving on its council from 1904. Already in August 1903 he read a paper before its members on "Variable stars", which was published in its Proceedings (Vol. 4, pp. 37-46). During 1904/5 he received a grant of 25 pounds sterling from the society to assist his magnetic survey. That same year, following the departure of William Crosley*, he took over the chairmanship of the society's Meteorological Committee, and in July 1905 spoke on "Meteorological observations at Bulawayo" (Vol. 5(2), pp. 69-97). The most important paper he contributed to the society, however, was an extensive report on "The rainfall of Rhodesia" (1908, Vol. 8 (3), pp. 1-129) - a detailed study of the monthly and seasonal rainfall of the territory, its dry and rainy seasons, regional variations in rainfall, the effects of atmospheric pressure, intensity of falls, rain-bearing winds, rainfall cycles, and so forth. This paper was published also as a monograph (London, 1909). His other papers on meteorology and climatology were "On some meteorological features of Southern Rhodesia" in the Report of the South African Association for the Advancement of Science (1905/6, pp. 125-134); "Dry season and drought in Rhodesia" and "The rainy season in Southern Rhodesia", in the Rhodesia Agricultural Journal (1912, Vol. 10, pp. 538-544 and 1913, Vol. 11, pp. 689-702); and "Rainfall and barometric variation in Bulawayo", in the South African Journal of Science (1920, Vol. 17, pp. 155-157).
In June-July 1909 Goetz was commissioned by G. Pauling to make astronomical observations to fix the geographical positions of points along the route of the proposed railway line from Broken Hill (now Kabwe, Zambia) to the Katanga copper mining region in the Belgian Congo (now the Democratic Republic of the Congo) - a distance of over 400 km. A few years later, in May 1914, he set out on a journey of over 600 km up the Zambezi River from Livingstone to Lealui, to make a magnetic survey of Barotseland, in western Zambia. On this journey he was accompanied by H.E. Wood* of the Transvaal Observatory, who made astronomical observations. Next he made a magnetic survey in west-central Matabeleland during 1916, funded by grants from the Royal Society of South Africa and the Rhodesia Scientific Association. The results of both surveys were published under the title "Magnetic observations in Rhodesia" in the Transactions of the Royal Society of South Africa (1919-1920, Vol. 8, pp. 297-303).
In 1910, during the return of Halley's comet, Goetz gave public lectures on the comet in Bulawayo and Salisbury (now Harare). He was elected a Fellow of the Royal Astronomical Society in 1903. The next year he became a member of the South African Philosophical Society and remained a member when it became the Royal Society of South Africa in 1908. Two years later he was elected a Fellow of the latter. He also joined the South African Association for the Advancement of Science and when the association met in Bulawayo in 1911 served as president of Section A (which included astronomy and meteorology). He delivered papers at the South African Dry Farming Congress at Klerksdorp in 1910 (on "Dry farming") and in Pretoria in 1912 (on "Rainfall and evaporation"). Goetz spent his last years on the staff of St George's College in Harare, where he taught mathematics and French. He was a naturalised British subject.