After finishing school Schjellerup was added to a watchmaker in teaching. It does not meet his scientific pursuits, so he continued formed in the self-study and in 1848 passed the entrance examination at the Polytechnic College in Copenhagen. After only two years he was able in 1850 to study with the final exam in Applied Mathematics and Mechanics finish. In 1851 he accepted a position as Observer at the old University Observatory. Some years later he was also a teacher of mathematics and astronomy at the Naval Officers' School and drawing teacher at the Polytechnic educational institution. He retained this post until his death.
The old observatory was built some 200 years earlier than under Longomontanus tower in downtown. Despite several equipment with new instruments she was now limited because of their cramped premises which allowed no fixed established instruments, as well as because of their unfavorable city able to fit astronomical work. Schjellerups monitoring activities therefore first had to be limited to the time service. He therefore devoted to more theoretical studies such as railway calculations of minor planets and comets, including in particular the comet of 1580 based on the original observations of Tycho Brahe.
When in 1855 the chair of astronomy at the University was free, Schjellerup not received this item because it was not a graduate of the University. When the construction of a new observatory was being considered, they moved him Heinrich Louis d'Arrest for the post of director, as he had already made a name in astronomy. The new 1861 finished University Observatory offered Schjellerup but now much better conditions for astronomical observations. 1875, after the death of d' arrest him the professorship of astronomy was offered. However, he declined, partly because of the associated financial losses, partly because he had lost the leisure for own studies, which left the routine work of the observatory and the other obligations to him.
The new observatory was equipped with a zehnzölligen refractor by Merz and a meridian circle by Pistor & Martins. This meridian circle Schjellerup began in September 1861 Stars - primarily eighth and ninth magnitude - in the zone between 15 ° and -15 ° declination observed. Already in 1864 he was able to present a catalog of the calculated average for 1865 Örtern of 10,000 stars of the Royal Danish Academy of Sciences.
1866 Schjellerup published a catalog of red stars, which were for the then newly introduced spectroscopy as a supposed final stages of stellar evolution of particular interest.
Schjellerup began to learn oriental languages , mainly Arabic and Chinese. In the Danish Royal Library, he found a manuscript of the Persian astronomer al - Sufi, in which he gave a thorough and based on our own observations description of the fixed stars. These observations were from the 10th century, that were temporally approximately in the middle between the Almagest and modern star catalogs. Since no other observations of star brightness from that era are known Schjellerup translated this work ( using the services of a second manuscript from St. Petersburg) and made the brightness observations of astronomical research as accessible. However, his plan to tap into another work also by other ancient observations translations, he gave up in the face of difficulties, who had opposed him in the publication of Stars fixes. He instead began in 1881 with a series of individual publications under the title " Recherches sur l' Astronomy des Anciens " ( Studies on the astronomy of the ancients ), but of which appeared to his death only three. The first dealt with the used method in Alexandria, at night to measure time based on Sternkulminationen; the second examined Chinese observations of solar eclipses; the third compared seven reported by Ptolemy conjunctions between the Moon and fixed stars with modern lunar tables.
The lunar crater Schjellerup is named after him.
- Stjernefortegnelse indeholdende 10000 Positioner af teleskopiske Fixstjerner imellem - 15 og 15 grader declination. Copenhagen 1864 ( digitized )
- Description of Stars fixes, composée au milieu du siècle de notre dixième ère par l' Persan astronomer Abd- al -Rahman al - Sufi. St. Petersburg 1874 ( digitized )