Among his activities, he worked on the calculation of the periods of comets and asteroids, measured the distance from the Earth to the Sun, and made observations of the planet Saturn.

He studied mathematics and astronomy from 1811 at the University of Göttingen under Carl Friedrich Gauss, but he enlisted in the Hanseatic Legion for the campaign of 1813–1814, serving as a sergeant in the artillery of the Prussian army, in Holstein and Mecklenburg.

In 1814 he resumed his studies at the University, but after Napoleon's escape from Elba he returned to the military, serving until 1815 by which time he had become a lieutenant.

His former mathematics professor published this note and Encke became famous as the discoverer of the short periodic comets.

The importance of the predicted return based on the calculation by Encke was rewarded by the Royal Astronomical Society in London by presenting their Gold Medal to him in 1824.

[1] His results were published in two separate tracts, entitled Die Entfernung der Sonne (The distance to the Sun, 1822–1824).

He directed the preparation of the star maps of the Academy (1830–1859); beginning in 1830, he edited and greatly improved the Astronomisches Jahrbuch; and he issued four volumes of the Astronomische Beobachtungen auf der Sternwarte zu Berlin (Observations of the Berlin observatory, 1840–1857).

[1] Thereafter Encke was involved in the discovery and orbital parameter determination of other short periodic comets and asteroids.

With this end in view he expounded to the Berlin Academy in 1849 a mode of determining an elliptic orbit from three observations, and communicated to that body in 1851 a new method of calculating planetary perturbations by means of rectangular coordinates (republished in W. Ostwald's Klassiker der exacten Wissenschaften, No.