It may be a motu proprio or an encyclical, depending upon the purpose.
An encyclical is a letter from the pope to the Church. Regular bishops do not send letters to the entire Church.
Pope Leo XIII Wrote This Encyclical.
Mysterium Fidei - encyclical - was created in 1965.
The Catholic encyclical "Arcanum" was promulgated by Pope Leo XIII on February 10, 1880.
An encyclical, which is a lengthy treatise on a subject or a motu proprio which is generally a short letter covering a particular action or subject and is meant as a clarification.
Encyclical
An encyclical
Pius XII wrote Miranda Prorsus, the official name of the encyclical, on September 8, 1957. (The title of the encyclical would be perhaps more accurately translated as Remarkable Inventions.)
Popes do not elect popes. Popes are elected by the cardinal electors.
encyclical
the encyclical