It was found by the prolific comet discoverer Ernst Tempel on 30 September 1864.

[4] It is named after Terpsichore, the Muse of dance in Greek mythology.

Photometric observations of the minor planet in 2011 gave a rotation period of 10.945±0.001 h with an amplitude of 0.09±0.01 in magnitude.

[5] Two stellar occultation events involving this asteroid were observed from multiple sites in 2009.

[6] A space station orbiting 81 Terpsichore is the main setting in the science fiction story The Dark Colony (Asteroid Police Book 1) by Richard Penn.