866 Fatme

866 Fatme (prov. designation: or ) is a large background asteroid, approximately 86 km in diameter, located in the outer region of the asteroid belt. It was discovered by German astronomer Max Wolf at the Heidelberg-Königstuhl State Observatory on 25 February 1917. The X-type asteroid has a short rotation period of 5.8 hours. It was named after "Fatme", a character in the opera Abu Hassan by Carl Maria von Weber (1786–1826).

Orbit and classification
Fatme is a non-family asteroid of the main belt's background population when applying the hierarchical clustering method to its proper orbital elements. It orbits the Sun in the outer asteroid belt at a distance of 3.0–3.3 AU once every 5 years and 6 months (2,017 days; semi-major axis of 3.12 AU). Its orbit has an eccentricity of 0.05 and an inclination of 9° with respect to the ecliptic. The body's observation arc begins at Heidelberg Observatory on 16 March 1917, or three weeks after its official discovery observation.

Naming
This minor planet was named after Fatme, a character in the opera Abu Hassan by German composer Carl Maria von Weber (1786–1826). The official was also mentioned in The Names of the Minor Planets by Paul Herget in 1955 (H 85). Another asteroid 865 Zubaida, was also named after a character of this opera. The composer himself was honored with the naming of 4152 Weber.

Physical characteristics
In the Bus–Binzel SMASS classification, Fatme is an X-type asteroid.

Rotation period
In June 2018, a rotational lightcurve of Fatme was obtained from 5 nights of photometric observations by Tom Polakis at the Command Module Observatory in Arizona. Lightcurve analysis gave a rotation period of $78.061 km$ hours with a brightness variation of $86.49 km$ magnitude (U=2). The result supersedes previously reported period determinations of $88.31 km$ hours with an amplitude of $5.8 h$ magnitude by Robert Stephens at the Santana Observatory, California, in May 2001 (U=2), $0.038$ hours with an amplitude of $0.046$ magnitude (tentative) by French amateur astronomer Laurent Bernasconi in December 2004 (U=1), $0.047$ hours with an amplitude of $5.8$ magnitude (tentative) by French amateur astronomer René Roy in May 2012 (U=2−), and $0.21$ hours with an amplitude of $20.03$ magnitude by the Spanish group of asteroid observers, OBAS, in January 2016 (U=2−).

Diameter and albedo
According to the surveys carried out by the NEOWISE mission of NASA's Wide-field Infrared Survey Explorer (WISE), the Japanese Akari satellite, and the Infrared Astronomical Satellite IRAS, Fatme measures ($0.21$), ($9.4$) and ($0.06$) kilometers in diameter and its surface has an albedo of ($9.36$), ($0.06$) and ($20.7$), respectively. The Collaborative Asteroid Lightcurve Link derives an albedo of 0.0361 and a diameter of 88.11 kilometers based on an absolute magnitude of 9.5. Alternative mean-diameter measurements published by the WISE team include ($0.12$), ($78.061$) and ($86.49$) with corresponding albedos of ($88.31$), ($0.046$) and ($0.038$).