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A trans-Neptunian object (TNO or trans-Neptune object) is a minor planet that orbits beyond Neptune, specifically, an object with a semi-major axis larger than Neptune's (about 30 AU). Pluto now falls in this category and was the first one discovered, more having been discovered starting in the 1990s. Some others: Orcus, Ixion, Haumea, Makemake, Eris, and Lempo.
A resonant trans-Neptunian object (resonant TNO) is a TNO in an orbital resonance with Neptune. A scattered disk object (SDO or scattered Kuiper Belt object or SKBO) is a TNO with an orbit not much beyond Neptune at the closest, but with high eccentricity, possibly extending to 100 AU from the Sun and beyond, and often with a high orbital inclination, not remaining close to the ecliptic. As a group, the objects are termed the scattered disk. Examples: Sedna, 2002 TC302, and 2004 XR190. The term sednoid refers to those much like Sedna, specifically with a aphelion greater than 50 AU and a semi-major axis greater than 150 AU.
An extreme trans-Neptunian object (ETNO or extreme trans-Neptune object) is a TNO with semi-major axis beyond 150 AU. The term detached object refers to a minor planet separated enough from Neptune to be unaffected by it, and the detached population is the set of those objects.
A binary trans-Neptune object (binary TNO or trans-Neptune binary) is a pair of such objects orbiting each other, or if one is significantly smaller, it might be described as a TNO and its moon. In some cases, more than one moon has been detected, such as Pluto and Haumea.