3361 Orpheus (1982 HR) is an Apollo asteroid that was discovered on 24 April 1982 by Carlos Torres at Cerro El Roble Astronomical Station. Its eccentric orbit crosses that of Mars and Earth, and approaches Venus as well. From 1900 to 2100 it passes closer than 30 Gm (0.20 AU; 78 LD; 30 million km; 19 million mi) to Venus, 11; Earth, 33; and Mars, 14 times. It passed by Earth at a distance of about 0.03 AU (12 LD; 4.5 Gm; 4.5 million km; 2.8 million mi) in 1937, 1978, 1982, and 2021, and will do so again in 2025.^[1]

3361 Orpheus is a potentially hazardous asteroid (PHA) because its minimum orbit intersection distance (MOID) is less than 0.05 AU (19 LD; 7.5 Gm; 7.5 million km; 4.6 million mi) and its diameter is greater than 140 metres (460 ft). The Earth-MOID is 0.0139 AU (5.4 LD; 2.08 Gm; 2.08 million km; 1.29 million mi).^[1] With an observation arc of 36 years, the orbit is well-determined for the next several hundred years.

The orbital solution includes non-gravitational forces.^[1]

3361 Orpheus had been one of the originally proposed targets for the Near Earth Asteroid Rendezvous (NEAR) mission.

The proposed AIDA mission's spacecraft, Double Asteroid Redirection Test was a fly-by observation of 3361 Orpheus during its trajectory to asteroid 65803 Didymos but later cancelled.^{[4][clarification needed]}