# (706765) 2010 TK7

(706765) 2010 TK$_7$ (provisional designation 2010 TK$_7$) is a sub-kilometer Near-Earth asteroid and the first Earth trojan discovered; it precedes Earth in its orbit around the Sun. Trojan objects are most easily conceived as orbiting at a Lagrangian point, a dynamically stable location (where the combined gravitational force acts through the Sun's and Earth's barycenter) 60 degrees ahead of or behind a massive orbiting body, in a type of 1:1 orbital resonance. In reality, they oscillate around such a point. Such objects had previously been observed in the orbits of Mars, Jupiter, Neptune, and the Saturnian moons Tethys and Dione.
2010 TK$_7$ has a diameter of about 300 meters (1,000 ft). Its path oscillates about the Sun–Earth L$_4$ Lagrangian point (60 degrees ahead of Earth), shuttling between its closest approach to Earth and its closest approach to the L$_3$ point (180 degrees from Earth).
The asteroid was discovered in October 2010 by the NEOWISE team of astronomers using NASA's Wide-field Infrared Survey Explorer (WISE).

## Discovery

WISE, a space telescope launched into Earth orbit in December 2009, imaged 2010 TK$_7$ in October 2010 while carrying out a program to scan the entire sky from January 2010 to February 2011. Spotting an asteroid sharing Earth's orbit is normally difficult from the ground, because their potential locations are generally in the daytime sky. After follow-up work at the University of Hawaii and the Canada–France–Hawaii Telescope, its orbit was evaluated on 21 May 2011 and the trojan character of its motion was published in July 2011. The orbital information was published in the journal Nature by Paul Wiegert of the University of Western Ontario, Martin Connors of Athabasca University and Christian Veillet, the executive director of the Canada–France–Hawaii Telescope.

## Physical and orbital characteristics

2010 TK$_7$ has an absolute magnitude of luminosity (determinable because of its known location) of about 20.8. Based on an assumed albedo of 0.1, its estimated diameter is about 300 meters. No spectral data are yet available to shed light on its composition. 2010 TK$_7$ would exert a surface gravitational force of less than 1⁄20,000 that of Earth.
At the time of discovery, the asteroid orbited the Sun with a period of 365.389 days, close to Earth's 365.256 days. As long as it remains in 1:1 resonance with Earth, its average period over long time intervals will exactly equal that of Earth. On its eccentric (e = 0.191) orbit, 2010 TK$_7$'s distance from the Sun varies annually from 0.81 AU to 1.19 AU. It orbits in a plane inclined about 21 degrees to the plane of the ecliptic.
Trojans do not orbit right at Lagrangian points but oscillate in tadpole-shaped loops around them (as viewed in a corotating reference frame in which the planet and Lagrangian points are stationary); 2010 TK$_7$ traverses its loop over a period of 395 years. 2010 TK$_7$'s loop is so elongated that it sometimes travels nearly to the opposite side of the Sun with respect to Earth. Its movements do not bring it any closer to Earth than 20 million kilometers (12.4 million miles), which is more than 50 times the distance to the Moon. 2010 TK$_7$ was at the near-Earth end of its tadpole in 2010–2011, which facilitated its discovery.
2010 TK$_7$'s orbit has a chaotic character, making long-range predictions difficult. Prior to 500 AD, it may have been oscillating about the L$_5$ Lagrangian point (60 degrees behind Earth), before jumping to L$_4$ via L$_3$. Short-term unstable libration about L$_3$, and transitions to horseshoe orbits are also possible. Newer calculations based on an improved orbit determination confirm these results.

## Accessibility from Earth

Because Earth trojans share Earth's orbit and have little gravity of their own, less energy might be needed to reach them than the Moon, even though they are much more distant. However, 2010 TK$_7$ is not an energetically attractive target for a space mission because of its orbital inclination: It moves so far above and below Earth's orbit that the required change in velocity for a spacecraft to match its trajectory coming from Earth's would be 9.4 km/s, whereas some other near-Earth asteroids require less than 4 km/s.
During the 5 December 2012 Earth close approach of 0.197 AU (29,500,000 km; 18,300,000 mi), the asteroid had an apparent magnitude of about 21.