2010 TK7

2010 TK₇

Asteroid 2010 TK7 (circled in green) in image from the Wide-field Infrared Survey Explorer spacecraft
Designations
Minor planet category	Apollo,[1] Earth trojan
Orbital characteristics[1]
Epoch September 30, 2012 (JD 2456200.5)
Aphelion	1.1910871 AU
Perihelion	0.809410 AU
Semi-major axis	1.0002487 AU
Eccentricity	0.190791
Orbital period	365.3932 d (1.0003921 a)
Mean anomaly	251.4032°
Inclination	20.8823°
Longitude of ascending node	96.5283°
Argument of perihelion	45.8527°
Physical characteristics
Dimensions	~300 m[2]
Apparent magnitude	20.8 (when near Earth) to 23.6
Absolute magnitude (H)	20.627 [1]

2010 TK₇ is the first Earth trojan asteroid to be discovered; it precedes Earth in its orbit around the Sun.^[3][4] Trojan objects are most easily conceived as orbiting at a Lagrangian point, a dynamically stable location (where gravitational and centrifugal forces balance) 60 degrees ahead of or behind a massive orbiting body, in a type of 1:1 orbital resonance. In reality, they oscillate (librate) 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 TK₇ has a diameter of about 300 meters (1,000 ft).^[2] Its path oscillates about the Sun–Earth L₄ Lagrangian point (60 degrees ahead of Earth), shuttling between its closest approach to Earth and its closest approach to the L₃ point (180 degrees from Earth) about every 400 years.

The asteroid was discovered in October 2010 by the NEOWISE team of astronomers using NASA's Wide-field Infrared Survey Explorer (WISE).^[5]

Discovery

WISE, a space telescope launched into Earth orbit in December 2009, imaged 2010 TK₇ 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.^[6] 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.^[3][6]

A paper published in the Journal of Modern Physics by G. Giovannetti-Singh^[7] established its gravitational attraction to Earth, angular momentum, and mass of 2010 TK₇.

Physical and orbital characteristics

Effective potential plot showing Earth's Lagrangian points (not to scale); contours around L₄ and L₅ represent tadpole loop paths

2010 TK₇'s spiraling path (green) relative to Earth and its orbit (blue dots) over the course of half a tadpole loop; each spiral turn represents a year's motion

2010 TK₇ has an absolute magnitude of luminosity (determinable because of its known location) of about 20.6.^[8] Based on an assumed albedo of 0.1, its estimated diameter is about 300 meters.^[3] No spectral data are yet available to shed light on its composition. 2010 TK₇ would exert a surface gravitational force of less than 1/20,000 times 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 TK₇'s distance from the Sun varies annually from 0.81 AU to 1.19 AU.^[3] It orbits in a plane inclined about 21 degrees to the plane of the ecliptic.

Trojan asteroids in actuality 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 TK₇ traverses its loop over a period of 395 years.^{[note 1][3]} 2010 TK₇'s loop is so unusually elongated that it sometimes travels nearly to the opposite side of the Sun from the Earth. Its movements do not bring it any closer to the Earth than 20 million kilometers (12.4 million miles), which is more than 50 times the distance to the Moon. In 2010/2011, TK₇ was at the near-Earth end of its tadpole,^[3] which facilitated its discovery.

2010 TK₇'s orbit has a chaotic character, making long-range predictions difficult. Prior to A.D. 500, it may have been oscillating about the L₅ Lagrangian point (60 degrees behind Earth), before jumping to L₄ via L₃. Short-term unstable libration about L₃, and transitions to horseshoe orbits are also possible.^[3]

Accessibility from Earth

Position of 2010TK₇ relative to Earth in 2011

Since Earth trojans share Earth's orbit and have little gravity of their own, it can sometimes be less energetically costly to reach them than the Moon, even though they are dozens of times more distant. However, 2010 TK₇ is not an energetically attractive target for a space mission because of its orbital inclination:^[9] It moves so far above and below the 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, while some other near-Earth asteroids require less than 4 km/s.^[3]

During the 5 December 2012 Earth close approach of 0.197 AU (29,500,000 km; 18,300,000 mi),^[10] the asteroid only had an apparent magnitude of about 21.^[11]

See also

• Other moons of Earth
• Provisional designation in astronomy, the naming convention used for astronomical objects immediately following their discovery

Notes

References

• Jonathan Amos (28 July 2011). "Trojan asteroid seen in Earth's orbit by Wise telescope". BBC. Archived from the original on 28 July 2011. Retrieved 2011-07-29. 

External links

• MPC Database entry for 2010 TK₇
• NASA animation of its motion