2010 TK7

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2010 TK7
PIA14405-full crop.jpg
Asteroid 2010 TK7 (circled in green) in image from the WISE spacecraft
Discovery [1]
Discovered by WISE spacecraft
Discovery site LEO, polar orbit
Discovery date1 October 2010
Designations
Orbital characteristics [2]
Epoch 13 January 2016 (JD  2457400.5)
Uncertainty parameter 0
Observation arc 768 days (2.10 yr)
Aphelion 1.1903  AU (178.07  Gm)
Perihelion 0.80918 AU (121.052 Gm)
0.99972 AU (149.556 Gm)
Eccentricity 0.19059
1.00  yr (365.10  d)
Average orbital speed
29.8 km/s [lower-alpha 1]
354.14°
0° 59m 9.672s / day
Inclination 20.890°
96.498°
45.927°
Earth  MOID 0.0837911 AU (12.53497 Gm)
Physical characteristics
Mean diameter
379±123 m [2]
0.059±0.049 [2]
20.8 (when near Earth) to 23.6
20.8 [2]

    2010 TK7 is a sub-kilometer Near-Earth asteroid and the first Earth trojan discovered; it precedes Earth in its orbit around the Sun. [4] [5] 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.

    Contents

    2010 TK7 has a diameter of about 300 meters (1,000 ft). [6] 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).

    The asteroid was discovered in October 2010 by the NEOWISE team of astronomers using NASA's Wide-field Infrared Survey Explorer (WISE). [7]

    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. [8] 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. [4] [8]

    Physical and orbital characteristics

    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 EarthTrojan1st path.jpg
    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 20.8. [2] Based on an assumed albedo of 0.1, its estimated diameter is about 300 meters. [4] 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 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. [4] 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 TK7 traverses its loop over a period of 395 years. [lower-alpha 2] [4] 2010 TK7'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 TK7 was at the near-Earth end of its tadpole in 2010–2011, [4] which facilitated its discovery.

    2010 TK7's orbit has a chaotic character, making long-range predictions difficult. Prior to 500 AD, 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. [4] Newer calculations based on an improved orbit determination confirm these results. [9]

    Animation of 2010 TK7 orbit from 1600 to 2500
    Animation of 2010 TK7.gif
    Relative to Sun and Earth
    Animation of 2010 TK7 around Earth.gif
    Around Earth
    Animation of 2010 TK7 around Sun.gif
    Around Sun
      Sun ·  Earth ·  2010 TK7

    Accessibility from Earth

    Position of 2010 TK7 relative to Earth in 2011 2010TK7 Viwe form plar coordinates.png
    Position of 2010 TK7 relative to Earth in 2011
    Effective potential plot showing Earth's Lagrangian points (not to scale); contours around L4 and L5 represent tadpole loop paths Lagrange points2.svg
    Effective potential plot showing Earth's Lagrangian points (not to scale); contours around L4 and L5 represent tadpole loop paths

    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 TK7 is not an energetically attractive target for a space mission because of its orbital inclination: [10] 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. [4]

    During the 5 December 2012 Earth close approach of 0.197  AU (29,500,000  km ; 18,300,000  mi ), [11] the asteroid had an apparent magnitude of about 21. [12]

    See also

    Notes

    1. ↑ v = 42.1219 √1/0.9989 − 0.5/0.9989.
    2. ↑ Because of its orbital inclination and eccentricity, 2010 TK7's position relative to Earth is actually a complicated, tightly coiled spiral; however, if its average position relative to Earth over a year is represented by a single point, that point will follow the tadpole loop.

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    References

    1. ↑ "2010 TK7 Orbit". Minor Planet Center . Retrieved 1 September 2015.
    2. 1 2 3 4 5 6 "JPL Small-Body Database Browser: 2010 TK7" (2012-11-07 last obs). Retrieved 31 March 2016.
    3. ↑ WayBack Machine 2013 Epoch@MPC
    4. 1 2 3 4 5 6 7 8 Connors, Martin; Wiegert, Paul; Veillet, Christian (27 July 2011). "Earth's Trojan asteroid". Nature . 475 (7357): 481–483. Bibcode:2011Natur.475..481C. doi:10.1038/nature10233. PMID   21796207. S2CID   205225571.
    5. ↑ "NASA's WISE Mission Finds First Trojan Asteroid Sharing Earth's Orbit". NASA. 27 July 2011. Retrieved 1 September 2015.
    6. ↑ Choi, Charles Q. (27 July 2011). "First Asteroid Companion of Earth Discovered at Last". Space.com . Retrieved 27 July 2011.
    7. ↑ Keys, Sonia (7 October 2010). "MPEC 2010-T45 : 2010 TK7". IAU Minor Planet Center . Retrieved 31 July 2011.
    8. 1 2 "Earth's first Trojan asteroid: 2010 TK7". Astro.uwo.ca. 27 July 2011. Retrieved 1 September 2015.
    9. ↑ de la Fuente Marcos, Carlos; de la Fuente Marcos, Raúl (18 February 2021). "Transient Terrestrial Trojans: Comparative Short-term Dynamical Evolution of 2010 TK7 and 2020 XL5". Research Notes of the American Astronomical Society. 5 (2): 29. Bibcode:2021RNAAS...5...29D. doi: 10.3847/2515-5172/abe6ad .
    10. ↑ "Found at last: First Earth companion asteroid". NBC News . 27 July 2011. Retrieved 28 July 2011.
    11. ↑ "JPL Close-Approach Data: (2010 TK7)" (2011-08-03 last obs (arc=40 days; Uncertainty=2)). Retrieved 21 January 2012.
    12. ↑ "AstDyS 2010TK7 Ephemerides for 2012". Department of Mathematics, University of Pisa, Italy. Retrieved 21 January 2012.
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