2010 TK7
Encyclopedia
2010 TK7 is the first Earth trojan asteroid
to be 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 gravitation
al 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 only in the orbits of Mars, Jupiter, Neptune
and several moons of Saturn.
2010 TK7 has a diameter of about 300 metre. 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).
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. 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.
Also, a paper published in the Journal of Modern Physics (G. Giovannetti-Singh) establishes the gravitational attraction to Earth, Angular Momentum, and mass of 2010 TK7.
of luminosity (determinable because of its known location) of about 20.6. 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 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. 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. 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, 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 orbit
s are also possible.
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.
Earth Trojan asteroid
Earth trojans are asteroids that orbit in the vicinity of the Earth-Sun Lagrangian points and . They are named after the Trojan asteroids that are associated with the analogous Lagrangian points of Jupiter....
to be discovered; it precedes Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
in its orbit
Earth's orbit
In astronomy, the Earth's orbit is the motion of the Earth around the Sun, at an average distance of about 150 million kilometers, every 365.256363 mean solar days .A solar day is on average 24 hours; it takes 365.256363 of these to orbit the sun once in the sense of returning...
around the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
. Trojan objects
Trojan (astronomy)
In astronomy, a Trojan is a minor planet or natural satellite that shares an orbit with a larger planet or moon, but does not collide with it because it orbits around one of the two Lagrangian points of stability , and , which lie approximately 60° ahead of and behind the larger body,...
are most easily conceived as orbiting at a Lagrangian point
Lagrangian point
The Lagrangian points are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects...
, a dynamically stable location (where gravitation
Gravitation
Gravitation, or gravity, is a natural phenomenon by which physical bodies attract with a force proportional to their mass. Gravitation is most familiar as the agent that gives weight to objects with mass and causes them to fall to the ground when dropped...
al and centrifugal forces balance) 60 degrees ahead of or behind a massive orbiting body, in a type of 1:1 orbital resonance
Orbital resonance
In celestial mechanics, an orbital resonance occurs when two orbiting bodies exert a regular, periodic gravitational influence on each other, usually due to their orbital periods being related by a ratio of two small integers. Orbital resonances greatly enhance the mutual gravitational influence of...
. In reality, they oscillate (librate
Libration
In astronomy, libration is an oscillating motion of orbiting bodies relative to each other, notably including the motion of the Moon relative to Earth, or of Trojan asteroids relative to planets.-Lunar libration:...
) around such a point. Such objects had previously been observed only in the orbits of Mars, Jupiter, Neptune
Neptune Trojan
Neptune trojans are Kuiper belt object-like bodies in solar orbit that have the same orbital period as Neptune and follow roughly the same orbital path...
and several moons of Saturn.
2010 TK7 has a diameter of about 300 metre. Its path oscillates about the Sun–Earth L4 Lagrangian point
Lagrangian point
The Lagrangian points are the five positions in an orbital configuration where a small object affected only by gravity can theoretically be stationary relative to two larger objects...
(60 degrees ahead of Earth), shuttling between its closest approach to Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
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
NASA
The National Aeronautics and Space Administration is the agency of the United States government that is responsible for the nation's civilian space program and for aeronautics and aerospace research...
's Wide-field Infrared Survey Explorer
Wide-field Infrared Survey Explorer
Wide-field Infrared Survey Explorer is a NASA infrared-wavelength astronomical space telescope launched on December 14, 2009, and decommissioned/hibernated on February 17, 2011 when its transmitter was turned off...
(WISE).
Discovery
WISE, a space telescopeSpace observatory
A space observatory is any instrument in outer space which is used for observation of distant planets, galaxies, and other outer space objects...
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. After follow-up work at the University of Hawaii
University of Hawaii
The University of Hawaii System, formally the University of Hawaii and popularly known as UH, is a public, co-educational college and university system that confers associate, bachelor, master, and doctoral degrees through three university campuses, seven community college campuses, an employment...
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
Nature (journal)
Nature, first published on 4 November 1869, is ranked the world's most cited interdisciplinary scientific journal by the Science Edition of the 2010 Journal Citation Reports...
by Paul Wiegert of the University of Western Ontario
University of Western Ontario
The University of Western Ontario is a public research university located in London, Ontario, Canada. The university's main campus covers of land, with the Thames River cutting through the eastern portion of the main campus. Western administers its programs through 12 different faculties and...
, Martin Connors of Athabasca University
Athabasca University
Athabasca University is a Canadian university in Athabasca, Alberta. It is an accredited research institution which also offers distance education courses and programs. Courses are offered primarily in English with some French offerings. Each year, 32,000 students attend the university. It offers...
and Christian Veillet, the executive director of the Canada–France–Hawaii Telescope.
Also, a paper published in the Journal of Modern Physics (G. Giovannetti-Singh) establishes the gravitational attraction to Earth, Angular Momentum, and mass of 2010 TK7.
Physical and orbital characteristics
2010 TK7 has an absolute magnitudeAbsolute magnitude
Absolute magnitude is the measure of a celestial object's intrinsic brightness. it is also the apparent magnitude a star would have if it were 32.6 light years away from Earth...
of luminosity (determinable because of its known location) of about 20.6. Based on an assumed albedo
Albedo
Albedo , or reflection coefficient, is the diffuse reflectivity or reflecting power of a surface. It is defined as the ratio of reflected radiation from the surface to incident radiation upon it...
of 0.1, its estimated diameter is about 300 meters. 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
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
with a period
Orbital period
The orbital period is the time taken for a given object to make one complete orbit about another object.When mentioned without further qualification in astronomy this refers to the sidereal period of an astronomical object, which is calculated with respect to the stars.There are several kinds of...
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
Orbital eccentricity
The orbital eccentricity of an astronomical body is the amount by which its orbit deviates from a perfect circle, where 0 is perfectly circular, and 1.0 is a parabola, and no longer a closed orbit...
(e = 0.191) orbit, 2010 TK7's distance from the Sun varies annually from 0.81 AU
Astronomical unit
An astronomical unit is a unit of length equal to about or approximately the mean Earth–Sun distance....
to 1.19 AU. It orbits in a plane inclined
Inclination
Inclination in general is the angle between a reference plane and another plane or axis of direction.-Orbits:The inclination is one of the six orbital parameters describing the shape and orientation of a celestial orbit...
about 21 degrees to the plane of the ecliptic
Plane of the ecliptic
The plane of the ecliptic is the plane of the Earth's orbit around the Sun. It is the primary reference plane when describing the position of bodies in the Solar System, with celestial latitude being measured relative to the ecliptic plane. In the course of a year, the Sun's apparent path through...
.
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
Rotating reference frame
A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. A rotating frame of reference is a special case of a non-inertial reference...
in which the planet and Lagrangian points are stationary); 2010 TK7 traverses its loop over a period of 395 years. 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
Moon
The Moon is Earth's only known natural satellite,There are a number of near-Earth asteroids including 3753 Cruithne that are co-orbital with Earth: their orbits bring them close to Earth for periods of time but then alter in the long term . These are quasi-satellites and not true moons. For more...
. In 2010/2011, TK7 was at the near-Earth end of its tadpole, which facilitated its discovery.
2010 TK7's orbit has a chaotic
Chaos theory
Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...
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
Libration
In astronomy, libration is an oscillating motion of orbiting bodies relative to each other, notably including the motion of the Moon relative to Earth, or of Trojan asteroids relative to planets.-Lunar libration:...
about L3, and transitions to horseshoe orbit
Horseshoe orbit
A horseshoe orbit is a type of co-orbital motion of a small orbiting body relative to a larger orbiting body . The orbital period of the smaller body is very nearly the same as for the larger body, and its path appears to have a horseshoe shape in a rotating reference frame as viewed from the...
s are also possible.
Accessibility from Earth
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: It moves so far above and below the Earth's orbit that the required change in velocityDelta-v
In astrodynamics a Δv or delta-v is a scalar which takes units of speed. It is a measure of the amount of "effort" that is needed to change from one trajectory to another by making an orbital maneuver....
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.
See also
- Other moons of Earth
- Provisional designation in astronomyProvisional designation in astronomyProvisional designation in astronomy is the naming convention applied to astronomical objects immediately following their discovery. The provisional designation is usually superseded by a permanent designation once a reliable orbit has been calculated...
, the naming convention used for astronomical objects immediately following their discovery