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# 2010 TK7: Earth's Trojan Asteroid

In 1772, French astronomer and mathematician Joseph-Louis Lagrange proposed an interesting idea in his prize-winning essay on the mathematical three-body problem. This problem had been challenging astronomers and mathematicians since it was first proposed by Isaac Newton a century earlier.

While the movements of two gravitationally-bound objects were relatively easy to model using Newton's laws of motion and universal gravitation, the movements of three gravitationally-bound objects were much more complicated. Such systems usually proved unstable in the long term, with one of the three bodies either crashing into one of the other bodies, or being ejected from the system altogether.

In his calculations, Lagrange found five points around the orbit of a planet in a two-body system at which a third, smaller body could remain in a stable orbit, synchronized with the orbit of the larger planet. These five points of libration have since been dubbed Lagrangian points after their discoverer.

The idea of an asteroid existing at one of these points remained a hypothetical one until 1906, when German astronomer Max Wolf discovered the Delaware-sized asteroid 588 Achilles orbiting at one of Jupiter's Lagrangian points.

## The Lagrangian Points

There are five Lagrangian points in a two-body orbital system:

• L1 - The first Lagrangian point lies between the orbiting body and the system's center of gravity. In the Sun-Earth system, this point is about 930,000 miles (1.5 million km) from Earth, inside Earth;s orbit. The Sun-Earth L1 point hosts several Sun-observing satellites, such as the Solar and Heliospheric Observatory (SOHO).
• L2 - This point lies on the far side of the orbiting body, relative to the system's center of gravity. The Sun-Earth L2 point is 930,000 miles (1.5 million km) from Earth on the opposite side of L1. Although this location is too far from Earth to be within our shadow, its stability relative to the Earth and Sun makes L2 an ideal location for space telescopes observing the universe. The L2 point was home to the Wilkinson Microwave Anisotropy Probe (WMAP) during its active observation period mapping the background radiation of the Big Bang.
• L3 - The L3 point lies 180 degrees around the orbiting body's orbit. This location has been used in science fiction as home to a habitable planet permanently hidden from Earth behind the Sun. However, the reality of Earth's elliptical orbit and the Sun's Jupiter-powered wobble means that this locations is visible from Earth at several times during the year.
• L4 - The first of the "Trojan" groups, L4, lies 60 degrees ahead of the orbiting body in its orbit around the center of gravity. Asteroids discovered near the L4 point of the Sun-Jupiter system are in the "Greek Camp," and are named after Greek characters from The Iliad (with a few notable mistakes).
• L5 - The other "Trojan" group lies lies 60 degrees behind the orbiting body. Asteroids at the L5 point in the Sun-Jupiter system are known as the "Trojan Camp," and are named for Trojan characters from The Iliad (again, with a few mistakes).

Of these points, the L4 and L5 are the most stable. Small bodies at the first three points are somewhat like a marble balanced on top of an overturned bowl - the slightest nudge in any direction will cause them to roll downhill, accelerating away. Space probes stationed at these points must use onboard thrusters to maintain their positions.

L4 and L5, on the other hand, behave more like a bowl turned right-side-up. Objects nudged away from these points will either drift back toward them or remain in orbit around them. Given the known stability of the L4 and L5 points and the discovery of natural satellites at these points in the orbits of Jupiter, Mars, Neptune, and several of Saturn's moons, astronomers wondered for many years whether Earth might have its own trojans.

## Discovering 2010 TK7

The Wide-field Infrared Survey Explorer (WISE) was an orbiting telescope launched by NASA in 2009 to survey the sky in four bands of the infrared spectrum. WISE operated until October 2010, when its hydrogen coolant (and NASA funding) ran out. During that time, the probe discovered 154 thousand solar system objects, including some 33,500 asteroids and comets. Though most of these were distant objects, in the main asteroid belt or beyond, 136 of the asteroids were near Earth, and 19 were considered potentially hazardous.

Soon after the data was released, Martin Connors, Canada Research Chair in Space Science, Instrumentation and Networking at Athabasca University in Alberta, Canada, noted that one of the observed Near Earth Asteroids had some interesting characteristics. 2010 TK7 seemed to be synchronized with the orbit of Earth. Connors then worked with Christian Veillet, Resident Astronomer at the Canada-France-Hawaii Telescope atop Mauna Kea to take additional images of 2010 TK7.

This new orbital data then allowed University of Western Ontario professor Paul Wiegert to simulate computer simulations of the asteroid's orbit and confirm that it was co-orbiting the Sun synchronously with the Earth. The skyscraper-sized 2010 TK7 is in an elliptical orbit tilted 20 degrees to the ecliptic, the plane of Earth's orbit around the Sun. In the 365.4 days it takes to orbit the Sun, its position relative to Earth forms a twisted, tadpole-shaped loop centered around the L4 point. In other words, the asteroid is orbiting the Sun-Earth L4 point in the same amount of time it takes to make a loop around the Sun.

Since 2010 TK7's year is longer than Earth's by about three hours, its position relative to Earth also shifts slightly every year. Viewed over a period of hundreds of years, the asteroid traces a spiraling tadpole loop pattern that takes it from a closest point of 12 million miles (20 million km) to a farthest point that is near the opposite end of Earth's orbit. The combined tugs of gravity from the Earth and Sun keep the asteroid from getting any closer to us or farther away, however, so there is no danger of a collision with Earth - at least over the next few millennia.

While the asteroid's occasional proximity to Earth makes it seem like a potential target for human or robotic exploration, its high inclination to our orbit would require a huge expenditure of fuel in order for a mission to reach it. It is also an extremely faint object, with an apparent magnitude comparable to the brightness of Pluto's smallest moons.

## Could Earth Have Other Trojans?

Although 2010 TK7 is the only currently known Trojan asteroid in the Sun-Earth system, it may be the first of many. There are other known "horseshoe" asteroids such as 3753 Cruithne that are in co-orbital relationships with Earth, orbiting the Sun in such a way that they seem to trace a horseshoe shape around our planet over hundreds of years. We've even created some - the 100-foot (30-meter) asteroid J002E3 discovered in 2002 is widely believed to be the spent S-IVB stage of the Saturn rocket used by Apollo 12, recaptured by Earth's gravity after dancing around the Sun-Earth system for more than 30 years. It is certainly possible that other small bodies similar to TK7 will be discovered in future surveys of our Solar System.

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