Extraordinary Near-Earth Asteroids II: 2010 TK7

 

Another denizen of the zoo of Near Earth Asteroids is a little rock called 2010 TK₇.  The first clue to its unusual nature comes from its orbital period: 1.00039 Earth years.  The second clue is the orbit it pursues to permit it to avoid collision with Earth.  This 300-meter NEA follows the L4 Lagrange point on Earth’s orbit, 60 degrees ahead of Earth.  Its behavior is similar to that of the Trojan asteroids on Jupiter's orbit, 60 degrees ahead of and 60 degrees behind Jupiter: we can call it an "Earth Trojan". It circulates slowly around the exact L4 point because its orbit is quite eccentric (eccentricity 0.1908) and inclined (20.882 degrees).  As it ranges from perihelion, 0.8094 AU from the Sun (closer to Venus’ orbit than to Earth’s), out to aphelion at 1.1911 AU, its orbital velocity constantly changes

There have been numerous suggestions that this asteroid would be a very easy target for spacecraft missions from Earth.  The usual rationale is that, unlike most NEAs, it is always close to Earth and therefore easy to reach.  But this argument is simplistic and requires scrutiny.  Suppose the spacecraft departs from the Earth-Moon system with a relative velocity of 2 km per second.  The mean distance between Earth and the L4 point is 150,000,000 kilometers; to get there would then require 75 million seconds (about two and a half years), after which the spacecraft would fly by the asteroid at a relative speed of 2 kilometers per second, traversing the diameter of the asteroid in 1/7 of a second.   To reduce the flyby speed to the point at which the spacecraft could rendezvous with, orbit around, or land on the asteroid requires a velocity change (“delta V” to rocketeers) even larger than that required to take off from the Moon and get into orbit. 

The size of 2010 TK is poorly known.  Its apparent brightness and distance, measured at the time of discovery, permit us to calculate an absolute magnitude of 25.3, which is about 30 meters in diameter if the asteroid has “average” composition and reflectivity; probably 20 to 50 meters within the uncertainties of our data.

In case you haven’t seen the concept of “absolute magnitude” explained, it is the apparent magnitude a body would have if observed at a distance of 1 AU form Earth and 1 AU from the Sun.  The scale for measuring magnitude is an adaptation of the ancient naked-eye system: a bright star is “of the first magnitude”, a noticeably fainter star is 2^nd magnitude, and so on down to the practical limit of naked-eye observation, 6^th magnitude.  Every interval of 5 magnitudes corresponds to a factor of 100 ratio in the intensity of visible light.  Thus Vega is about magnitude 1, the faintest star your naked eye can see, about magnitude 6, provides 100 times less light, and a body of magnitude 26 is 25 magnitudes fainter than Vega, or five factors of 100 (10 billion times) fainter.

Is there anything about this rock that would attract the attention of explorers or miners?  Because of its orbit, it can never approach Earth closely enough to make it a practical target for spectroscopy or for radar observations.  If we needed to know what it is made of, its chemistry, mineralogy, and physical structure, we would have to go there.  In other words, to find out whether it would make sense to send a spacecraft there we would have to send a spacecraft.  This is not a compelling argument for planning a mission.