The single most astounding fact I learned when taking introductory (undergrad) astronomy was that two objects can actually occupy the same orbit, at the same distance from the Sun. Previous to that I always had believed it was one orbit to one planet or other body, i.e. minor planet or asteroid. But no, Joseph Louis Lagrange had shown hundreds of years earlier that there should be two points in Jupiter's orbit at or near where a minor planet could remain almost indefinitely. The name for these objects became known as 'the Trojans' after the Homeric heroes.
In 1906, Max Wolf - a German astronomer who developed a photographic technique to detect asteroids - found one occupying the same orbit as Jupiter, but always ahead of the planet by 60 degrees. Lagrange's mathematical prediction had been vindicated. Later observers found other asteroids, including that lagged Jupiter by the same margin.
Subsequently, Trojans were detected at the Lagrange points of other planets, including Mars, Venus, Uranus, Neptune and even more at Jupiter. Jupiter alone has since been found to have more than 11,000 Trojans that appear to be primordial remnants from the solar system's formation. In fact, last October NASA launched a probe named 'Lucy' - after the fossilized skeleton of an early hominid ancestor- to visit several of them.
Most startling, the first "Earth Trojan" (2010 TK7) was identified in 2010 at the Lagrange point L4 - which puts it 60 degrees ahead of Earth in the same orbit. Detected by the WISE, space telescope the asteroid is about 300 m in diameter and shuttles between its closest point to Earth and closest point to the Lagrangian point L3. The graphic below shows the Lagrange points for Earth.
Note that three Lagrange points (L1, L2, L3) lie along the line of centers connecting the two major bodies, Sun and Earth. Recall again what Lagrange investigated mathematically is the 'restricted three body problem' in celestial mechanics. This entailed mathematically examining the dynamics of a small particle (too small for gravitational effects on larger bodies) in the G-field of two larger objects. He found that there were five positions relative to the two larger objects in which the small mass once placed will move in a circular orbit - always maintaining a fixed orientation to the other two, larger masses. It turns out the 3 points already identified are unstable, while the points L4 and L5 are stable.
Now, in the latest work, an international team from the University of Alicante and the University of Barcelona has confirmed the existence of a second Earth Trojan asteroid (2020 XL5 ) oscillating between the L4 and L5 point. This has been after a decade of searching and the study has been published in the journal Nature Communications. Blog readers can access the full paper at the link below:
From the work, we now know the new Earth Trojan is significantly larger than the earlier one, 1 km in diameter as opposed to 0.3 km. Where exactly is it, at L4 or L5? How do we determine the position? As the researchers note this entails more detailed celestial mechanics:
"The key parameter to quantify the state is the relative mean longitude λr is defined as the difference between the mean longitude of the asteroid λa and the mean longitude of the Earth λE: when the resonant angle λr librates around 60°, i.e., 0° < λr < 180° the asteroid is called an L4 Trojan, when the resonant angle λr librates around 300°, i.e., 180° < λr < 360° the asteroid is called an L5 Trojan, when λr circulates then the asteroid leaves the Trojan-like orbit"
Thus, we certainly would not fancy a potential collision, given it would cause mass devastation. Current simulations show that it will slip from the Earth's gravitational grasp in 4,000 years and head into the wider solar system. From appearances, as the researchers note, 2020XL5 appears to be a dark, carbon-rich object which might be an interloper from the main asteroid belt between Mars and Jupiter. Why is it these asteroids are so difficult to detect? The researchers point out that the primary problem is these objects are usually only observable close to the Sun, making the observational window exceedingly small.
The initial observations of 2020 XL5 though insufficient to pin down its orbit, ultimately succeeded after recovering additional sightings (going back to 2o12) using ground-based telescope records. The asteroid was found, but at the time nobody recognized it as one. Finally, after a decade's worth of data, and 'tweaking' the orbit 800 times in different simulation, the orbital elements were identified. These are shown in Table 1 of the paper in the preceding link.
One of the most encouraging conclusions of the work is that further analysis of Earth Trojans (ETs) might prove useful for space missions. In the words of the researchers (op. cit.):
Discovering ETs having lower orbital inclination and eccentricity might have another important implication: unlike 2020 XL5, objects librating near to the Lagrangian points with low inclinations could be reached from the Earth with a very low delta-v budget. Therefore these objects may become ideal targets for space missions and, in the more distant future, to settle human bases or install scientific hardware that would benefit from their peculiar location .
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