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Scientists have finally discovered a Trojan asteroid for Saturn, thereby establishing the presence of these celestial bodies alongside all giant planets in our solar system. For a very long time, Saturn remained the only giant planet in our solar system with no Trojan asteroid.

What are Trojan asteroids? 

Trojan asteroids are a class of asteroids that occupy a stable Lagrange Point in a planet’s orbit around the sun. According to NASA, a Lagrange Point is essentially a position in space where objects can “stay put”. At these positions, the gravitational forces of two larger objects balance out with the motion of the smaller object. This balancing of forces allows the smaller object to stay in a relatively stable position without drifting away. 

For all celestial bodies in orbit, five Lagrange Points exist. L1, L2, and L3 are unstable, and L4 and L5 are stable. 

Trojan asteroids are usually found around L4 or L5 points, which makes them gravitationally stable. Their orbit around the sun is similar to the orbit of the planet they are associated with. 

Trojan asteroids were discovered by German astrophotographer Max Wolf in 1906, but they were named so later. 

Since Trojan asteroids have unusual orbits, the Austrian astronomer Johann Palisa suggested naming them after Achilles, Patroclus, and Hektor, characters in the Greek epic poem Iliad. As astronomers continued to find more of these celestial bodies, they continued to name them after heroes of the Trojan War, with which the Iliad is concerned. This tradition led to the whole class being called Trojan asteroids, although names of Trojan War characters are reserved for Jupiter’s trojans.  

Trojan asteroids remain gravitationally stable for long periods of time and studying them can provide useful insights into the evolution of the solar system. 

What are the findings of the new research? 

According to the new study, Saturn’s Trojan asteroids may have gone unseen because of the movement or migration of planets, destruction due to collisions, smaller stable regions around L4 and L5 compared to those of other planets like Jupiter, and/or long-term gravitational interactions.

The object in question – 2019 UO14 – was first discovered in 2019. The new research used previously collected data and refined the calculated orbit to reach the conclusion that 2019 UO14 is a Trojan asteroid associated with Saturn. It probably became trapped at Saturn’s L4 position around 2,000 years ago and is likely to maintain its orbit for another thousand years.

The researchers uploaded a preprint paper describing their findings to the arXiv repository on September 29, 2024. 

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Geometry is full of familiar shapes like triangles, parallelograms, cylinders, etc. It’s possible for some of these shapes to cover a surface such that they leave no gaps between them — like how square tiles in your house cover the floor completely. In mathematics this activity is called tilling. The shapes most commonly used as tiles have distinct corners and straight edges.

Now, scientists have found a new kind of cell that doesn’t follow these shape rules. Each of these “soft cells” has two pointed corners in a 2D shape and none in a 3D version, plus rounded edges.

The scientists described their findings in the journal PNAS Nexus on September 10. They found the soft cells were able to completely tile a surface in two dimensions, and in a way that the team characterised as organic. Many natural structures like muscle cells, zebra stripes, and the layers of onion bulbs are covered in 2D tiles. These natural systems display a biological preference for curved, smooth-edged shapes.

The soft cells also offer a new tiling paradigm that stands apart from classical geometric forms in mathematics. In this scheme a key challenge to understanding soft cells is their relationship with curvature. A ‘classical’ shape such as a square has “positive curvature” at its vertices, whereas soft cells have a form of “distributed curvature”: instead of sharp deviations at specific points, the curvature is spread smoothly along their edges. Mathematically, this distribution minimises the number of high-curvature points — i.e. corners — while still allowing the shape to tile a space.

Soft cells become more fascinating in 3D. Examples of classical 3D tiles — or space-fillers — are cubes or tetrahedra, which have sharp corners and flat faces. The researchers found they could make 3D soft cells by softening the edges and eliminating sharp corners completely. In this process, the cells acquire a smooth, curved form that seamlessly fills a 3D volume without the need for angled protrusions.

The researchers said they were inspired by natural examples like the nautilus shell. The chambers inside these shells lack sharp corners in 3D — and when they’re sliced open, they reveal a 2D soft-cell tiling. This relationship between 2D and 3D forms illustrates how soft cells could be involved in both biological tissue formation and processes like tip growth.

The mathematics of soft cells also suggests nature prefers to minimise sharp corners for structural reasons and functional efficiency. This shift in geometric understanding paves the way for new insights into why certain biological and natural patterns emerge while others don’t, and offer researchers a novel mathematical framework to explore these questions.

Indeed, the discovery of soft cells opens new avenues of mathematical study as well as has significant implications for biology, architecture, and materials science.

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