Our solar system contains one massive object – the sun – and many smaller planets and asteroids.
Now researchers from Duke University in Durham, N.C. have proposed a new explanation for the size diversity, which is found throughout the universe and is called hierarchy.
Adrian Bejan, the J.A. Jones Professor of Mechanical Engineering at Duke University, says there's a very good reason why objects in the universe come in a wide variety of sizes, from the largest stars to the smallest dust motes – and it has a lot to do with how paint cracks when it dries.
In a paper published March 1 in the Journal of Applied Physics, Bejan explains how the need to release internal tension shaped the universe as we see it.
"Since the 1700s scientists have known that gravity causes objects in the universe to get bigger, but the phenomenon of growth does not explain the hierarchy," said Bejan. "To my huge surprise this question has been overlooked."
Though unknowably large and spread out, the very early universe can be thought of as a finite volume of suspended particles.
And because every object in the universe exerts a gravitational force on every other object in the universe, this volume was in internal tension.
It was only a matter of time before particles began coming together to form larger objects. But why did they come together to form objects in such a wide variety of sizes, rather than in a uniform manner?
"We know from common experiences that things in volumetric tension crack, and they crack instantly everywhere," said Bejan. "The easiest example is paint drying on a wall. As it dries, it shrinks, putting the entire system in tension. Then boom, it suddenly cracks overnight, relieving the tension. And the design responsible for that relief is hierarchical, meaning few large and many small."
According to Bejan – whose specialty is thermodynamic – this pattern of relief follows the constructal law, which he penned in 1996.
The constructal law states that any flowing system allowed to change freely over time will trend toward an easier flowing architecture (see http://us.macmillan.com/thephysicsoflife/adrianbejan ).
For rivers, roots and vascular systems, this means a few large channels carry massive flows to numerous smaller branches for evacuation.
For a young universe with particles pulling every which way, this means its internal tension released in the fastest way possible.
Bejan had already applied the law of evolution to explain the shape of snowflakes, river basins, lungs and even airplanes, when a conversation with an undergraduate student prompted him to consider how the constructal law would manifest itself in the cosmos.
"This is my first trespass into planetary science," he said.
Bejan and his student, Russell Wagstaff, started by calculating the tension caused by gravitational attraction between bodies of the same size, uniformly distributed in space.
They showed that if the bodies coalesce into some large bodies and some small bodies, the tension is reduced faster than if the bodies merged uniformly.
In a series of thought experiments and simple physics equations, Bejan's paper shows that the fastest way for the tension to be released was through the formation of bodies in a hierarchy.
That is, he demonstrates that if all bodies formed were of the same size, the tension would not be released as affectively as when a few large bodies were formed along with many smaller bodies.
Just like the cracks in the paint.
"The discovery is that hierarchy 'snaps' from the very beginning, spontaneously," Bejan said. The break-up of the uniform suspension of bodies into a few large and many small bodies occurs because it's the fastest way to ease the internal tension caused by gravity, he said.
The natural tendency of a system to evolve toward a state of reduced tension is a manifestation of the constructal law, Bejan said, and can be seen in other phenomena, such as soil cracking under a drying wind. "The working title for our paper was actually 'The Universe as Cracked Mud,'" he said.
"All volumetric cracking is hierarchical. You never see uniform cracking or shattering," said Bejan. "In celestial mechanics, there is this very old idea that bodies coalesce and grow due to gravity, which is of course correct. Growth is one thing, but growing hierarchically rather than all in the same size is another, which is called nature."
Bejan said he hopes the application of the constructal law to the cosmological scale will inspire other researchers to consider how the law could be applied in their own fields.
"I never thought I would have anything to say about celestial bodies in pure physics, but by chance I realized I have a key to open a new door," he said. "Everything has evolution and the constructal law can help predict it. The plan is to keep exploring."
Space News: Why celestial bodies come in different sizes
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