Time and Space: The Strange Reality of Reality

Image of the Andromeda Galaxy, showing Messier 32 to the lower left, which is currently merging with Andromeda. Credit: Wikipedia Commons/Torben Hansen
Credit: Unknown artist, Public Domain

“Are the dilation calculations correct” the jump coordinator asks you as he approaches your desk. You look over some papers in front of you that contain various equations scribbled down with certain values circled. The equations are more for your own sense of security, as the computer console in front of you displays the same values you’ve circled. You look back up at the jump coordinator and reply,

“The numbers are solid and the contraction values are set for the trip. Helios II has a copy on board for their astrophysics department to review. Their cryo-engineers have already begun checking the nap-tubes to make sure they have the appropriate wake time in their reference frame.” The jump coordinator nods and walks over to the launch director of Lunar Launch Base Bravo (LLB Bravo). He leans over to relay this information to her and she nods while tapping the screen of her console.

Continue reading “Time and Space: The Strange Reality of Reality”

Stellar Ghosts: Understanding Our Origins

Eta Carinae, one of the most massive stars known. Image credit: NASA
Eta Carinae, one of the most massive stars known. Credit: NASA

The Crab Nebula; at its core is a long dead star... Image credit: NASA, ESA, J. Hester and A. Loll (Arizona State University)
The Crab Nebula; at its core is a long dead star… Image credit: NASA, ESA, J. Hester and A. Loll (Arizona State University)

Our sky is blanketed in a sea of stellar ghosts; all potential phantoms that have been dead for millions of years and yet we don’t know it yet. That is what we will be discussing today. What happens to the largest of our stars, and how that influences the very makeup of the universe we reside in.

We begin this journey by observing the Crab Nebula. Its beautiful colors extend outward into the dark void; a celestial tomb containing a violent event that occurred a millennia ago. You reach out and with the flick of your wrist, begin rewinding time and watch this beautiful nebulae begin to shrink. As the clock winds backwards, the colors of the nebula begin to change, and you notice that they are shrinking to a single point. As the calendar approaches July 5, 1054, the gaseous cloud brightens and settles onto a single point in the sky that is as bright as the full moon and is visible during the day. The brightness fades and eventually there lay a pinpoint of light; a star that we don’t see today. This star has died, however at this moment in time we wouldn’t have known that. To an observer before this date, this star appeared eternal, as all the other stars did. Yet, as we know from our privileged vantage point, this star is about to go supernova and birth one of the most spectacular nebulae that we observe today.

Stellar ghosts is an apt way of describing many of the massive stars we see scattered throughout the universe. What many don’t realize is that when we look out deep into the universe, we are not only looking across vast distances, but we are peering back into time. One of the fundamental properties of the universe that we know quite well is that light travels at a finite speed: approximately 300,000,000 m/s (roughly 671,000,000 mph). This speed has been determined through many rigorous tests and physical proofs. In fact, understanding this fundamental constant is a key to much of what we know about the universe, especially in respect to both General Relativity and Quantum Mechanics. Despite this, knowing the speed of light is key to understanding what I mean by stellar ghosts. You see, information moves at the speed of light. We use the light from the stars to observe them and from this understand how they operate.

A decent example of this time lag is our own sun. Our sun is roughly 8 light-minutes away. Meaning that the light we see from our star takes 8 minutes to make the journey from its surface to our eyes on earth. If our sun were to suddenly disappear right now, we wouldn’t know about it for 8 minutes; this doesn’t just include the light we see, but even its gravitational influence that is exerted on us. So if the sun vanished right now, we would continue in our orbital path about our now nonexistent star for 8 more minutes before the gravitational information reached us informing us that we are no longer gravitationally bound to it. This establishes our cosmic speed limit for how fast we can receive information, which means that everything we observe deep into the universe comes to us as it was an ‘x’ amount of years ago, where ‘x’ is its light distance from us. This means we observe a star that is 10 lightyears away from us as it was 10 years ago. If that star died right now, we wouldn’t know about it for another 10 years. Thus, we can define it as a “stellar ghost”; a star that is dead from its perspective at its location, but still alive and well at ours.

As covered in a previous article of mine (Stars: A Day in the Life), the evolution of a star is complex and highly dynamic. Many factors play an important role in everything from determining if the star will even form in the first place, to the size and thus the lifetime of said star. In the previous article mentioned above, I cover the basics of stellar formation and the life of what we call main sequence stars, or rather stars that are very similar to our own sun. Whereas the formation process and life of a main sequence star and the stars we will be discussing are fairly similar, there are important differences in the way the stars we will be investigating die. Main sequence star deaths are interesting, but they hardly compare to the spacetime-bending ways that these larger stars terminate.

As mentioned above, when we were observing the long gone star that lay at the center of the Crab Nebula, there was a point in which this object glowed as bright as the full moon and could be seen during the day. What could cause something to become so bright that it would be comparable to our nearest celestial neighbor? Considering the Crab Nebula is 6,523 lightyears away, that meant that something that is roughly 153 billion times farther away than our moon was shining as bright as the moon. This was because the star went supernova when it died, which is the fate of stars that are much larger than our sun. Stars larger than our sun will end up in two very extreme states upon its death: neutron stars and black holes. Both are worthy topics that could span weeks in an astrophysics course, but for us today, we will simply go over how these gravitational monsters form and what that means for us.

Inward force of gravity versus the outward pressure of fusion within a star (hydrostatic equilibrium) Credit: NASA
Inward force of gravity versus the outward pressure of fusion within a star (hydrostatic equilibrium)
Credit: NASA

A star’s life is a story of near runaway fusion contained by the grip of its own gravitational presence. We call this hydrostatic equilibrium, in which the outward pressure from the fusing elements in the core of a star equals that of the inward gravitational pressure being applied due to the star’s mass. In the core of all stars, hydrogen is being fused into helium (at first). This hydrogen came from the nebula that the star was born from, that coalesced and collapsed, giving the star its first chance at life. Throughout the lifetime of the star, the hydrogen will be used up, and more and more helium “ash” will condense down in the center of the star. Eventually, the star will run out of hydrogen, and the fusion will briefly stop. This lack of outward pressure due to no fusion taking place temporarily allows gravity to win and it crushes the star downwards. As the star shrinks, the density, and thus the temperature in the core of the star increases. Eventually, it reaches a certain temperature and the helium ash begins to fuse. This is how all stars proceed throughout the main portion of its life and into the first stages of its death. However, this is where sun-sized stars and the massive stars we are discussing part ways.

The core and subsequent layers of a dying star. Each layer has been left over from millions of years of fusing each subsequent element into the next one. This is a snapshot of a massive star about to erupt. Credit: Wikimedia
The core and subsequent layers of a dying star. Each layer has been left over from millions of years of fusing each subsequent element into the next one. This is a snapshot of a massive star about to erupt. Credit: Wikimedia

A star that is roughly near the size of our own sun will go through this process until it reaches carbon. Stars that are this size simply aren’t big enough to fuse carbon. Thus, when all the helium has been fused into oxygen and carbon (via two processes that are too complex to cover here), the star cannot “crush” the oxygen and carbon enough to start fusion, gravity wins and the star dies. But stars that have sufficiently more mass than our sun (about 7x the mass) can continue on past these elements and keep shining. They have enough mass to continue this “crush and fuse” process that is the dynamic interactions at the hearts of these celestial furnaces.

These larger stars will continue their fusion process past carbon and oxygen, past silicon, all the way until they reach iron. Iron is the death note sung by these blazing behemoths, as when iron begins to fill their now dying core, the star is in its death throws. But these massive structures of energy do not go quietly into the night. They go out in the most spectacular of ways. When the last of the non-iron elements fuse in their cores, the star begins its decent into oblivion. The star comes crashing in upon itself as it has no way to stave off gravity’s relentless grip, crushing the subsequent layers of left over elements from its lifetime. This inward free-fall is met at a certain size with an impossible force to breach; a neutron degeneracy pressure that forces the star to rebound outwards. This massive amount of gravitational and kinetic energy races back out with a fury that illuminates the universe, outshining entire galaxies in an instant. This fury is the life-blood of the cosmos; the drum beats in the symphony galactic, as this intense energy allows for the fusion of elements heavier than iron, all the way to uranium. These new elements are blasted outwards by this amazing force, riding the waves of energy that casts them deep into the cosmos, seeding the universe with all the elements that we know of.

Artistic impression of a star going supernova, casting its chemically enriched contents into the universe. Credit: NASA/Swift/Skyworks Digital/Dana Berry
Artistic impression of a star going supernova, casting its chemically enriched contents into the universe. These new elements are blasted outwards by this amazing force, riding the waves of energy that casts them deep into the cosmos, seeding the universe with all the elements that we know of. Credit: NASA/Swift/Skyworks Digital/Dana Berryto

But what is left? What is there after this spectacular event? That all depends again on the mass of the star. As mentioned earlier, the two forms that a dead massive star takes are either a Neutron Star or a Black Hole. For a Neutron Star, the formation is quite complex. Essentially, the events that I described occurs, except after the supernovae all that is left is a ball of degenerate neutrons. Degenerate is simply a term we apply to a form that matter takes on when it is compressed to the limits allowed by physics. Something that is degenerate is intensely dense, and this holds very true for a neutron star. A number you may have heard tossed around is that a teaspoon of neutron star material would weigh roughly 10 million tons, and have an escape velocity (the speed needed to get away from its gravitational pull) at about .4c, or 40% the speed of light. Sometimes the neutron star is left spinning at incredible velocities, and we label these as pulsars; the name derived from how we detect them.

A pulsar with its magnetic field lines illustrated. The beams emitting from the poles are what washes over our detectors as the dead star spins.
A pulsar with its magnetic field lines illustrated. The beams emitting from the poles are what washes over our detectors as the dead star spins.

These types of stars generate a LOT of radiation. Neutron stars have an enormous magnetic field. This field accelerates electrons in their stellar atmospheres to incredible velocities. These electrons follow the magnetic field lines of the neutron star to its poles, where they can release radio waves, X-Rays, and gamma rays (depending on what type of neutron star it is). Since this energy is being concentrated to the poles, it creates a sort of lighthouse effect with high energy beams acting like the beams of light out of a lighthouse. As the star rotates, these beams sweep around many times per second. If the Earth, and thus our observation equipment, happens to be oriented favorably with this pulsar, we will register these “pulses” of energy as the stars’ beams wash over us. For all the pulsars we know about, we are much too far away for these beams of energy to hurt us. But if we were close to one of these dead stars, this radiation washing over our planet continuously would spell certain extinction for life as we know it.

What of the other form that a dead star takes; a black hole? How does this occur? If degenerate material is as far as we can crush matter, how does a black hole appear? Simply put, black holes are the result of an unimaginably large star and thus a truly massive amount of matter that is able to “break” this neutron degeneracy pressure upon collapse. The star essentially falls inward with such force that it breaches this seemingly physical limit, turning in upon itself and wrapping up spacetime into a point of infinite density; a singularity. This amazing event occurs when a star has roughly 18x the amount of mass that our sun has, and when it dies, it is truly the epitome of physics gone to the extreme. This “extra bit of mass” is what allows it to collapse this ball of degenerate neutrons and fall towards infinity. It is both terrifying and beautiful to think about; a point in spacetime that is not entirely understood by our physics, and yet something that we know exists. The truly remarkable thing about black holes is that it is like the universe working against us. The information we need to fully understand the processes within a black hole are locked behind a veil that we call the event horizon. This is the point of no return for a black hole, for which anything beyond this point in spacetime has no future paths that lead out of it. Nothing escapes at this distance from the collapsed star at its core, not even light, and thus no information ever leaves this boundary (at least not in a form we can use). The dark heart of this truly astounding object leaves a lot to be desired, and tempts us to cross into its realm in order to try and know the unknowable; to grasp the fruit from the tree of knowledge.

A black hole is the final form a massive star collapses to. The light (and spacetime itself) is warped around the black hole's event horizon due to extreme gravitational effects. This is as accurate as we can be to visualizing an actual black hole as it was generated with a code that implemented General Relativity accurately. Credit and Copyright: Paramount Pictures/Warner Bros. Mathematical Model used to create the image developed by Dr. Kip Thorne
A black hole is the final form a massive star collapses to. The light (and spacetime itself) is warped around the black hole’s event horizon due to extreme gravitational effects. This is as accurate as we can be to visualizing an actual black hole as it was generated with a code that implemented General Relativity accurately. Credit and Copyright: Paramount Pictures/Warner Bros. From “Interstellar” the film. Mathematical model used to create the image developed by Dr. Kip Thorne

Now it must be said, there is much in the way of research with black holes to this day. Physicists such as Professor Stephen Hawking, among others, have been working tirelessly on the theoretical physics behind how a black hole operates, attempting to solve the paradoxes that frequently appear when we try to utilize the best of our physics against them. There are many articles and papers on such research and their subsequent findings, so I will not dive into their intricacies for both wishing to preserve simplicity in understanding, and to also not take away from the amazing minds that are working these issues. Many suggest that the singularity is a mathematical curiosity that does not completely represent what physically happens. That the matter inside an event horizon can take on new and exotic forms. It is also worth noting that in General Relativity, anything with mass can collapse to a black hole, but we generally hold to a range of masses as creating a black hole with anything less than is in that mass range is beyond our understanding of how that could happen. But as someone who studies physics, I would be remiss to not mention that as of now, we are at an interesting cross section of ideas that deal very intimately with what is actually going on within these specters of gravity.

All of this brings me back to a point that needs to be made. A fact that needs to be recognized. As I described the deaths of these massive stars, I touched on something that occurs. As the star is being ripped apart from its own energy and its contents being blown outwards into the universe, something called nucleosynthesis is occurring. This is the fusion of elements to create new elements. From hydrogen up to uranium. These new elements are being blasted outwards an incredible speeds, and thus all of these elements will eventually find their way into molecular clouds. Molecular clouds (Dark Nebulae) are the stellar nurseries of the cosmos. This is where stars begin. And from star formation, we get planetary formation.

Planets coalescing out of the remaining molecular cloud the star formed out of. Within this accretion disk lay the fundamental elements necessary for planet formation and potential life. Credit: NASA/JPL-Caltech/T. Pyle (SSC) - February, 2005
Planets coalescing out of the remaining molecular cloud the star formed out of. Within this accretion disk lay the fundamental elements necessary for planet formation and potential life. Credit: NASA/JPL-Caltech/T. Pyle (SSC) – February, 2005

As a star forms, a cloud of debris that is made up of the molecular cloud that birthed said star begins to spin around it. This cloud, as we now know, contains all those elements that were cooked up in our supernovae. The carbon, the oxygen, the silicates, the silver, the gold; all present in this cloud. This accretion disk about this new star is where planets form, coalescing out of this enriched environment. Balls of rock and ice colliding, accreting, being torn apart and then reformed as gravity works its diligent hands to mold these new worlds into islands of possibility. These planets are formed from those very same elements that were synthesized in that cataclysmic eruption. These new worlds contain the blueprints for life as we know it.

Upon one of these worlds, a certain mixture of hydrogen and oxygen occurs. Within this mixture, certain carbon atoms form up to create replicating chains that follow a simple pattern. Perhaps after billions of years, these same elements that were thrust into the universe by that dying star finds itself giving life to something that can look up and appreciate the majesty that is the cosmos. Perhaps that something has the intelligence to realize that the carbon atom within it is the very same carbon atom that was created in a dying star, and that a supernovae occurred that allowed that carbon atom to find its way into the right part of the universe at the right time. The energy that was the last dying breath of a long dead star was the same energy that allowed life to take its first breath and gaze upon the stars. These stellar ghosts are our ancestors. They are gone in form, but yet remain within our chemical memory. They exist within us. We are supernova. We are star dust. We are descended from stellar ghosts…

We are awash in the light from long dead stars, each contributing essential ingredients to the universe that are necessary for life. Image Credit: Hubble
We are awash in the light from long dead stars, each contributing essential ingredients to the universe that are necessary for life. Image Credit: Hubble

Mathematics: The Beautiful Language of the Universe

Let us discuss the very nature of the cosmos. What you may find in this discussion is not what you expect. Going into a conversation about the universe as a whole, you would imagine a story full of wondrous events such as stellar collapse, galactic collisions, strange occurrences with particles, and even cataclysmic eruptions of energy. You may be expecting a story stretching the breadth of time as we understand it, starting from the Big Bang and landing you here, your eyes soaking in the photons being emitted from your screen. Of course, the story is grand. But there is an additional side to this amazing assortment of events that oftentimes is overlooked; that is until you truly attempt to understand what is going on. Behind all of those fantastic realizations, there is a mechanism at work that allows for us to discover all that you enjoy learning about. That mechanism is mathematics, and without it the universe would still be shrouded in darkness. In this article, I will attempt to persuade you that math isn’t some arbitrary and sometimes pointless mental task that society makes it out to be, and instead show you that it is a language we use to communicate with the stars.

We are currently bound to our solar system. This statement is actually better than it sounds, as being bound to our solar system is one major step up from being bound simply to our planet, as we were

A defining moment for humanity: Galileo turing his spyglass towards the sky
A defining moment for humanity: Galileo turing his spyglass towards the sky

before some very important minds elected to turn their geniuses toward the heavens. Before those like Galileo, who aimed his spyglass towards the sky, or Kepler discovering that planets move about the sun in ellipses, or Newton discovering a gravitational constant, mathematics was somewhat  limited, and our understanding of the universe rather ignorant. At its core, mathematics allows a species bound to its solar system to probe the depths of the cosmos from behind a desk. Now, in order to appreciate the wonder that is mathematics, we must first step back and briefly look at its beginnings and how it is integrally tied into our very existence.

Mathematics almost certainly came about from very early human tribes (predating Babylonian culture which is attributed to some of the first organized mathematics in recorded history), that may have used math as a way of keeping track of lunar or solar cycles, and keeping count of animals, food and/or people by leaders. It is as natural as when you are a young child and you can see that you have

Ancient Babylonian tablet displaying early mathematics
Ancient Babylonian tablet displaying early mathematics

one toy plus one other toy, meaning you have more than one toy. As you get older, you develop the ability to see that 1+1=2, and thus simple arithmetic seems to be interwoven into our very nature. Those that profess that they don’t have a mind for math are sadly mistaken because just as we all have a mind for breathing, or blinking, we all have this innate ability to understand arithmetic. Mathematics is both a natural occurrence and a human designed system. It would appear that nature grants us this ability to recognize patterns in the form of arithmetic, and then we systematically construct more complex mathematical systems that aren’t obvious in nature but let us further communicate with nature.

All this aside, mathematics developed alongside of human development, and carried on similarly with each culture that was developing it simultaneously. It’s a wonderful observation to see that cultures that had no contact with one another were developing similar mathematical constructs without conversing. However, it wasn’t until mankind decidedly turned their mathematical wonder towards the sky that math truly began to develop in an astonishing way. It is by no mere coincidence that our scientific revolution was spurred by the development of more advanced mathematics built not to tally sheep or people, but rather to further our understandings of our place within the universe. Once Galileo began measuring the rates at which objects fell in an attempt to show mathematically that the mass of an object had little to do with the speed in which it fell, mankind’s future would forever be altered.

This is where the cosmic perspective ties in to our want to further our mathematical knowledge. If it were not for math, we would still think we were on one of a few planets orbiting a star amidst the backdrop of seemingly motionless lights. This is a rather bleak outlook today compared to what we now know

Johannes Kepler used mathematics to model his observations of the planets.
Johannes Kepler used mathematics to model his observations of the planets.

about the awesomely large universe we reside in. This idea of the universe motivating us to understand more about mathematics can be inscribed in how Johannes Kepler used what he observed the planets doing, and then applied mathematics to it to develop a fairly accurate model (and method for predicting planetary motion) of the solar system. This is one of many demonstrations that illustrate the importance of mathematics within our history, especially within astronomy and physics.

The story of mathematics becomes even more amazing as we push forward to one of the most advanced thinkers humanity has ever known. Sir Isaac Newton, when pondering the motions of Halley’s Comet, came to the realization that the math that had been used thus far to describe physical motion of massive

Isaac Newton
Isaac Newton

bodies, simply would not suffice if we were to ever understand anything beyond that of our seemingly limited celestial nook. In a show of pure brilliance that lends validity to my earlier statement about how we can take what we naturally have and then construct a more complex system upon it, Newton developed the Calculus in which this way of approaching moving bodies, he was able to accurately model the motion of not only Halley’s comet, but also any other heavenly body that moved across the sky.

In one instant, our entire universe opened up before us, unlocking almost unlimited abilities for us to converse with the cosmos as never before. Newton also expanded upon what Kepler started. Newton recognized that Kepler’s mathematical equation for planetary motion, Kepler’s 3rd Law ( P2=A3 ), was purely based on empirical observation, and was only meant to measure what we observed within our solar system. Newton’s mathematical brilliance was in realizing that this basic equation could be made universal by applying a gravitational constant to the equation, in which gave birth to perhaps one of the most important equations to ever be derived by mankind; Newton’s Version of Kepler’s Third Law.

You can still see where Kepler's 3rd Law remains, but with the added values of the gravitational constant G, and M and m representing the masses of the two bodies in question, this equation is no longer restricted to just our solar system
You can still see where Kepler’s 3rd Law remains, but with the added values of the gravitational constant G, and M and m representing the masses of the two bodies in question, this equation is no longer restricted to just our solar system

What Newton realized was that when things move in non-linear ways, using basic Algebra would not produce the correct answer. Herein lays one of the main differences between Algebra and Calculus. Algebra allows one to find the slope (rate of change) of straight lines (constant rate of change), whereas Calculus allows one to find the slope of curved lines (variable rate of change). There are obviously many more applications of Calculus than just this, but I am merely illustrating a fundamental difference between the two in order to show you just how revolutionary this new concept was. All at once, the motions of planets and other objects that orbit the sun became more accurately measurable, and thus we gained the ability to understand the universe a little deeper. Referring back to Netwon’s Version of Kepler’s Third Law, we were now able to apply (and still do) this incredible physics equation to almost anything that is orbiting something else. From this equation, we can determine the mass of either of the objects, the distance apart they are from each other, the force of gravity that is exerted between the two, and other physical qualities built from these simple calculations.

With his understanding of mathematics, Newton was able to derive the aforementioned gravitational constant for all objects in the universe ( G = 6.672×10-11 N m2 kg-2 ). This constant allowed him to unify astronomy and physics which then permitted predictions about how things moved in the universe. We could now measure the masses of planets (and the sun) more accurately, simply according to Newtonian physics (aptly named to honor just how important Newton was within physics and mathematics). We could now apply this newfound language to the cosmos, and begin coercing it to divulge its secrets. This was a defining moment for humanity, in that all of those things that prohibited our understandings prior to this new form of math were now at our fingertips, ready to be discovered. This is the brilliance of understanding Calculus, in that you are speaking the language of the stars.

There perhaps is no better illustration of the power that mathematics awarded us then in the discovery of the planet Neptune. Up until its discovery in September of 1846, planets were discovered simply by observing certain “stars” that were moving against the backdrop of all the other stars in odd ways. The term planet is Greek for “wanderer”, in that these peculiar stars wandered across the sky in noticeable patterns at different times of the year. Once the telescope was first turned upwards towards the sky by Galileo, these wanderers resolved into other worlds that appeared to be like ours. If fact, some of these worlds appeared to be little solar systems themselves, as Galileo discovered when he began recording the moons of Jupiter as they orbited around it.

After Newton presented his physics equations to the world, mathematicians were ready and excited to begin applying them to what we had been keeping track of for years. It was as if we were thirsty for the knowledge, and finally someone turned on the faucet. We began measuring the motions of the planets and gaining more accurate models for how they behaved. We used these equations to approximate the mass of the Sun. We were able to make remarkable predictions that were validated time and again simply by observation. What we were doing was unprecedented, as we were using mathematics to make almost impossible to know predictions that you would think we could never make without actually going to these planets, and then using actual observation to prove the math correct. However, what we also did was begin to figure out some odd discrepancies with certain things. Uranus, for instance, was behaving not as it should according to Newton’s laws.

Here you can see that the inner planet is being perturbed by the outer planet, in our situation, that outer planet was Neptune, not yet discovered.
Here you can see that the inner planet is being perturbed by the outer planet. In our situation, that outer planet was Neptune, which had yet to be discovered.

What makes the discovery of Neptune so wonderful was the manner in which it was discovered. What Newton had done was uncover a deeper language of the cosmos, in which the universe was able to reveal more to us. And this is exactly what happened when we applied this language to the orbit of Uranus. The manner in which Uranus orbited was curious and did not fit what it should have if it was the only planet that far out from the sun. Looking at the numbers, there had to be something else out there perturbing its orbit. Now, before Newton’s mathematical insights and laws, we would have had no reason to suspect anything was wrong in what we observed. Uranus orbited in the way Uranus orbited; it was just how it was. But, again revisiting that notion of mathematics being an ever increasing dialogue with the universe, once we asked the question in the right format, we realized that there really must be something else beyond what we couldn’t see. This is the beauty of mathematics writ large; an ongoing conversation with the universe in which more than we may expect is revealed.

It came to a French mathematician Urbain Le Verrier who sat down and painstakingly worked through the mathematical equations of the orbit of Uranus. What he was doing was using Newton’s mathematical equations backwards, realizing that there must be an object out there beyond the orbit of Uranus that was also orbiting the sun,

French mathematician who discovered the planet Neptune by using only mathematics
French mathematician who discovered the planet Neptune by using only mathematics

and then looking to apply the right mass and distance that this unseen object required for perturbing the orbit of Uranus in the way we were observing it was. This was phenomenal, as we were using parchment and ink to find a planet that nobody had ever actually observed. What he found was that an object, soon to be Neptune, had to be orbiting at a specific distance from the sun, with the specific mass that would cause the irregularities in the orbital path of Uranus. Confident of his mathematical calculations, he took his numbers to the New Berlin Observatory, where the astronomer Johann Gottfried Galle looked exactly where Verrier’s calculations told him to look, and there lay the 8th and final planet of our solar system, less than 1 degree off from where Verrier’s calculations said for him to look. What had just happened was an incredible confirmation of Newton’s gravitational theory and proved that his mathematics were correct.

Are There Oceans on Neptune
Neptune is more than just the 8th planet in our solar system; it is a celestial reminder of the power that mathematics grants us.

These types of mathematical insights continued on long after Newton. Eventually, we began to learn much more about the universe with the advent of better technology (brought about by advances in mathematics). As we moved into the 20th century, quantum theory began to take shape, and we soon realized that Newtonian physics and mathematics seemed to hold no sway over what we observed on the quantum level. In another momentous event in human history, yet again brought forth by the advancement in mathematics, Albert Einstein unveiled his theories of General and Special Relativity, which was a new way to look not only at gravity, but

Einstein's Relativity, yet another momentous advancement for humanity brought forth from an ongoing mathematical dialogue. Image via Pixabay.
Einstein’s equation for the energy-mass equivalency, yet another incredible advancement for humanity brought forth from an ongoing mathematical dialogue. Image via Pixabay.

also on energy and the universe in general. What Einstein’s mathematics did was allow for us to yet again uncover an even deeper dialogue with the universe, in which we began to understand its origins.

Continuing this trend of advancing our understandings, what we have realized is that now there are two sects of physics that do not entirely align. Newtonian or “classical” physics, that works extraordinarily well with the very large (motions of planets, galaxies, etc…) and quantum physics that explains the extremely small (the interactions of sub-atomic particles, light, etc…). Currently, these two areas of physics are not in alignment, much like two different dialects of a language. They are similar and they both work, but they are not easily reconcilable with one another. One of the greatest challenges we face today is attempting to create a mathematical grand “theory of everything” which either unites the laws in the quantum world with that of the macroscopic world, or to work to explain everything solely in terms of quantum mechanics. This is no easy task, but we are striving forward nonetheless.

As you can see, mathematics is more than just a set of vague equations and complex rules that you are required to memorize. Mathematics is the language of the universe, and in learning this language, you are opening yourself up the core mechanisms by which the cosmos operates. It is the same as traveling to a new land, and slowly picking up on the native language so that you may begin to learn from them. This mathematical endeavor is what allows us, a species bound to our solar system, to explore the depths of the universe. As of now, there simply is no way for us to travel to the center of our galaxy and observe the supermassive black hole there to visually confirm its existence. There is no way for us to venture out into a Dark Nebula and watch in real time a star being born. Yet, through mathematics, we are able to understand how these things exist and work. When you set about to learn math, you are not only expanding your mind, but you are connecting with the universe on a fundamental level. You can, from your desk, explore the awesome physics at the event horizon of a black hole, or bear witness to the destructive fury behind a supernova. All of those things that I mentioned at the beginning of this article come into focus through mathematics. The grand story of the universe is written in mathematics, and our ability to translate those numbers into the events that we all love to learn about is nothing short of amazing. So remember, when you are presented with the opportunity to learn math, accept every bit of it because math connects us to the stars.

We are connected to the universe through mathematics...
We are connected to the universe through mathematics…


Stars: A Day in the Life

Region of active star formation

There is something about them that intrigues us all. These massive spheres of gas burning intensely from the energy of fusion buried many thousands of kilometers deep within their cores. The stars have been the object of humanity’s wonderment for as far back as we have records. Many of humanity’s religions can be tied to worshiping these celestial candles. For the Egyptians, the sun was representative of the God Ra, who each day vanquished the night and brought light and warmth to the lands. For the Greeks, it was Apollo who drove his flaming chariot across the sky, illuminating the world. Even in Christianity, Jesus can be said to be representative of the sun given the striking characteristics his story holds with ancient astrological beliefs and figures. In fact, many of the ancient beliefs follow a similar path, all of which tie their origins to that of the worship of the sun and stars.


Humanity thrived off of the stars in the night sky because they recognized a correlation in the pattern in which certain star formations (known as constellations) represented specific times in the yearly cycle. One of which meant that it was to become warmer soon, which led to planting food. The other constellations foretold the coming of a

The familiar constellation of Orion. Orion's Belt can be clearly seen, as well as Betelgeuse (red star in the upper left corner) and Rigel (bright blue star in the lower right corner) Credit: NASA Astronomy Picture of the Day Collection NASA
The familiar constellation of Orion. Orion’s Belt can be clearly seen, as well as Betelgeuse (red star in the upper left corner) and Rigel (bright blue star in the lower right corner)
Credit: NASA Astronomy Picture of the Day Collection

colder period, so you were able to begin storing food and gathering firewood. Moving forward in humanity’s journey, the stars then became a way to navigate. Sailing by the stars was the way to get around, and we owe our early exploration to our understandings of the constellations. For many of the tens of thousands of years that human eyes have gazed upwards toward the heavens, it wasn’t until relatively recently that we fully began to understand what stars actually were, where they came from, and how they lived and died. This is what we shall discuss in this article. Come with me as we venture deep into the cosmos and witness physics writ large, as I cover how a star is born, lives, and eventually dies.

We begin our journey by traveling out into the universe in search of something special. We are looking for a unique structure where both the right circumstances and ingredients are present. We are looking for what astronomer’s call a Dark Nebula. I’m sure you’ve heard of nebulae before, and have no doubt seen them. Many of the amazing images that the Hubble Space Telescope has obtained are of beautiful gas clouds, glowing amidst the backdrop of billions of stars. Their colors range from deep reds, to vibrant blues, and even some eerie greens. This is not the type of nebula we are in search of though. The nebula we need is dark, opaque, and very, very cold.

You may by wondering to yourself, “Why are we looking for something dark and cold when stars are bright and hot?”

Image of a Dark Nebula  Credit: ESO   http://www.eso.org/public/images/eso1501a

Indeed, this is something that would appear puzzling at first. Why does something need to be cold first before it can become extremely hot? First, we must cover something elementary about what we call the Interstellar Medium (ISM), or the space between the stars. Space is not empty as its name would imply. Space contains both gas and dust. The gas we are mainly referring to is Hydrogen, the most abundant element in the universe. Since the universe is not uniform (the same density of gas and dust over every cubic meter), there are pockets of space that contain more gas and dust than others. This causes gravity to manipulate these pockets to come together and form what we see as nebulae. Many things go into the making of these different nebulae, but the one that we are looking for, a Dark Nebula, possesses very special properties. Now, let us dive into one of these Dark Nebulae and see what is going on.

As we descend through the outer layers of this nebula, we notice that the temperature of the gas and dust is very low. In some nebulae, the temperatures are very hot. The more particles bump into each other, excited by the absorption and emission of exterior and interior radiation, means higher temperatures. But in this Dark Nebula, the opposite is happening. The temperatures are decreasing the further into the cloud we get. The reason these Dark Nebulae have specific properties that work to create a great stellar nursery has to deal with the basic properties of the nebula and the region type that the cloud exists in, which has some difficult concepts associated with it that I will not fully illustrate here. They include the region where the molecular clouds form which are called Neutral Hydrogen Regions, and the properties of these regions have to deal with electron spin values, along with magnetic field interactions that effect said electrons. The traits that I will cover are what allows for this particular nebula to be ripe for star formation.

Excluding the complex science behind what helps form these nebulae, we can begin to address the first question of why must we get colder to get hotter. The answer comes down to gravity. When particles are heated, or excited, they move faster. A cloud with sufficient energy will contain far too much momentum among each of the dust and gas particles for any type of formations to occur. As in, if dust grains and gas atoms are moving too quickly, they will simply bounce off of one another or just shoot past each other, never achieving any type of bond. Without this interaction, you can never have a star. However, if the temperatures are cold enough, the particles of gas and dust are moving so slow that their mutual gravity will allow for them to start to “stick” together. It is this process that allows for a protostar to begin to form.

Generally what supplies energy to allow for the faster motion of the particles in these molecular clouds is radiation. Of course, there is radiation coming in from all directions at all times in the universe. As we see with other nebulae, they are glowing with energy and stars aren’t being born amid these hot gas clouds. They are being heated by external radiation from other stars and from its own internal heat. How does this Dark Nebula prevent external radiation from heating up the gas in the cloud and causing it to move too fast for gravity to take hold? This is where

Barnard 68 is a large molecular cloud that is so thick, it blocks out the light from stars that we normally would be able to see.  Credit: ESO     http://www.eso.org/public/images/eso0102a

the opaque nature of these Dark Nebulae comes into play. Opacity is the measure of how much light is able to move through an object. The more material in the object or the thicker the object is, the less light is able to penetrate it. The higher frequency light (Gamma Rays, X-Rays, and UV) and even the visible frequencies are affected more by thick pockets of gas and dust. Only the lower frequency types of light, including Infrared, Microwaves, and Radio Waves, has any success of penetrating gas clouds such as these, and even it is somewhat scattered so that generally they do not contain nearly enough energy to begin to disrupt this precarious process of star formation. Thus, the inner portions of the dark gas clouds are effectively “shielded” from the outside radiation that disrupts other, less opaque nebulae. The less radiation that makes it into the cloud, the lower the temperatures of the gas and dust within it. The colder temperatures means less particle motion within the cloud, which is key for what we will discuss next.

Indeed, as we descend towards the core of this dark molecular cloud, we notice that less and less visible light makes it to our eyes, and with special filters, we can see that this is true of other frequencies of light. As a result, the cloud’s temperature is very low. It is worth noting that the process of star formation takes a very long time, and in the interest of not keeping you reading for hundreds of thousands of years, we shall now fast forward time. In a few thousand years, gravity has pulled in a fair amount of gas and dust from the surrounding molecular cloud, causing it to clump together. Dust and gas particles, still shielded from outside radiation, are free to naturally come together and “stick” at these low temperatures. Eventually, something interesting begins to happen. The mutual gravity of this ever growing ball of gas and dust begins a snowball (or star-ball) effect. The more layers of gas and dust that are coagulated together, the denser the interior of this protostar becomes. This density increases the gravitational force near the protostar, thus pulling more material into it. With every dust grain and hydrogen atom that it accumulates, the pressure in the interior of this ball of gas increases.

If you remember anything from any chemistry class you’ve ever taken, you may recall a very special relationship between pressure and temperature when dealing with a gas. PV=nRT, the Ideal Gas Law, comes to mind. Excluding the constant scalar value ‘n’ and the gas constant R ({8.314 J/mol x K}), and solving for Temperature (T), we get T=PV, which means that the temperature of a gas cloud is directly proportional to pressure. If you increase the pressure, you increase the temperature. The core of this soon-to-be star residing in this Dark Nebula is becoming very dense, and the pressure is skyrocketing. According to what we just calculated, that means that the temperature is also increasing.

NASA/JPL-Caltech/R. Hurt (SSC)
Artistic rendition of a star forming within a dark nebula. Credit: NASA/JPL-Caltech/R. Hurt (SSC)


We yet again consider this nebula for the next step. This nebula has a large amount of dust and gas (hence it being opaque), which means it has a lot of material to feed our protostar. It continues to pull in the gas and dust from its surrounding environment and begins heating up. The hydrogen particles in the core of this object are bouncing around so quick that they are releasing energy into the star. The protostar begins to get very hot and is now glowing with radiation (generally Infrared). At this point, gravity is still pulling in more gas and dust which is adding to the pressures exerted deep within the core of this protostar. The gas of the Dark Nebula will continue to collapse in on itself until something important happens. When there is little to nothing left near the star to fall onto its surface, it begins to lose energy (due to it radiating away as light). When this happens, that outward force lessens and gravity starts to contract the star faster. This greatly increases the pressure in the core of this protostar. As the pressure grows, the temperature in the core reaches a value that is crucial for the process that we are witnessing. The protostar’s core has become so dense and hot, that it reaches roughly 10 million Kelvin. To put that into perspective, this temperature is roughly 1700x hotter than the surface of our sun (at around 5800K). Why is 10 million Kelvin so important? Because at that temperature, the thermonuclear fusion of Hydrogen can occur, and once fusion starts, this newborn star “turns on” and bursts to life, sending out vast amounts of energy in all directions.

In the core, it is so hot that the electrons that zip around the hydrogen’s proton nuclei are stripped off (ionized), and all you have are free moving protons. If the temperature isn’t hot enough, these free flying protons (which have positive charges), will simply glance off one another. However, at 10 Million Kelvin, the protons are moving so fast that they can get close enough to allow for the Strong Nuclear Force to take over, and when it does the Hydrogen protons begin slamming into each other with enough force to fuse together, creating Helium atoms and releasing lots of energy in the form of radiation. It’s a chain reaction that can be summed up as 4 Protons yield 1 Helium atom + energy. This fusion is what ignites the star and causes it to “burn”. The energy liberated by this reaction goes into helping other Hydrogen protons fuse and also supplies the energy to keep the star from collapsing in on itself. The energy that is pumping out of this star in all directions all comes from the core, and the subsequent layers of this young star all transmit that heat in their own way (using radiation and convection methods depending upon what type of star has been born).

Newborn stars glow through their parent molecular cloud Credit: ESA/Hubble & NASA Acknowledgement: Judy Schmidt
Newborn stars glow through their parent molecular cloud
Credit: ESA/Hubble & NASA Acknowledgement: Judy Schmidt

What we have witnessed now, from the start of our journey when we dove down into that cold Dark Nebula, is the birth of a young, hot star. The nebula protected this star from errant radiation that would have disrupted this process, as well as providing the frigid environment that was needed for gravity to take hold and work its magic. As we witnessed the protostar form, we may also have seen something incredible. If the contents of this nebula are right, such as having a high amount of heavy metals and silicates (left over from the supernovae of previous, more massive stars) what we could begin to see would be planetary formation taking place in the accretion disk of material around the protostar.

Remaining gas and dust in the vicinity of our new star would begin to form dense pockets by the same mechanism of

Artistic rendition of a protoplanet forming within the accretion disk of a protostar Credit: ESO/L. Calçada http://www.eso.org/public/images/eso1310a/
Artistic rendition of a protoplanet forming within the accretion disk of a protostar
Credit: ESO/L. Calçada

gravity, eventually being able to accrete into protoplanets that will be made up of gas or silicates and metal (or a combination of the two). That being said, planetary formation is still somewhat a mystery to us, as there seems to be things that we cannot explain yet at work. But this model of star system formation seems to work well.

The life of the star isn’t nearly as exciting as its birth or death. We will continue to fast forward the clock and watch this star system evolve. Over a few billion years, the remnants of the Dark Nebula have been blown apart and have also formed other stars like the one we witnessed, and it no longer exists. The planets we saw being formed as the protostar grew begin their billion year dance around their parent star. Maybe on one of these worlds, a world that sits at just the right distance away from the star, liquid water exists. Within that water contains the amino acids that are needed for proteins (all composed of the elements that were left over by previous stellar eruptions). These proteins are able to link together to start to form RNA chains, then DNA chains. Maybe at one point a few billion years after the star has been born, we see a space-faring species launch itself into the cosmos, or perhaps they never achieve this for various reasons and remain planet-bound. Of course this is just speculation for our amusement. However, now we come to the end of our journey that began billions of years ago. The star begins to die.

The Hydrogen in its core is being fused into Helium, which depletes the Hydrogen over time; the star is running out of gas. After many years, the hydrogen fusion process begins to stop, and the star puts out less and less energy. This lack of outward pressure from the fusion process upsets what we call the hydrostatic equilibrium, and allows gravity (which is always trying to crush the star) to win. The star begins to shrink rapidly under its own weight. But, just as we discussed earlier, as the pressure increases, so too does the temperature. All of that Helium that was left over

Inward force of gravity versus the outward pressure of fusion within a star (hydrostatic equilibrium) Credit: NASA
Inward force of gravity versus the outward pressure of fusion within a star (hydrostatic equilibrium)
Credit: NASA

from the billions of years of hydrogen fusion now begins to heat up in the core. Helium fuses at a much hotter temperature than Hydrogen does, which means that the Helium rich core is able to be pressed inward by gravity without fusing (yet). Since fusion isn’t occurring in the Helium core, there is little to no outward force (given off by fusion) to prevent the core from collapsing. This matter becomes much denser, which we now label as degenerate, and is pushing out massive amounts of heat (gravitational energy becoming thermal energy). This causes the remaining Hydrogen that is in subsequent layers above the Helium core to fuse, which causes the star to expand greatly as this Hydrogen shell burns out of control. This makes the star “rebound” and it expands rapidly; the more energetic fusion from the Hydrogen shells outside of the core expanding the diameter of the star greatly. Our star is now a red giant. Some, if not all of the inner planets that we witnessed form will be incinerated and swallowed up by the star that first gave them life. If there happened to be any life on any of those planets that didn’t manage to leave their home world, they would certainly be erased from the universe, never to be known of.

This process of the star running out of fuel (first Hydrogen, then Helium, etc…) will continue for a while. Eventually, the Helium in the core will reach a certain temperature and begin to fuse into Carbon, which will put off the collapse (and death) of the star. The star we are currently watching live and die is an average-sized Main Sequence Star, so its life ends once it is finished fusing Helium into

Different planetary nebulae, all remnants of low mass stars ejecting their outer material as they die Credit: NASA
Different planetary nebulae, all remnants of low mass stars ejecting their outer material as they die
Credit: NASA

Carbon. If the star was much larger, this fusion process would proceed until we reached Iron. Iron is the element in which fusion does not take place spontaneously, meaning it requires more energy to fuse it than it gives off after fusion. However, our star will never make it to Iron in its core, and thus it has died after it exhausts its Helium reservoir. When the fusion process finally “turns off” (out of gas), the star slowly begins to cool and the outer layers of the star expand and are ejected into space. Subsequent ejections of stellar material proceed to create what we call a planetary nebula, and all that is left of the once brilliant star we watched spring into existence is now just a ball of dense carbon that will continue to cool for the rest of eternity, possibly crystallizing into diamond.


The death we witnessed just now isn’t the only way a star dies. If a star is sufficiently large enough, its death is much more violent. The star will erupt into the largest explosion in the universe, called a supernova. Depending on many variables, the remnant of the star could end up as a neutron star, or even a black hole. But for most of what we call the average sized Main Sequence Stars, the death that we witnessed will be their fate.

Artistic representation of the material around the supernova 1987A. Credit: ESO/L. Calçada
Artistic representation of the material around the supernova 1987A. Supernovae are among the most violent events in the universe
Credit: ESO/L. Calçada

Our journey ends with us pondering what we have observed. Seeing just what nature can do given the right circumstances, and watching a cloud of very cold gas and dust turn into something that has the potential to breathe life into the cosmos. Our minds wander back to that species that could have evolved on one of those planets. You think about how they may have gone through phases similar to us. Possibly using the stars as supernatural deities that guided their beliefs for thousands of years, substituting answers in for where their ignorance reigned. These beliefs could possibly turn into religions, still grasping that notion of special selection and magnanimous thought. Would the stars fuel their desire to understand the universe as the stars did for us? Your mind then ponders what our fate will be if we do not attempt to take the next step into the universe. Are we to allow our species to be erased from the cosmos as our star expands in its death? This journey you just made into the heart of a Dark Nebula truly exemplifies what the human mind can do, and shows you just how far we have come even though we are still bound to our solar system. The things you have learned were found by others like you simply asking how things occur and then bringing the full weight of our knowledge of physics to bare. Imagine what we can accomplish if we continue this process; being able to fully achieve our place among the stars.

The vastness of space awaits us... Credit: NASA
The vastness of the cosmos awaits us…
Credit: NASA (Hubble Deep Field)

Spectroscopy: The Key to Humanity’s Future in Space


Imagine, if you would, a potential future for humanity… Imagine massive space-elevators lifting groups of men, women, and children skyward off Earth’s surface. These passengers are then loaded onto shuttles and ferried to the Moon where interstellar starships are docked, waiting to rocket to the stars. These humans are about to begin the greatest journey humanity has ever embarked upon, as they will be the first interstellar colonists to leave our home Solar System in order to begin populating other worlds around alien stars.

There are many things we must tackle first before we can make this type of science-fiction scene a reality. Obviously much faster methods of travel are needed, as well as some sort of incredible material that can serve to anchor the aforementioned space elevators. These are all scientific and engineering questions that humanity will need to overcome in the face of such a journey into the cosmos.

But there is one particular important feature that we can begin to tackle today: where do we point these starships? Towards which system of exoplanets are we to send our brave colonists?

Of all of the amazing things we need to discover or invent to make this scene a reality, discovering which worlds to aim our ships at is something that is actually being worked on today.

Artistic view of a possible space elevator. Image Credit: NASA
Artistic view of a possible space elevator. Image Credit: NASA

It’s an exciting era in astronomy, as astronomers are currently discovering that many of the stars that we view in the night sky have their own planets in orbit around them. Many of them are massive worlds, all orbiting at varying distances from their parent star. It is no surprise that we are discovering a vast majority of these Jupiter-sized worlds first; larger worlds are much easier to detect than the smaller worlds would be. Imagine a bright spotlight pointing at you some 500 yards away (5 football fields). Your job is to detect something the size of a period on this page that is orbiting around it that emits no light of its own. As you can see, the task would be daunting. But nevertheless, our planet hunters have been utilizing methods that enable us to accurately find these tiny specks of gas and rock despite their rather large and luminous companion suns.

However, it is not the method of finding these planets that this article is about; but rather what we do to figure out which of these worlds are worthy of our limited resources and attention. We very well cannot point those starships in random directions and just hope that they happen across an earth-sized planet that has a nitrogen-oxygen rich atmosphere with drinkable water. We need to identify which planets appear to have these mentioned characteristics before we go launching ourselves into the vast universe.

How can we do this? How is it possible that we are able to say with any level of certainty what a planet’s atmosphere is composed of when this planet is so small and so very far away? Spectroscopy is the answer, and it just might be the key to our future in the cosmos.

Artistic impression of what Kepler-186f may look like. Image Credit:  NASA Ames/SETI Institute/JPL-CalTech
Artistic impression of what Kepler-186f may look like. Image Credit: NASA Ames/SETI Institute/JPL-CalTech

Just so I may illustrate how remarkable our scientific methods are for this very field of research, I will first need to show you the distances we are talking about. Let’s take Kepler 186f. This is the first planet we have discovered that is very similar to Earth. It is around 1.1 times larger than Earth and orbits within the habitable zone of its star which is very similar to our own star.

Let’s do the math, to show you just how distant this planet is. Kepler 186f is around 490 lightyears from Earth.

Kepler 186f = 490 lightyears away

Light moves at 186,282 miles/ 1 second.

186,282 mi/s x 60s/1min x 60min/1hr x 24hrs/1day x 356days/1year = 5.87 x 1012 mi/yr

Kepler 186f: 490 Lyrs x 5.87 x 1012miles/ 1 Lyr = 2.88 x 1015 miles or 2.9 QUADRILLION MILES from Earth.

Just to put this distance into perspective, let’s suppose we utilize the fastest spacecraft we have to get there. The Voyager 1 spacecraft is moving at around 38,500 mi/hr. If we left on that craft today and headed towards this possible future Earth, it would take us roughly 8.5 MILLION YEARS to get there. That’s around 34 times longer than the time between when the first proto-humans began to appear on earth 250,000 years ago until today. So the entire history of human evolution from then till now replayed 34 times BEFORE you would arrive at this planet. Knowing these numbers, how is it even possible that we can know what this planet’s atmosphere, and others like it, are made of?

First, here’s a bit of chemistry in order for you to understand the field that is spectroscopy, and then how we apply it to the astronomical sciences. Different elements are composed of a differing number of protons, neutrons, and electrons. These varying numbers are what set the elements apart from one another on the periodic table. It is the electrons, however, that are of particular interest in the majority of what chemistry studies. These different electron configurations allow for what we call spectral signatures to exist among the elements. This means that since every single element has a specific electron configuration, the light that it both absorbs and emits acts as a sort of photon fingerprint; a unique identifier to that element.

A list of the elements with their corresponding visible light emission spectra. Image Credit: MIT Wavelength Tables, NIST Atomic Spectrum Database, umop.net
A list of the elements with their corresponding visible light emission spectra. Image Credit: MIT Wavelength Tables, NIST Atomic Spectrum Database, umop.net


The standard equation for determining the characteristics of light is:

c= v λ

c is the speed of light in a vacuum (3.00 x 108 m/s)

v  is the frequency of the light wave (in Hertz)

λ (lambda) represents the wavelength (in meters, but will usually be converted to nanometers) which will determine what color of light will be emitted from the element(s), or simply where the wavelength of light falls on the electromagnetic spectrum (infrared, visible, ultraviolet, etc.)

If you have either the frequency or the wavelength, you can determine the rest. You can even start with the energy of the light being detected by your instruments and then work backwards with the following equations:

The energy of a photon can be described mathematically as this:

Ephoton = h v
Ephoton = h c / λ

What these mean is that the energy of a photon is the product of the frequency (v) of the light wave emitted multiplied by Planck’s Constant (h), which is 6.63 x 10-34 Joules x seconds. Or in the case of the second equation, the energy of the photon is equal to Planck’s Constant x the speed of light divided by the wavelength. This will give you the amount of energy that a specific wavelength of light contains. This equation is also known as the Planck-Einstein Relation. So, if you take a measurement and you are given a specific energy reading of the light coming from a distant star, you can then deduce what information you need about said light and determine which element(s) are either emitting or absorbing these wavelengths. It’s all mathematical detective work.

So, the electrons that orbit around the nucleus of atoms exist in what we call orbitals. Depending on the atom (and the electrons associated with it), there are many different orbitals. You have the “ground” orbital for the electron, which means that the electron(s) there are closest to the nucleus. They are “non-excited”. However, there are “higher” quantum orbitals that exist that the electron(s) can “jump” to when the atom is excited. Each orbital can have different quantum number values associated with it. The main value we will use is the Principle Quantum Number. This is denoted by the letter “n”, and has an assigned integer value of 1, 2, 3, etc. The higher the number, the further from the nucleus the electron resides, and the more energy is associated with it. This is best described with an example:

A hydrogen atom has 1 electron. That electron is whipping around its 1 proton nucleus in its ground state orbital. Suddenly, a burst of high energy light hits the hydrogen. This energy is transferred throughout the hydrogen atom, and the electron reacts. The electron will instantaneously “vanish” from the n1 orbital and then reappear on a higher quantum orbital (say n4). This means that as that light wave passed over this hydrogen atom, a specific wavelength was absorbed by the hydrogen (this is an important feature to remember for later).

Diagram of an electron dropping from a higher orbital to a lower one and emitting a photon. Image Credit: Wikicommons
Diagram of an electron dropping from a higher orbital to a lower one and emitting a photon. Image Credit: Wikimedia Commons

Eventually, the “excited” electron will drop from its higher quantum orbital (n4) back down to the n1 orbital. When this happens, a specific wavelength of light is emitted by the hydrogen atom. When the electron “drops”, it emits a photon of specific energy or wavelength (dependent upon many factors, including the state the electron was in prior to its “excitement”, the amount of levels the electron dropped, etc.) We can then measure this energy (or wavelength, or frequency,) to determine what element the photon is coming from (in this case, hydrogen). It is in this feature that each element has its own light signature. Each atom can absorb and emit specific wavelengths of light, and they are all tied together by the equations listed above.

So how does this all work? Well, in reality, there are many factors that go into this sort of astronomical study. I am simply describing the basic principle behind the work. I say this so that the many scientists that are doing this sort of work do not feel as though I have discredited their research and hard work; I promise you, it is painstakingly difficult and tedious and involves many more details that I am not mentioning here. That being said, the basic concept works like this:

We find a star that gives off the telltale signs that it has a planet orbiting around it. We do this with a few methods, but how it all first started was by detecting a “wobble” in the star’s apparent position. This “wobble” is caused by a planet orbiting around its parent star. You see, when a planet orbits a star (and when anything orbits anything else), the planet isn’t really orbiting the star, the planet AND the star are orbiting a common focal point. Usually with this type of orbital system, that common focal point is fairly close to the center of the star, and thus it’s safe to say that the planet orbits the star. However, this causes the star to move ever so slightly. We can measure this.

Once we determine that there are planets orbiting the star in question, we can study it more closely. When we do, we turn our instruments towards it and begin taking highly detailed measurements, and then we wait. What we are waiting for is a dimming of the star at a regular interval. What we are hoping for is this newly-found exoplanet to transit our selected star. When a planet transits a star, it moves in front of the star relative to us (this also means we are incredibly lucky, as not all planets will orbit “in front” of the star relative to our view). This will cause the star’s brightness to dip ever so slightly at a regular interval. Now we have identified a prime exoplanet candidate for study.

Diagram of how we can use aborbstion specral reading to determine the atmosphere of an exoplanet. Image Credit: A. Feild, STScl, NASA
Diagram of how we can use absorption spectral reading to determine the atmosphere of an exoplanet. Image Credit: A. Feild, STScl, NASA

We can now introduce the spectroscopic principles to this hunt. We can take all sorts of measurements of the light that is coming from this star. Its brightness, the energy it’s kicking out per second, and even what that star is made of (the emission spectrum I discussed earlier). Then what we do is wait for the planet to transit the start, and begin taking readings. What we are doing is reading the light passing THROUGH the exoplanet’s atmosphere, and then studying what we can call an Absorption Spectrum reading. As I mentioned earlier, specific elements will absorb specific wavelengths of light. What we get back is a spectral reading of the star’s light signature (the emission spectra of the star), but with missing wavelengths that show up as very tiny black lines where there used to be color. These are called Fraunhofer lines, named after the “father” of astrophysics Joseph Fraunhofer, who discovered these lines in the 19th century.

The dark lines represent the light frequencies that were absorbed by specific chemicals that this particular light passed through. Image Credit: Wikimedia Commons
The dark lines represent the light frequencies that were absorbed by specific chemicals that this particular light passed through. Image Credit: Wikimedia Commons

What we now have in our possession is a chemical fingerprint of what this exoplanet’s atmosphere is composed of. The star’s spectrum is splayed out before us, but the barcode of the planet’s atmospheric composition lay within the light. We can then take those wavelengths that are missing and compare them to the already established absorption/emission spectra of all of the known elements. In this way, we can begin to piece together what this planet has to offer us. If we get high readings of sulfur and hydrogen, we have probably just discovered a gas giant. However if we discover a good amount of nitrogen and oxygen, we may have found a world that has liquid water on its surface (provided that this planet resides within its host star’s “habitable” zone: a distance that is just far enough from the star to allow for liquid water). If we find a planet that has carbon dioxide in its atmosphere, we may just have discovered alien life (CO2 being a waste product of both cellular respiration and a lot of industrial processes, but it can also be a product of volcanism and other non-organic phenomena).

What this all means is that by being able to read the light from any given object, we can narrow our search for the next Earth. Regardless of distance, if we can obtain an accurate measurement of the light moving through an exoplanet’s atmosphere, we can tell what it is made of.

We have discovered some 2000 exoplanets thus far, and that number will only increase in the coming decades. With so many candidates, it will be a wonder if we do not find a planet that we humans can live on without the help of technology. Obviously our techniques will further be refined, and as new technologies, methods, and instruments become available, our ability to pinpoint planets that we can someday colonize will become increasingly more accurate.

With such telescopes like the James Webb Space Telescope launching soon, we will be able to image these exoplanets and get even better spectroscopic readings from them. This type of science is on the leading edge of humanity’s journey into the cosmos. Astrophysicists and astrochemists that work in this field are the necessary precursors to the brave men and women who will one day board those interstellar spacecraft and launch our civilization into the Universe to truly become an interstellar species.

Possible glimpse into our future... Image Credit: Battlestar Wiki Media
Possible glimpse into our future… Image Credit: Battlestar Wiki Media

A Fun Way of Understanding E=mc2

Einstein's Relativity, yet another momentous advancement for humanity brought forth from an ongoing mathematical dialogue. Image via Pixabay.

Many people fail to realize just how much energy there is locked up in matter. The nucleus of any atom is an oven of intense radiation, and when you open the oven door, that energy spills out; oftentimes violently. However, there is something even more intrinsic to this aspect of matter that escaped scientists for years.

It wasn’t until the brilliance of Albert Einstein that we were able to fully grasp this correlation between mass and energy. Enter E=mc2. This seemingly simple algebraic formula represents the correlation of energy to matter (energy equivalence of any given amount of mass). Many have heard of it, but not very many understand what it implies. Many people are unaware of just how much energy is contained within matter. So, for the next few minutes, I will attempt to convey to you the magnitude of your own personal potential energy equivalence.

First, we must break down this equation. What do each of the letters mean? What are their values? Let’s break it down from left to right:

Albert Einstein's Inventions
Albert Einstein. Image credit: Library of Congress

E represents the energy, which we measure in Joules. Joules is an SI measurement for energy and is measured as kilograms x meters squared per seconds squared [kg x m2/s2]. All this essentially means is that a Joule of energy is equal to the force used to move a specific object 1 meter in the same direction as the force.

m represents the mass of the specified object. For this equation, we measure mass in Kilograms (or 1000 grams).

c represents the speed of light. In a vacuum, light moves at 186,282 miles per second. However in science we utilize the SI (International System of Units), therefore we use measurements of meters and kilometers as opposed to feet and miles. So whenever we do our calculations for light, we use 3.00 × 108m/s, or rather 300,000,000 meters per second.

So essentially what the equation is saying is that for a specific amount of mass (in kilograms), if you multiply it by the speed of light squared (3.00×108)2, you get its energy equivalence (Joules). So, what does this mean? How can I relate to this, and how much energy is in matter? Well, here comes the fun part. We are about to conduct an experiment.

This isn’t one that we need fancy equipment for, nor is it one that we need a large laboratory for. All we need is simple math and our imagination. Now before I go on, I would like to point out that I am utilizing this equation in its most basic form. There are many more complex derivatives of this equation that are used for many different applications. It is also worth mentioning that when two atoms fuse (such as Hydrogen fusing into Helium in the core of our star) only about 0.7% of the mass is converted into total energy. For our purposes we needn’t worry about this, as I am simply illustrating the incredible amounts of energy that constitutes your equivalence in mass, not illustrating the fusion of all of your mass turning into energy.

Let’s begin by collecting the data so that we can input it into our equation. I weigh roughly 190 pounds. Again, as we use SI units in science, we need to convert this over from pounds to grams. Here is how we do this:

1 Josh = 190lbs
1 lbs = 453.6g
So 190lbs × 453.6g/1 lbs = 86,184g
So 1 Josh = 86,184g

Since our measurement for E is in Joules, and Joule units of measurement are kilograms x meters squared per seconds squared, I need to convert my mass in grams to my mass in kilograms. We do that this way:

86,184g × 1kg/1000g = 86.18kg.

So 1 Josh = 86.18kg.
Now that I’m in the right unit of measure for mass, we can plug the values into the equation and see just what we get:
E= (86.18kg)(3.00 × 108m/s)2
E= 7.76 × 1018 J

That looks like this: 7,760,000,000,000,000,000 or roughly 7.8 septillion Joules of energy.

Artistic rendition of energy released in an explosion. Via Pixabay.
Artistic rendition of energy released in an explosion. Via Pixabay.

This is an incredibly large amount of energy. However, it still seems very vague. What does that number mean? How much energy is that really? Well, let’s continue this experiment and find something that we can measure this against, to help put this amount of energy into perspective for us.

First, let’s convert our energy into an equivalent measurement. Something we can relate to. How does TNT sound? First, we must identify a common unit of measurement for TNT. The kiloton. Now we find out just how many kilotons of TNT are in 1 Joule. After doing a little searching I found a conversion ratio that will let us do just this:

1 Joule = 2.39 × 10-13 kilotons of explosives. Meaning that 1 Joule of energy is equal to .000000000000239 kilotons of TNT. That is a very small number. A better way to understand this relationship is to flip that ratio around to see how many Joules of energy is in 1 kiloton of TNT. 1 kiloton of TNT = 4.18×1012 Joules or rather 4,184,000,000,000 Joules.

Now that we have our conversion ratio, let’s do the math.

1 Josh (E) = 7.76 x 1018 J
7.76 x 1018 J x 1 kT TNT/ 4.18 x 1012 J = 1,856,459 kilotons of TNT.

Thus, concluding our little mind experiment we find that just one human being is roughly the equivalence of 1.86 MILLION kilotons of TNT worth of energy. Let’s now put that into perspective, just to illuminate the massive amount of power that this equivalence really is.

The bomb that destroyed Nagasaki in Japan during World War II was devastating. It leveled a city in seconds and brought the War in the Pacific to a close. That bomb was approximately 21 kilotons of explosives. So that means that I, 1 human being, have 88,403 times more explosive energy in me than a bomb that destroyed an entire city… and that goes for every human being.

So when you hear someone tell you that you’ve got real potential, just reply that they have no idea….

Hydrogen Bomb Blast. Image via Pixabay.
Hydrogen Bomb Blast. Image via Pixabay.