As we celebrate the Earth completing another lap around the Sun, let’s take a moment to imagine what life would be like in a world without years – a world that somehow ceased to orbit its star. Admittedly, it’s a strange question, but its’s one that I’ve been obsessively wondering about lately. Not because it’s of any particular relevance, but simply because it’s amusing (at least to me) and fun to think about.

What would happen to us if a giant space finger were to gently stop the Earth in its orbit?

Nothing good.

Here, try it out for yourself. Press ‘start’ in the simulation below (created by Michael Dubson and the folks at Phet Interactive Simulations / University of Colorado). You should see a planet orbiting the Sun.

Now press ‘reset’, and drag the circle with the letter ‘v’ to shrink the planet’s speed . Then press ‘start’ again. What happens? (While you’re playing with this, you might enjoy trying out some of the different scenarios in the drop-down menus, and watching the gravitational ballet that ensues.)

If you slowed down the planet enough, you should see it crash into the Sun.

To see why, let’s first remember why things stay in orbit. Every child looking at the sky has at some point wondered, “why doesn’t the moon fall down?” The answer is beautifully simple, yet it took a mind as brilliant as Isaac Newton’s to work it out. (Perhaps a sign of genius is coming up with simple answers to children’s questions.)

Newtons’ response to the child’s question would have been – the moon does fall. It’s constantly falling. Being in orbit is a state of always falling, and always missing what you’re falling towards. In The Hitchiker’s Guide to the Galaxy, Douglas Adams describes the secret to flight. “The knack”, he writes, “lies in learning how to throw yourself at the ground and miss”. As it turns out, this is also a great description of what it means to orbit something.

Here’s how Newton explained it. Imagine a cannonball is fired from a height. If you fire the cannonball with more speed, it’ll travel further before it hits the ground. The faster the cannonball, the further it travels.

But wait – the Earth is round. That means that if you shoot the cannonball with enough speed, then by the time it would have hit the ground, it’s travelled far enough that the ground has curved away beneath it. So the cannonball continues to fall towards the ground, and the ground continues to curve away from it. It’s now in a state of perpetual free fall – the cannonball is in orbit!

(Newton’s idea is masterfully explained in this wonderful Radiolab segment.)

So the only thing that makes an orbit different from plain-old falling is having enough speed to miss the thing you’re falling towards. Think dropping a cannonball with zero speed versus shooting it into orbit. And for the same reason, if the Earth were robbed of all of its orbital speed, it would fall straight into the Sun. It would no longer have the speed it needs to miss the Sun.

How long would this ‘Earthfall’ take?

(If you remember some high school physics and want to work out the answer for yourself, here’s a hint for solving it without any calculus.)

I’ll skip the math, but it turns out that we’d have 64 and a half days before we plunged into the fiery depths of the center of the Sun. But don’t worry, we’d be quite dead before that happens.

As the Earth falls towards the Sun, it picks up speed. The further it falls, the more intense the sunlight, and so Earth  starts to heat up.

Here’s a plot of the Earth’s average temperature over these 64 and a half days.

If we zoom out, we see that most of the action happens in Earth’s last day.

You can see that things are going to get pretty uncomfortable fairly soon.

Let’s take this flight of fancy a step further, and imagine what things would be like on Earth as it descends into the Sun. What follows is my attempt at a science-based play-by-play of Earth’s final 64 and a half days.

Day 0

We begin our plunge towards the Sun.

Day 6

After 6 days of falling to the Sun, the Earth’s temperature has risen by about 0.8 degrees celsius. That’s the same amount by which we’ve increased our planet’s temperature since 1880. You may not feel the heat as yet, but you will soon.

Day 21

The average global temperature has now risen by about 10 degrees celsius, to 35 C (95 F). The planet is now experiencing an extremely intense global heat wave, whose temperature rise rivals the record-breaking 2003 European heat wave. Crops are beginning to fail.

Day 35

It’s been over a month of Earthfall, and we’re now 20% of the way to the Sun. The Sun in unbearably bright and intense, and noticeably larger in the sky. At 58 C (137 F), the average global temperature now exceeds the historic hottest temperature recorded on Earth, which was 56.7 C (134 F) measured in Death Valley, CA.

For most people on the planet, it’s now impossible to stay alive without air conditioning, and the electricity infrastructure is either tapped out or failing. Forest fires are ravaging through the wilderness. Land animals that can’t burrow in to the soil to get respite from the heat are going extinct. The insects, too, are feeling the heat and dying out. The increasing water temperature will cause fish to start dying out, because warmer water holds less oxygen and more ammonia (which is toxic to fish), and because the entire marine food chain would be disrupted and collapsing.

It’s so hot that even the Saharan silver ant, one of the most heat resistant land animals on Earth, can no longer survive the heat (for it can stay alive up to 53.6 C). However, the Sahara desert ant is thriving – it can survive surface temperatures of up to 70 C. As scavengers, these ants feed on the corpses of other creatures that have died from the heat, and there’s now plenty of food to go around.

Day 41

We’ve now crossed Venus’s orbit. The average temperature exceeds 76 C (169 F), a temperature too hot for even the Sahara desert ant.

The Pompeii Worm, however, is still holding on. These amazing creatures grow up to 13 centimeters (5 inches) long, and are known to survive temperatures of up to 80 C. It’s thought that they owe this heat-resisting superpower to a protective “fleece-like” layer of bacteria on their backs, which insulates them from the heat. These worms are “the most heat-tolerant complex animal known to science”, with the exception of tardigrades (whom we’ll hear from soon).

Day 47

We just left the habitable zone, that Goldilocks region of a solar system (not too hot, not too cold) capable of sustaining life as we know it.

At 103 C (217 F), the ambient temperature now exceeds the boiling point of water. The Earth’s oceans are boiling. Liquid water can no longer exist on much of Earth’s surface and steam envelopes the planet. Most life on Earth is extinct by now, particularly complex life forms, even the amazingly heat-resistant Pompeii Worm. Hyperthermophiles (such as heat-resistant bacteria) are surviving (perhaps even thriving) deeper in the ocean where the water pressure prevents boiling. Fire tolerant plants are still holding on.

Tardigrades (or water bears) take the prize for the toughest known living things. Heck, these creatures have even survived in the vacuum, extreme cold and high radiation of outer space for a whopping 10 days. Truly, they are among Earth’s extreme survivors.

At this point, the Tardigrades are perhaps just beginning to notice that something is awry. They’re probably bunkering down by suspending their metabolism, curling up and dehydrating themselves into a desiccated state that contains only 1% of their original water. In this dehydrated state, called a tun, they can stay alive and dormant for nearly a decade.

Day 54

Farewell, dear tardigrades. You outlived us all. Although you can endure a crazily impressive temperature range, from near absolute zero to 151 C, Earth’s temperature now exceeds 160 C, too hot even for you.

Day 57

We’ve crossed Mercury’s orbit, and are now the closest planet to the Sun, a distinction that we will hold for another week. The ambient temperature exceeds 200 C.

Day 64

The Earth is now in its final day. Because of the Earth’s immense accumulated speed, and the intense gravitational force of the nearby Sun, we’ll cover the last 7 percent of our journey’s length by 1 pm today. The Sun’s gravity is now so extreme, that it pulls the front of the Earth with significantly more force than the back of the Earth. This differential gravity, or tidal force, is stretching Earth out into an oval shape. Magma erupts throughout cracks and fissures in the planet’s crust.

The day starts off at a balmy 800 C, with the Sun fourteen times its regular size in our sky. By noon the temperature hits 2000 C, more than hot enough to melt rock. Earth’s surface melts into magma.

At half past noon, we’ve nearly arrived. The Sun is so close that it fills most of the day sky. The Earth is crossing an imaginary line of no return called the Roche Limit. This is the point where the tidal forces pulling Earth apart exceed Earth’s ability to hold itself together. As it crosses this critical radius, the tidal effect of gravity rips the Earth into smaller balls of magma and melting rock.

And this is how our disintegrating planet finally meets the end of its journey to the Sun. I hope you enjoyed the trip.

P.S. Before you begin to fret about Earth falling into the Sun, consider this. Earth’s speed in our orbit is about 30 kilometers/second. That’s a lot of speed that we’d have to shed for the scenario in this blog post. It would actually be (very slightly) easier for the giant space finger to give us a shove and increase our speed to 42.1 kilometers/second, the escape velocity at which Earth would break free of the Sun’s gravity and become a rogue planet. I really did start off this paragraph trying to help. Sigh.

Nerdy Footnotes

To calculate the temperature of the planet, I used the rule of thumb for the Sun that the equilibrium temperature of a planet is 250/sqrt(d) where d is the distance to the Sun in astronomical units. You can find a derivation of that here. Additionally, I used a simplified model of the atmosphere as a single layer to account for the greenhouse effect – this boils down to multiplying the temperature by the fourth root of 2. I used Mathematica to numerically solve for the relation between time in Earthfall and distance covered by the Earth. Combining this piece with the above relation of temperature vs. distance, I arrived at the plot of temperature versus time in this post.

There are tons of reasons why this calculation is a massive simplification – for one, the greenhouse effect will increase considerably as the melting Earth’s atmosphere probably contains way more greenhouse gases from all the burning carbon. But, hopefully, this post should give a reasonable order-of-magnitude estimate of life (and lack thereof) during Earthfall. Also, I’m totally sweeping under the rug the force that would arise during Earth’s deceleration as it’s being slowed down by the giant finger, because life’s too short.

When I was about 10, I broke my first skateboard by riding it into a ditch. A decade later, in college, I broke another skateboard within an hour of owning it (surely a record) in a short-lived attempt at doing an ollie. (Surprisingly, the store accepted a return on that board even though it was in two pieces.) Then I was gifted a really nice, high-quality skateboard. The first thing I did with it was ride it down a big hill, a valiant but ill-fated adventure which ended with me jumping off the skateboard, rolling down the grass, and arriving scraped up, deflated, and rather disoriented near the entrance to my college cafeteria. (In my defense, the wheels and ball-bearings on that skateboard had been pre-lubricated to minimize friction, and why would anyone do that, that’s just crazy.)

So believe me when I tell you that I am incredibly envious of skaters who can pull off tricks like this.

Now, I might not be able to skate to save my life, but I can do a little physics. So here’s a thought – maybe I can use physics to learn how to do an ollie. Here’s the plan. I’m going to open up the above video of skateboarder Adam Shomsky doing an ollie, filmed in glorious 1000 frames-per-second slow motion, and analyze it in the open source physics video analysis tool Tracker.

The first thing I did was track the motion of the front and back wheels (Tracker has a very convenient autotracker feature that can do this for you.)

One useful physics trick here is to track the center of mass of the skateboard, i.e. the average of the positions of the front and back wheels. Here is that curve overlapped in green.

Now, if you were to do the same tracking exercise for a soccer ball that’s been kicked, you’d get a neat arc-like shape called a parabola. This is the characteristic shape you get when the only force influencing an object’s motion is gravity.*

But the green curve in the above gif — the motion of the center of mass of the skateboard — is nowhere close to being a parabola. It’s lumpy and weird. This means that gravity isn’t the only force affecting the skateboard. Unlike a soccer ball in mid-flight, a skateboard mid-ollie is being actively steered.

This is exactly what makes doing an ollie so hard. It’s not enough to get the skateboard up into the air – you also have to steer it while it’s in the air.

In fact, we can work out how you need to steer the skateboard. Tracker has a nice feature that we’ll call ‘force arrows’. These arrows show you how much force acts on an object at every instant, and in which direction the force acts. So for example, if you were to kick a ball into the air, while the ball was mid-flight, this arrow would always point down and be the same length, even though the ball is moving forward. That’s because the only force acting on the ball is gravity, which pulls it straight down, and acts with a constant strength. (For those of you who’ve studied physics, these arrows denote the acceleration of the center of mass, which by Newton’s second law is proportional to the net force acting on the skateboard.)

Here’s what we find when we work out the force arrows for the skateboard.

Or, if you prefer to see all the arrows overlaid,

It’s a neat piece of science art, and it also tells us something interesting. The arrows show us that the force on the skateboard is constantly changing, both in magnitude as well as in direction. Now the force of gravity obviously isn’t changing, so the reason that these force arrows are shrinking and growing and tumbling around is that the skater is changing how their feet pushes and pulls against the board. By applying a variable force that changes both in strength and direction, they’re steering the board.

In fact, we can go back and see how much force each wheel experiences.

Crucially, at any instant, each foot applies a different amount of force. These unequal forces at each end is what causes the skateboard to turn (in physics lingo, it creates a torque). It’s how the skater steers the board.

We can see this more clearly if we subtract away the motion of the center of mass (i.e. subtract the green arrows above from the red and the blue arrows). Now, we’re only looking at how the wheels accelerate relative to the center of the board, not relative to the ground.

You can see there how the skater uses unequal forces to turn the board, shifting their weight from their front foot while moving up, to their back foot while descending.

To summarize, a skateboarder’s feet need to do two things successfully to complete an ollie. They need to provide a changing force to move the board correctly (so that the combined force of gravity and the skater’s feet add up to the green arrows above), and they need to provide different amounts of force with each foot (shown by the red and blue arrows above) to steer and turn the board into the right orientation.

Sadly, after all this geeking out, I’m no more successful in my attempts to do an ollie. But at least now I can explain why I suck at it.

Footnotes

Thanks to Robin Wylie for helping me headline this post.

*Technically this curve is a (segment of an) ellipse, but so long as you aren’t kicking the football into orbit, it’s close enough to a parabola.

I want to tell you about one of the most beautiful ideas that I know.

It’s a physics experiment, and it’s beautiful because in one elegant stroke, it expands our consciousness, forcing us to realize that objects can behave in ways that are impossible for us to picture (but remarkably, possible for us to calculate). It’s beautiful because it calls into question the bedrock of logic on which we’ve built our understanding of the world. It’s beautiful because it’s deceivingly simple to understand, and yet its consequences are deeply unsettling. And it’s beautiful because I refused to accept it until I ran the experiment for myself, and I distinctly remember watching my worldview shatter as the picture slowly built up on the computer monitor.

This was eleven years ago. I was a college freshman, sitting in a physics lab with all the lights turned out, staring at a blank computer screen, and for reasons that I won’t go into here, listening to a best-of compilation of 80s pop hits.

Here’s the setup. On the table in front of me there’s a box with two thin slit-like openings at one end. We’re shooting particles into this box through these slits. I did the experiment with photons, i.e. chunks of light, but others have done it with electrons and, in principle, it could be done with any kind of stuff. It’s even been done with buckyballs, which are soccer ball shaped arrangements of 60 carbon atoms that are positively ginormous compared to electrons. For convenience, I’m going to call the objects in this experiment electrons but think of that word as a stand-in for any kind of stuff that comes in chunks, really.

At the other end of the box is a CCD camera, that takes a snapshot of whatever hits it. Every time a particle makes it to the other side of the box, I see a dot light up at the corresponding point on my computer screen.

Just to be extra careful, we’ve set up the experiment so that there is only one particle inside the box at any given time. Picture, if you like, very tiny baseballs being flung into the box, one at a time. The 80s music plays on, and we sit and wait.

What would you expect to see on the other side of the box? Well, if electrons behaved like waves, you’d expect to see fringes of bright and dark bands, like ripples in a tank of water. That’s because waves can interfere with each other, canceling out when the peak of one wave meets the trough of another, and getting reinforced when the peaks line up.

But electrons aren’t waves – they come in chunks. I know this, because I can see them arriving at the screen one at a time, and they strike at a single place, like raindrops falling on dry pavement. And if electrons are chunk-like, then you’d expect to see them piling up behind the slits and nowhere else. In short, you’d expect them to behave like baseballs.

And indeed, if you do this experiment with only one slit open, they behave just like baseballs, hitting the wall in a single band behind the open slit. A reasonable prediction, then, is that when we run the experiment with both slits open, we should see two bands – one behind each slit.

So what do the electrons do?

Here, see for yourself. You can watch the electrons coming in one at a time in this video produced by scientists at Hitachi in 1989. The video has been sped up around 30X.

It takes a moment to realize just how odd this is. Somehow, the electrons created this interference pattern of bright and dark stripes. But they were sent in one at a time, so what could they possibly have interfered with? If you’re picturing the electron as a tiny baseball, you’re forced to conclude that an electron going through one slit ‘sniffs out’ that the other slit is open, and adjusts its behavior accordingly. Or that it’s somehow taking both paths and interfering with itself. This doesn’t make any kind of sense.

So let’s take a step back, and try to piece together what happened. Here’s an obvious question that you might ask. Think about an electron that arrives at the screen. Which slit did it go through?

Did the electron go through the left slit?

No! Because when you cover up the right slit, the stripey pattern disappears and you get a boring single band instead.

Did the electron go through the right slit?

No! For the same reason as above. When you cover up the left slit, instead of the stripey pattern you get a single band.

Does the electron go through both slits?

No! Because if that were true, we’d expect to see the electron split into two, and one electron (or maybe half) would go through each slit. But if you place detectors at the slits you find that this never happens. You always see only one electron at a time. It never, ever splits into two.

Did the electron go through neither slit?

No! Of course not, that’s just silly. If you cover both slits, nothing happens.

At this point you’re probably thinking that this is getting a bit ridiculous. Why can’t we just look at the damn electron and see which path it took? The problem with this idea is that looking at something means shining light on it, and shining light on it means bumping it with a photon. If you’re a tiny electron, this bump disturbs your original path.

Well, wait. Maybe you could make the bump really, really gentle, so you don’t disturb the electron much. Indeed, you can do that, but as you make the light more gentle (lower momentum), you also make it more spread out (larger wavelength), and you end up not being able to tell which slit the electron went through.

There’s no way to win here. Any scheme that you can invent to determine which route the electron took will also destroy the interference pattern.

To summarize, we’ve arrived at a pattern of fringes that’s built up one particle at a time. But when you try to work out exactly how those particles got there, you find that they didn’t take the left route, they didn’t take the right route, they didn’t take both routes, and they didn’t take neither routes. As MIT professor Allan Adams puts it, that pretty much exhausts all the logical possibilities!

An electron is not like a wave of water, because unlike a wave, it hits a screen at a single location. An electron is not like a baseball, because when you throw in a bunch of them through a double slit, they interfere and create patterns of fringes. There is no satisfying analogy that anyone can give you for what an electron is. As Allan Adams points out in his introductory lecture on quantum mechanics,

These electrons are doing something we’ve just never thought of before, something we’ve never dreamt of before, something for which we don’t really have good words in the English language.

Apparently, empirically, electrons have a way of moving, [..] a way of being, which is unlike anything that we’re used to thinking about.

And so do molecules.

And so do bacteria.

So does chalk.

It’s just harder to detect in those objects.

Physicists have a name for this new mode of being. We call it superposition.

It’s sometimes useful to think of an electron as behaving like a particle, and it’s sometimes useful to think of an electron as behaving like a wave. But these are just conveniences of language, and they’re both incomplete pictures. An electron is neither a wave nor a particle. An electron is an electron. The same goes for a photon, an atom, a buckyball, a giant molecule, or what have you. (The larger the object, the harder it is to see these fringes.)

Werner Heisenberg, one of the creators of quantum mechanics, understood this clearly. In 1930, he wrote,

The solution of the difficulty is that the two mental pictures which experiment lead us to form—the one of the particles, the other of the waves—are both incomplete and have only the validity of analogies which are accurate only in limiting cases. [..] the apparent duality arises in the limitations of our language.

As Heisenberg and others taught us, although language fails us, it’s possible to come up with rules that correctly predict how tiny things behave. Those rules are quantum mechanics. You can learn these rules for yourself by reading Richard Feynman’s classic book QED, or watching his lectures on the subject. Using these rules, physicists can throw around fancy sounding sentences like ‘the electron wavefunction is in a superposition of going through the left slit and going through the right slit’. These sentences have well defined mathematical meanings, and they make predictions that match the data. But what’s missing here is a coherent picture that you can hold in your head that will explain which path the electron took, and what’s more, we can be fairly confident that such a picture can never exist.

It’s perhaps not surprising that our ape-brains, which evolved in a middle-sized world throwing rocks and spears, can’t visualize the behavior of very small things. What’s surprising to me is that even though we’re unable to picture this quantum world, we’ve managed to work out the rules of the game.

References

This post has largely been inspired by watching Allan Adams’s excellent introduction to quantum physics made available by MIT OpenCourseWare. The first lecture is an fascinating and often hilarious look at the principle of superposition explained in a non-technical way. I highly recommend checking it out – he’s a very engaging lecturer.