Why Does The Sun Move So Slow?


I really wish I could remember what prompted this questions. I suspect it had to do with one of our conversations about time, and how “day” is from sunrise to sunset. There was probably something we were doing in the evening, something he was looking forward to doing, and the sun seemed to be just crawling through the sky. Whatever the reason, the question certainly seems to make sense. The sun takes all day to cross the sky, so it looks slow. It comes up gradually, takes four to six hours to reach noon, and then slowly sinks into the west.

Of course, appearances are deceiving.

How Fast Does The Sun Move Across The Sky?

This is actually sort of tricky, because the Sun isn’t actually moving around the Earth. To begin with, let’s refer back to the technical definition of sunrise and sunset:

Sunrise and sunset. For computational purposes, sunrise or sunset is defined to occur when the geometric zenith distance of center of the Sun is 90.8333 degrees. That is, the center of the Sun is geometrically 50 arcminutes below a horizontal plane. For an observer at sea level with a level, unobstructed horizon, under average atmospheric conditions, the upper limb of the Sun will then appear to be tangent to the horizon. The 50-arcminute geometric depression of the Sun’s center used for the computations is obtained by adding the average apparent radius of the Sun (16 arcminutes) to the average amount of atmospheric refraction at the horizon (34 arcminutes).

Now, an arcminute is 1/60th of a degree, so the day begins when the center of the sun is 5/6ths of a degree below the eastern horizon and ends when the center of the sun is 5/6ths of a degree below the western horizon. Assuming perfect viewing conditions, et cetera, et cetera. So, that means that the sun has to cover 181 2/3 degrees in a single day. Here in Cincinnati, sunrise on the day this article is published is(August 19, 2016) is 6:55 am, and sunset is 8:27 pm. So, it will require 13 hours and 33 minutes (813 minutes) to cover that distance. That works out to, let’s see… 181.6666 / 813 = 0.22345 degrees per minute, or 13.407 degrees per hour.

Now, let’s do some more math. Cincinnati is at 39.1031 degrees north. According to Ask Dr. Math, you “just multiply the equatorial circumference by the cosine of the latitude, and you will have the circumference at that latitude.” The equatorial circumference of the earth is 24,901 miles, so 24,901 * cos(39.1031) = 19323.48 miles. The Sun crosses 181.666/360 = 0.5046 of that distance in 813 minutes, so that’s 9751.197 miles in 813 minutes. That’s essentially 12 miles a minute or 719.65 miles an hour.

But that’s the speed at which the sun passes over the Earth at that latitude on August 19. It’s not how fast it appears to an observer on the ground! To an observer standing on the surface of the Earth, the distance to the horizon is approximately 2.9 miles. That means that my son, observing the motion of the Sun, is standing at the center of a perceptual circle with a circumference of 2(π)2.9 = 18.22 miles. Which means that he sees the Sun appear to take 813 minutes to cover 18.22 * 0.5046 = 9.19 miles. That works out to a perceived speed of 0.0113 miles per minute, or 0.678 miles an hour.

No wonder it looks so slow to him. When we’re out on walks, my son and I hit a pace almost four and a half times faster!

How Fast Does The Sun Move Through The Galaxy?

Of course, the speed of the sun gets even trickier. Because, although it doesn’t move through the sky (we move, creating the illusion), it still orbits Sagittarius A*, the supermassive black hole at the center of the Milky Way. This monster is some 26,000 light years from earth and weighs in at around 4,000,000 M☉. Our Sun travels in a roughly circular orbit around this distant behemoth at a speed between 217 amd 250 kilometers per second – let’s take the average of those five figures and call it 230.4 kilometers per second (143.16392 miles per second). That’s 829,440 kph (515,390.112 mph).

That sounds impressive, doesn’t it?

Here’s something to consider, though: the speed of light is 299,792,458 meters per second, or 299,792.458 kilometers per second. That means the Sun (and it’s attendant planets and dwarf planets and other detritus) are moving at 0.07685% of the speed of light. Remember that line above, the one that reads “this monster is some 26,000 light years from earth”? That means that our Sun orbits Sagittarius A* in a circle approximately 163,360 light years in circumference. As a result, it will take about 163.360/0.07685% = 212.5 million years to complete an orbit. (Actual calculations from real astronomers come in at between 225 and 250 million years, which makes sense – they have access to more accurate figures, and the sun would actually describe an ellipse instead of a circle.)

So, why is the sun moving so slow? It isn’t. It’s tearing through space at a pace five times faster than the New Horizons probe at it’s maximum velocity – the fastest ship ever built by humanity (although the Sun’s gravity had slowed it to ‘only’ 14 kilometers per second by the time it passed Pluto). We just don’t notice, because it’s a huge universe and we have a very small frame of reference.

How Do They Build A Planet?

More than once, I’ve mentioned my son’s love of (not to say obsession with) Star Wars. I can’t really complain that he does, either, since I’m the one that introduced him to the movies. He also loves Legos, which is why he really, really loves playing the Lego Star Wars games. And I get roped into playing with him, because he knows I love Star Wars and video games as well.

As we’re playing through the game one day, we get to the animated cut scene where the death Star blows up Alderaan. He’s seen the movie, so he knows it’s coming, but this time around it seems to strike a chord in him.

“Why did they blow up the planet?” he asks.

“Well,” I say, trying to strike a balance between answering the question and having to have an in-depth discussion on the nature of evil with my five-year-old son, “they’re bad guys. And they’re trying to make Princess Leia tell them where her friends are.”

“They’re not making good choices,” he decides upon hearing that, which makes me smile. Then, the level starts and we’re frantically button-mashing. But he’s still thinking. “Can they fix it?”

“Fix what?” I ask.

“The planet.”

“No, you can’t really put a planet back together.”

He thinks about that again. “Well,” he asks, “how do they build a planet?”

A Star Is Born

ALMA image of the young star HL Tau and its protoplanetary disk. This best image ever of planet formation reveals multiple rings and gaps that herald the presence of emerging planets as they sweep their orbits clear of dust and gas.

ALMA image of the young star HL Tau and its protoplanetary disk. This best image ever of planet formation reveals multiple rings and gaps that herald the presence of emerging planets as they sweep their orbits clear of dust and gas.

The current accepted model of solar system formation is the nebular hypothesis. It’s particularly considered a good model these days, thanks to the image above, which is an image of a planet-forming disk captured by the Atacama Large Millimeter/Submillimeter Array(ALMA). In brief, here’s how it works.

Solar systems begin as enormous clouds of gaseous matter – mostly, but not entirely, hydrogen – floating in interstellar space. These clouds are actually referred to as “molecular clouds” (or, sometimes, “stellar nurseries”), and they are huge – anywhere from 15 to 600 light years in diameter with masses of 100 to 10,000,000 solar masses. Which means that, despite their vast size and mass they are extremely diffuse, possessing between a hundrd and a thousand particles per cubic centimeter.

All matter exerts gravity, even matter as small as molecules and atoms. Over time (read “time” as “millions of years”), the particles begin to clump together and form molecular cores (with a density of 10,000 to 1,000,000 particles per cubic centimeter). As a molecular core grows bigger it generates more gravity, pulling more matter to it and making it generate more gravity. It also begins to spin, thanks to the principle of the conservation of angular momentum (the same principle that causes whirlpools and ice skaters to spin faster and faster).

If conditions are right, then eventually (over hundreds of thousands of years) the molecular core will grow dense enough that it becomes incompressible, and further attempts to compress it simply generate more heat. As more of the molecular cloud collapses into the heated molecular core, it eventually forms a protostar (which is just a young star that is still absorbing mass from the molecular cloud).

So Where Does A Solar System Come From?

When the protostar forms, there are three important facts to remember. First, it is spinning. Second, it has gravity. Third, it hasn’t eaten all of the molecular cloud yet. These are important facts, as you’ll see momentarily.

All of the particles in the molecular cloud are moving in a more-or-less random manner. However, the spinning protostar and its comparatively massive gravity lend a little uniformity to these random directions – all of the particles, in addition to their starting random direction, also move at least slightly in the same direction as the spin of the protostar. This leads to a phenomenon called accretion as all of the particles in the molecular cloud do one of three things:

  1. Fall into the protostar.
  2. “Go with the flow”.
  3. Get thrown away from the protostar until it leaves the star’s orbit completely.

Most of the particles will take option one, and be eaten by the protostar (our own sun has more than 99% of the entire of the mass of our solar system). Some of what is left will be flung out beyond the effective borders of the fledgling solar system. The particles that are left continue to engage in inelastic collisions, which cause them to lose momentum as they impact each other. Since they can’t effectively eliminate the rotational speed (they’re being dragged by the spinning of the protostar) they fall towards each other – flattening into an accretion disk in the process.

And The Planets?

So, we’ve got a flat spinning disk around the protostar at this point. The planets begin to form because of molecular cores. See, the core that formed into the protostar isn’t the only core that formed. Molecular clouds have any number of these structures, and the one that formed the protostar is simply the biggest, meanest one in the local area. Smaller cores get treated like any other particle in the cloud – they either get eaten, go into orbit, or get chucked out. The ones that go into orbit begin collecting other particles that are in orbit near them, since they’re the biggest nearby source of gravity (a process that can be observed by how satellites orbiting the Earth will fall towards the Earth more than they fall towards the Sun). They can’t accrete enough mass to ignite into a protostar as well, but they can become noticeably bigger. If they get big enough, they form into planets.

Could we make a planet?

Sure. In theory, at least. All we’d need is enough mass to clump together, and a way to move all of that mass close enough to get it to clump together. As a for example, Mercury (the smallest planet in our solar system) only weighs 60,830,000,000,000,000,000 tons. How hard could it be?

Is the Earth bigger than the Sun?

All week, in honor of the summer solstice, I’ve been writing about the sun and about astronomy. Why? Because my son unleashed a torrent of questions, once we started talking about Monday having been the longest day of the year. So far I’ve answered questions about why the sun doesn’t melt, what the hottest star is, and what would happen if the sun turned into a black hole. So now, we’re on to the final question:

“Is the Earth bigger than the Sun?”

This one made me chuckle, just a little. “No,” I told him, “the sun is lots bigger.”

“Well,” he said thoughtfully, “my friend says the Earth is bigger.”

“It isn’t,” I assured him. “It just looks bigger, because we stand on the earth and the sun is really far away.”

He thought about that for a minute. “But it could be bigger!”

No. It really couldn’t.

This is a clear cut answer. The sun has an equatorial diameter of 1,391,400 kilometers and masses 1.988 x 10^30 kg, while the Earth has an equatorial diameter of 12,756.2 kilometers and masses 5.972 x 10^24 kg. Put another way, the Sun’s diameter is about 109 times that of earth, and it is 333,000 times as massive. There is no way the sun could be smaller than the earth.

So why does it look so small in the sky?

I’ll be honest here:  this is not something I ever recall stopping to ask.  Not until I started writing this article.  Like so many things, I just took it for granted that things that are close look bigger than things that are far away.  It never occurred to me to ask “why”, before.  (Which is one of the cool things about writing these articles – I end up answering questions I never thought to ask.)

Researching this, I ended up on a couple of different physics forums, and both of them agreed with Cognition and the Visual Arts:

The size of the retinal image varies in inverse proportion to the distance of an object.  Near objects appear larger than far objects because they occupy more space on the retina.  In the perception of real world stimuli, an object 5 feet away casts an image on the retina twice the size as the same object viewed from 10 feet away.


The object on the left is an eye, and the two stick figures are identical.  However, the stick figure closer to the eye occupies a greater percentage of that eye’s field of vision, and so will appear larger.  Likewise, a small object held close can appear to be the same size (or even larger) than a large object that is far away.

The sun, on average, is 93 million miles away.  As a result, even though it’s more than a hundred times as wide as the Earth, it appears small enough that you could make your own solar eclipse by holding a quarter (or similar coin) at arm’s length in front of it.

Don’t try that, though.  You could really damage your eyes.


What if the Sun turned into a Black Hole?

This week, I’ve been writing about the sun. I blame the summer solstice for this, because the news that Monday was the longest day of the year fired my son’s imagination and got him asking question after question about the sun, and about the stars, and about related astronomical phenomena. So far, I’ve answered his questions about whether or not the sun can melt (it can’t) and what the hottest star is (H1504+65). Now it’s time to move on to his next question, one which demonstrates that he’s learned some interesting things.

“What if the sun turned into a black hole?” he asked, as we walked up the stairs to the front door of our condominium building. “Would it swallow the earth and all the planets?”

That one took me off guard, because I’m pretty sure that when I was five I didn’t even know what a black hole was. But then, I also realized that the first black hole was discovered the year I was born, so it’s not surprising the term wasn’t in common usage when I was five.

It’s a chilling thought, isn’t it? “Nothing escapes a black hole,” science fiction tells us. “Not even light.” Black holes are the great white sharks of space – remorseless predators consuming everything in their path. And we’d never see them coming. But they have one other thing in common with sharks.


They have an exaggerated reputation.

Newton’s Laws of Motion and Universal Gravitation

Although aspects of his laws have been superceeded by Einstein and his General and Special Theories, Newton’s laws remain an excellent (if ever so slightly inaccurate) model of motion. In brief, his three laws of motion state:

  1. If no forces act upon it, a body in motion will remain in motion and a body at rest will remain at rest, and velocity will remain constant in either case.
  2. If force is applied to an object, there will be a change in velocity proportional to the magnitude to which the force is applied.
  3. If body A exerts force on body B, then body B will exert a force of equal strength but in opposite direction on body A. This is also stated as “for every action there is an equal and opposite reaction”.

In addition, Newton put forth a law of universal gravitation. This law states that “two particles having masses m1 and m2 and separated by a distance r are attracted to each other with equal and opposite forces directed along the line joining the particles. The common magnitude F of the two forces is


where G is an universal constant, called the constant of gravitation, and has the value 6.67259×10^-11 N-m^2/kg^2.”

Yeah? What does this have to do with black holes?

I’ll get to that. But first, let’s cover what a black hole actually is.

Fine. What’s a black hole?

Does it surprise you to know that NASA has some good resources about black holes? It really shouldn’t.

A black hole is a region in space where the pulling force of gravity is so strong that light is not able to escape. The strong gravity occurs because matter has been pressed into a tiny space. This compression can take place at the end of a star’s life. Some black holes are a result of dying stars.

Because no light can escape, black holes are invisible. However, space telescopes with special instruments can help find black holes. They can observe the behavior of material and stars that are very close to black holes.

Black holes come in four size categories, representing both their mass and their physixal size. There are:

  1. Micro black holes. These can run all the way up to about 7.342 x 10-8 M (the mass of our Moon), and can get as big as 0.1 millimeters. Yes, it would suck if one hit you.
  2. Stellar black holes. These range up to 10 M in mass, and can be up to about 30 kilometers in diameter (0.5 x 10-4 R).
  3. Intermediate-mass black holes, which can get up to 1,000 M and up to about the mass of the Earth itself.
  4. Supermassive black holes. These are the monsters that lurk at the center of most galaxies, massing up to 1010 M and up to 400 astronomical units in size.

Wow. So, why do you say they have an exaggerated rep?

It’s true that the escape velocity of a black hole exceeds the speed of light, which is what it means to say that “no light can escape”. However, no black hole will be larger or more massive than the sum of all of the mass that went into making the black hole in the first place. So, outside the event horizon (the point at which gravity becomes too powerful to escape), the black hole has the same effect as any other object of the same mass. With that in mind, Newton’s law of universal gravitation tells us that – if the sun were to be instantly replaced with a 1 M black hole – there would no impact on our solar system. the r2 figure in the equation is measured from center of m1 to center of m2, so nothing changes.


Well, all right. That’s not true. Black holes have no luminosity – no energy would be generated and nothing would reach the Earth. So, to quote Randall Munroe’s Sunless Earth article, “We would all freeze and die.”

What is the Hottest Star?

This week, I’m writing about the sun. And about stars in general. Why? Because two days ago, while walking home from preschool, we started talking about the summer solstice and things escalated from there. Five year olds are fully capable of unleashing an avalanche of questions.

Yesterday, if you recall, I answered his question about why the sun didn’t melt. He accepted the explanation I gave him, but it led him to two more: “What is the hottest star? Is it the biggest?”

I was honest with im. I had no idea what the hottest star is, or if that star is the biggest star. Let’s find out the answer together, shall we?

Measuring Stars

Most commonly, stars are measured in “solar” or “stellar” units, based on the measure of our own star (aka “the sun”).

  • Solar Mass (M): the mass of the sun, which is 1.98855 x 1030 kilograms.
  • Solar Luminosity (L): the energy output of the sun, which is 3.828 x 1026 watts.
  • Solar Radius (R): the radius of the sun, which is 6.960 x 105 kilometers.

To put that in perspective, the Earth has a mass of 5.927 x 1024 kg and an equatorial radius of 6.378 x 103 kilometers. So that means that the sun has the mass of roughly a million earths, and is approximately 100 Earths wide.

None of these address temperature, though. The sun’s core is modeled to be 1.57 x 107 Kelvin (K), the photosphere is 5,772 K, and the corona is 5 x 106 K. (If you aren’t familiar, the kelvin is a measure of temperature; it’s identical to Celsius, except that 0 degrees kelvin is absolute zero, and water begins to melt at 273.15 kelvin.)

Harder. Better. Faster. Stronger.

So, what’s the brightest star? Based on luminosity it’s R136a1, located about 163,000 light years from Earth. It’s luminosity is 8,710,000 L, and it’s not a slouch in other matters as well. It’s the most massive star we know of as well, with an estimated 315 M. The radius, however, is “only” estimated at 28.8 to 35.4 R, so it’s a long way from being the largest star.

The honor of being the largest star belongs (right now) to Westerlund 1-26, which has a radius around 1,530 R. Although not the brightest or hottest, it does its best. Its luminosity is 380,000 L, but it’s photosphere temperature is a paltry 3,600 K – only 62% of the Sun’s and far cooler than R136a1’s 53,000 K.

R136a1 isn’t the hottest star going, though. That title belongs to H1504+65, which has an estimated photosphere temperature of 200,000 K – 34 times hotter than the sun.

Is there anything bigger?

Of course there is. There’s plenty of room for things to go big in space, after all. For example, there is a thing called a pair-instability supernova – technically a hypernova – that happens when a star with 130 to 250 M explodes. It generates 1011 L at peak output.

The single most massive, brightest thing we know of is S5 0014-81, “a distant, compact, hyperluminous, broad-absorption line quasar or blazar located near the high declination region of the constellation Cepheus”. It comes in with 40,000,000,000 M and about 300,000,000,000,000 L. To put that in perspective, if it was 280 light years away from us – about the distance to Theta Scorpii – it would give us as much energy as the Sun. Fortunatly, it’s more like 12,000,000,000 light years away.

Next to S5 0014-81, or Sagittarius A* at the heart of our own galaxy, or even our fairly ordinary home star, our Earth is a tiny speck in the universe.  But it’s home.

Why doesn’t the sun melt?

This week, it seems, I’ll be writing about the sun. Why? Well, when we were walking home from preschool yesterday, I asked my son if he knew what day it was. “It’s the first day of summer!” he declared. And then he asked me a whole bunch of questions, one right after the other:

To be honest, I felt like I’d been hit by an avalanche of curiosity. But they’re all great questions.

What is melting?

Let’s start with the Dictionary.com, and a definition of melt that states:

  1. to become liquefied by warmth or heat, as ice, snow, butter, or metal.
  2. to become liquid; dissolve
  3. to pass, dwindle, or fade gradually (often followed by away)
  4. to pass, change, or blend gradually (often followed by into)
  5. to become softened in feeling by pity, sympathy, love, or the like
  6. Obsolete. to be subdued or overwhelmed by sorrow, dismay, etc.

From a more technical perspective, ‘melting’ is a first-order phase transition in which a material’s latent heat increases and it’s density or volume decreases sufficiently that it moves from the solid phase to the liquid phase.

Wait. Phases? Phase transitions? What now?

You’ve probably seen a diagram like this before:


That is a phase diagram for water, showing the different states (solid, liquid, or vapor) that water can be in based on temperature and pressure. Under one atmosphere of pressure (1 bar or 100 kPa), it is a solid at or below 0 degrees Celsius, a liquid between 0 and 100 degrees Celsius, and a vapor above 100 degrees Celsius. Phase is just the technical term for these states, and a phase transition is simply where the material changes (or makes a transition) from one phase to another.

While researching these phase changes, I ran into the terms “first-order phase transitions” and “second-order phase transitions” a lot. I’ll be honest and say I don’t fully understand them, because the best definitions all seem to involve a whole lot more physics than I understand. But here’s my best attempt at an explanation, after reading several articles and staring hard at Wikipedia:

  • A first-order phase transition is driven by heat, and the material transitions from one phase to another at a set rate based on the energy added to the system. Think of melting ice, or boiling water.
  • A second-order transition is also called a continuous phase transition, and appears to a uniform change across the material – imagine a block of ice instantly becoming water, for example.

The first-order phase changes

The first-order phase changes are the ones we’re all familiar with. There are a whole lot of other types of phase change, so have fun reading up on them some time.

Right. So what does all of this have to do with a star?

All of this is a long walk to the answer I originally gave my son, when he asked me why the sun didn’t melt. “The sun can’t melt,” I told him. “Melting is when a solid turns into a liquid, and the sun is made of gas and plasma. It’s way hotter than melting.” Which is more or less true, and also led to the next question he asked me. But we’ll handle that tomorrow.

What is a star?

I’ll be honest here. I thought the International Astronomical Union would have a formal definition of a star, much like they do for planet and dwarf planet and the like. But, if they do, I couldn’t find it. So, in brief, a star is “a luminous sphere of plasma held together by its own gravity”. It can’t melt, because “melt” is not a phase transition available to plasma. Anything in it that could have melted has already melted, then vaporized, then ionized around 4.6 billion years ago.

Is It Still Night?

This question came up in early January. I wake up early most days, because the shift I work runs 5 am to 1:30 pm Monday through Friday, so “sleeping in” has become “sleeping to 6 am”. As a result, I’m sitting out in the living room when my son comes staggering out at 7 am, wearing his flannel pyjamas and clutching his favorite fleece blanket and clearly not quite awake. He flops down on the couch next to me, rests his head on my leg, and glances at the sliding glass doors. “Is it still night?” he asks, talking through a jaw-cracking yawn.

“No,” I tell him. “It’s seven in the morning.”

“But the sun’s not up!” he manages.

Which, if you think about it, makes perfect sense. Shouldn’t “night” be when the sun isn’t visible, and “day” be when it is visible?

What is night?

The first three definitions of “night” are as follows:

  1. the period of darkness between sunset and sunrise.
  2. the beginning of this period; nightfall.
  3. the darkness of night; the dark.

Interestingly enough, there is also a legal definition of night found in Title 14 of the Code of Federal Regulations, Part 1, Section 1.1: “Night means the time between the end of evening civil twilight and the beginning of morning civil twilight, as published in the Air Almanac, converted to local time”.

It turns out that there are three different types of twilight: civil twilight, nautical twilight, and astronomical twilight. Which one you use depends on what you are trying to achieve.

Civil twilight is defined to begin in the morning, and to end in the evening when the center of the Sun is geometrically 6 degrees below the horizon. This is the limit at which twilight illumination is sufficient, under good weather conditions, for terrestrial objects to be clearly distinguished; at the beginning of morning civil twilight, or end of evening civil twilight, the horizon is clearly defined and the brightest stars are visible under good atmospheric conditions in the absence of moonlight or other illumination. In the morning before the beginning of civil twilight and in the evening after the end of civil twilight, artificial illumination is normally required to carry on ordinary outdoor activities.

Nautical twilight is defined to begin in the morning, and to end in the evening, when the center of the sun is geometrically 12 degrees below the horizon. At the beginning or end of nautical twilight, under good atmospheric conditions and in the absence of other illumination, general outlines of ground objects may be distinguishable, but detailed outdoor operations are not possible. During nautical twilight the illumination level is such that the horizon is still visible even on a Moonless night allowing mariners to take reliable star sights for navigational purposes, hence the name.

Astronomical twilight is defined to begin in the morning, and to end in the evening when the center of the Sun is geometrically 18 degrees below the horizon. Before the beginning of astronomical twilight in the morning and after the end of astronomical twilight in the evening, scattered light from the Sun is less than that from starlight and other natural sources. For a considerable interval after the beginning of morning twilight and before the end of evening twilight, sky illumination is so faint that it is practically imperceptible.vening twilight, sky illumination from the Sun is so faint that it is practically imperceptible.

That’s the “conventional” definition. The technical definition is similar, but involves more geometry:

Twilight. There are three kinds of twilight defined: civil twilight, nautical twilight, and astronomical twilight. For computational purposes, civil twilight begins before sunrise and ends after sunset when the geometric zenith distance of the center of the Sun is 96 degrees – 6 degrees below a horizontal plane. The corresponding solar zenith distances for nautical and astronomical twilight are 102 and 108 degrees, respectively. That is, at the dark limit of nautical twilight, the center of the Sun is geometrically 12 degrees below a horizontal plane; and at the dark limit of astronomical twilight, the center of the Sun is geometrically 18 degrees below a horizontal plane.

Sunrise and Sunset

The United States Naval Observatory also defines sunrise and sunset: “Sunrise and sunset conventionally refer to the times when the upper edge of the disk of the Sun is on the horizon. Atmospheric conditions are assumed to be average, and the location is in a level region on the Earth’s surface.” They also provide a technical definition:

Sunrise and sunset. For computational purposes, sunrise or sunset is defined to occur when the geometric zenith distance of center of the Sun is 90.8333 degrees. That is, the center of the Sun is geometrically 50 arcminutes below a horizontal plane. For an observer at sea level with a level, unobstructed horizon, under average atmospheric conditions, the upper limb of the Sun will then appear to be tangent to the horizon. The 50-arcminute geometric depression of the Sun’s center used for the computations is obtained by adding the average apparent radius of the Sun (16 arcminutes) to the average amount of atmospheric refraction at the horizon (34 arcminutes).

So, is it still night?

Assuming you’re using civil twilight, dawn twilight begins when the center of the Sun is 6 degrees below the horizon and ends when the center of the Sun is 0.8333 degrees below the horizon. How long it takes to move from night through twilight to day depends on your latitude and the time of year. But ultimately, until the sun rises, it is still night.

Interestingly enough, having checked a sunrise and sunset table for Cincinnati, I was wrong.  It was 7 am, and I said it was daytime and the sun was up.  It wasn’t.  The earliest the sun rose in Cincinnati in January 2016 was 7:46 am, so it was actually twilight.