If black holes are infinitely tiny, how come we talk about them as having a size?

Given some of the popular literature depicting the Milky Way’s black hole as being “massive”, how does that square with the concept of a singularity being an extremely dense point in space? Is it a reference to the size of the aura around the singularity or the projected size of the Schwartzschild radius?
This computer-simulated image shows a supermassive black hole at the core of a galaxy. The black region in the center represents the black hole’s event horizon, where no light can escape the massive object’s gravitational grip. Image credit:    NASA, ESA, and D. Coe, J. Anderson, and R. van der Marel (STScI)

This computer-simulated image shows a supermassive black hole at the core of a galaxy. The black region in the center represents the black hole’s event horizon, where no light can escape the massive object’s gravitational grip. Image credit: NASA, ESA, and D. Coe, J. Anderson, and R. van der Marel (STScI)

The Milky Way’s black hole isn’t just referred to as “massive” - it’s “supermassive”! But an excellent question nonetheless, as this is a prime example of astronomers using different units interchangeably in a way that can be a bit opaque.

You’re absolutely correct that at the crux of every black hole is an entity called a singularity, which is something of infinite density - a huge amount of mass piled into functionally zero space. If you take the standard method of finding a density, which is “amount of mass, divided by the space it takes up”, this will guide us well for most objects on Earth, but breaks when it comes to singularities. A pound of feathers may weigh the same as a pound of lead, but the density is definitely higher for the pound of lead. Black hole singularities ask us to divide a very large number (its mass) by zero. Dividing by zero will break your calculator, but formally implies an infinite density.

There is a region around the singularity itself which is strongly distorted by the presence of a large amount of mass nearby. Where this distortion is the strongest, space is so warped that in order to escape, you would have to travel faster than the speed of light - an impossible task. Often, this impossible-to-escape region is bundled together with the impossibly dense singularity and referred to broadly as “the black hole”. The boundary of this region - where if you go exactly the speed of light, you go from being not being able to escape, to escaping - is called the Schwartzschild radius. (This is also the boundary known as the event horizon. These two terms are often used interchangeably.)

This computer-simulated image shows gas from a star that is ripped apart by tidal forces as it falls into a black hole. Some of the gas also is being ejected at high speeds into space. Image credit: Image Credit:    NASA, S. Gezari (The Johns Hopkins University), and J. Guillochon (University of California, Santa Cruz)

This computer-simulated image shows gas from a star that is ripped apart by tidal forces as it falls into a black hole. Some of the gas also is being ejected at high speeds into space. Image credit: Image Credit: NASA, S. Gezari (The Johns Hopkins University), and J. Guillochon (University of California, Santa Cruz)

If you're well beyond this radius, the mass of the black hole mostly behaves like any other mass, regardless of its density, since you’re now far enough away that the physical size of the object doesn’t really matter. However, this radius changes depending on how much mass is packed inside the singularity. The more mass packed in there, the larger the escape-is-impossible meet-your-gravitational-doom region surrounding the singularity is. So to classify black holes, we typically do this by their mass, but mass also controls how big the black hole region is. Classifying by mass also functionally classifies by physical size.

Our broad schema is stellar mass black holes, intermediate mass black holes, and supermassive black holes. This also goes in order from physically smallest to physically largest. Stellar mass black holes tend to be only a few kilometers across- an eight solar mass black hole would be 48 km across, or about 30 miles. That’s driveable, as long as you’re on Earth and not near a black hole. Supermassive black holes, by contrast, are much larger. The one in the core of the Milky Way, if we use its current mass estimate of 4.1 million times more massive than the Sun, is 1.8 au in diameter. (If you placed it where the Sun is, that means it would extend ~90% of the way to the Earth’s orbit. Not...ideal for the Earth.)

So the black hole at the center of the Milky Way, at its very core, is indeed a volumeless, infinitely dense point. But the inescapable region surrounding it is sizeable - measurable on the scale of the solar system.


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How realistic is it to have spacecraft brightly illuminated when journeying the solar system?

I’m watching a show on Netflix called Nightflyers and it got me thinking. Every time I watch a show about space travel, they all depict the space crafts cast in darkness; they’re lit, but its dark. So the Moon orbits the Earth, hence we have night and day every 24 hours... but if you’re a craft in space, flying above Earth, and not in the path of the Moon’s orbit, (or perhaps unaffected completely by it as you are no longer on Earth and stuck on its plane) wouldn’t the craft be constantly bombarded with the sun’s rays? (if not disintegrated from the heat all together?) I mean, if you climb a mountain or go snowboarding, even in the most cold places, you can get sunburn as you’re more close to the sun, so I would imagine spacecraft being extremely hot all the time? Can you please help me understand (other than setting a tone, or ambience) how you are affected by light/shade once you are in the solar system? Thanks SO much!
This image from NASA's Cassini spacecraft shows three moons -- Titan, Mimas,  and Rhea. Titan, the largest moon shown here, appear fuzzy because we only see its cloud layers.    Image credit: NASA/JPL-Caltech/Space Science Institute   

This image from NASA's Cassini spacecraft shows three moons -- Titan, Mimas,  and Rhea. Titan, the largest moon shown here, appear fuzzy because we only see its cloud layers. Image credit: NASA/JPL-Caltech/Space Science Institute 

This is a great question, but before we get to the meat of your query, I want to clear up two misconceptions that are present in the question itself. 

The first is that the Moon has something to do with the day/night cycle. Days and nights occur because the Earth is spinning rapidly on its own axis. The Sun, which is relatively stationary with respect to the Earth on the timeframes of a few days, continues to shine from the same point. As the part of the Earth that you or I live on rotates to face towards or away from the Sun, we get day and night respectively. The Moon orbits much, much slower around the Earth - approximately once every month. The Moon can occasionally cast a shadow onto the Earth, but that’s a rare event we know as a solar eclipse. 

The second is why you sunburn at altitude. You absolutely are more prone to sunburns at higher altitudes, but it’s not because you’re significantly closer to the Sun. The Sun is 93 million miles away - getting a single mile or two closer isn’t going to make a significant change to the amount of sunlight that your skin’s getting. What happens instead is that you’re rising above some of the protective layer of our atmosphere, which allows more ultraviolet radiation to reach you. This UV radiation is what triggers a sunburn, and the more atmosphere above you, the more protected you are. If you’re on a snowy mountain, you have the additional complication of being able to get sunburned in really strange places, like the underside of your earlobes and the bottom of your chin, because of the reflected light off of the snow.

This image of a crescent Jupiter and the iconic Great Red Spot was  created by a citizen scientist (Roman Tkachenko) using data from Juno's JunoCam instrument.    Image credit: NASA/JPL-Caltech/SwRI/MSSS/Roman Tkachenko   

This image of a crescent Jupiter and the iconic Great Red Spot was  created by a citizen scientist (Roman Tkachenko) using data from Juno's JunoCam instrument. Image credit: NASA/JPL-Caltech/SwRI/MSSS/Roman Tkachenko 

With those two points addressed, your question about lighting in space is an excellent one. There’s a couple things to think about with lighting, so let’s begin with a spacecraft which is near the Earth. If you are in a position where nothing is blocking the sunlight coming your way, you would be constantly bombarded by the Sun’s rays, exactly as you suspect. However, this is an extremely harsh lighting system - with no atmosphere in space to diffuse the light a little, spacecraft are in pure sunlight or deepest shade. If a spacecraft is moving around the Sun, that means that the sunward facing side of the spacecraft would be illuminated, and the other half of your spacecraft would be in shadow - triggering a pretty intensive temperature gradient between the two sides. As a point of reference, the temperature on the surface of the Moon swings between 224F (106C)  and negative 298F (-183C) when the surface is illuminated versus when it is in shadow. 

This temperature cycling causes stress on most materials you could build a spacecraft out of, and is a challenge we face already as a moderately spacefaring species. The International Space Station, which orbits around the Earth, alternates between spending 45 minutes in the shadow of the Earth and 45 minutes in direct sunlight. Without intensive, intensive insulation, our astronauts would alternate between freezing to death and boiling to death. We have to manage this same situation on a smaller scale for space suits; in the sunlight, your suit has to keep you cool and protect your eyes from glare. In the shadows, it must keep you warm.

These considerations will only get worse as you get closer to the Sun, or really around any star. As we proceed inwards, closer to the sun, the sunlight gets more intense, and the amount of work you’d need to do to stay cool would increase. The cool side of your craft wouldn’t get any colder, but the temperature stress would get more severe between the sun and shaded sides of your craft, so your insulation would have to get much better.  This intensity doesn’t change linearly though - if you got twice as close to the star, the sunlight won’t be twice as intense. It will be four times as intense. 

This works just as well in the other direction - go twice as far out in the solar system, and your sunlight will drop off by a factor of four. Go four times as far, and you’re dealing with light intensity 16 times fainter than you have at the distance of the Earth. However, the Sun is very bright. Jupiter is 5.2 au - and Neptune at 30 au. At 5.2 au, you’re dealing with sunlight 27 times fainter than what we receive on Earth. It’s still going to be the brightest thing in the sky. Neptune is much further, but even at 900 times fainter than the Sun appears from an Earth distance away, it still hasn’t faded to anywhere near the relative faintness of the full moon in the sky, and you can do a lot in the light of a full moon, visibility wise. 

Crescent Neptune and Triton.    Image credit: Voyager 2, NASA

Crescent Neptune and Triton. Image credit: Voyager 2, NASA

The way that astronomers measure brightness is with a counterintuitive system called a magnitude, where 1 magnitude is about a factor of 2.5 in brightness. Every magnitude is multiplicative, so five magnitudes is a difference in brightness of a factor of 100. A difference of ten magnitudes is a factor of 10,000 in brightness. At Jupiter’s distance, then, the Sun will appear about 3.6 magnitudes fainter than it does from the Earth. At Neptune’s distance, it’s something like 7.5 magnitudes fainter. The brightest star in the night sky, Sirius, is 25 magnitudes fainter than the Sun, so even at the distance of Neptune, the Sun will appear more than 10 million times brighter than Sirius appears on Earth. The full Moon, which I mentioned earlier, is fourteen magnitudes fainter than the Sun, so the Sun would be shining on Neptune about 390 times more intensely than the full moon. 

If your fictional craft is within the bounds of a solar system then, I’d say having the craft be brightly illuminated on one side is pretty reasonable. If you’re going beyond that, though, you’d start to descend into full darkness. You’d have to be very far away from our star before the Sun sank to the brightness of Sirius. In fact, you’d need to be almost 1.5 light years away from our star. The spaces within the stars, which is the majority of the Milky Way Galaxy, are going to be very dark. In those places, the only bright lights will be the ones you bring with you. You probably would want to have a few spotlights around, if any of the crew ever has to go outside for any kind of repair operations, but it wouldn’t have the same aesthetics as the harshly lit side of a spacecraft that many shows like to go for. 


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Is the far side of the Moon dark?

This picture of the Earth and Moon in a single frame was taken by the Galileo spacecraft from about 3.9 million miles away. Antarctica is visible through clouds (bottom). The Moon's far side is seen.  Image credit: NASA

This picture of the Earth and Moon in a single frame was taken by the Galileo spacecraft from about 3.9 million miles away. Antarctica is visible through clouds (bottom). The Moon's far side is seen. Image credit: NASA

Only some of the time! With the exception of the times when the Moon wanders into the shadow of the Earth, the Moon spends its journey around the Earth with half its surface in sunlight, and half its surface in darkness. The far side is harder to watch directly, though, because all of us humans are on the surface of the Earth, which only ever sees the near side. We can observe the far side thanks to the technological advancements that come with sending spacecraft out beyond the Moon, but few human eyeballs have seen the far side of the Moon directly.

Even without going there, we can figure out what should be happening on the far side of the Moon by looking at what isn’t happening on the near side of the Moon. If half the sphere of the Moon is illuminated, and we here on Earth are looking at a full Moon, then the far side of the Moon must be dark. But a full Moon doesn’t last very long- the next night the Moon will begin to look less circular in the sky, until a few days later, you’ll definitely be able to tell that the surface of the Moon facing us is not entirely illuminated.

The fully illuminated far side of the Moon, as seen by the DSCOVR spacecraft's EPIC camera. From the Earth, this would be a New Moon. Image credit: NASA

The fully illuminated far side of the Moon, as seen by the DSCOVR spacecraft's EPIC camera. From the Earth, this would be a New Moon. Image credit: NASA

The rest of that sunlight isn’t missing; it’s illuminating the side of the Moon that’s not facing us. As the month progresses, more and more of the far side of the Moon will be in sunlight, and less and and less of that sunlight will be visible to us on Earth. When we on Earth see a thin crescent Moon, the far side of the Moon is almost totally illuminated.

There are some permanently dark places on the Moon, but the far side of the Moon isn’t where you find them. They’re near the poles of the Moon - craters that are so deep, and the sunlight that reaches them is at such a shallow angle, that the light from our Sun only ever skims the surfaces of them. These are interesting places because they are so dark and cold - they’re one of the places that water seems to exist on the surface of the Moon.

An animation of the phases of the Moon. Libration, the minor wobble of the Moon that lets us see slightly more than 50% of its surface is also apparent. Image credit: public domain

An animation of the phases of the Moon. Libration, the minor wobble of the Moon that lets us see slightly more than 50% of its surface is also apparent. Image credit: public domain

With the exception of these deeply shadowed craters, the rest of the surface of the Moon spends about half its time in the sun, and half in the shade. What’s fun is that these periods of sun and shade each last about two weeks.

This is easiest to think about with the near side of the Moon; imagine some point (you can pick your favorite) on the surface of the Moon. As an example, let’s pick the very center of the near side. When the Moon is dark from our perspective, so is our test point in the middle of the near side. As the Moon progresses through crescent phases, our point in the middle is still dark! That part of the Moon is still in its nighttime period. When half the Moon is illuminated, our point on the Moon is dealing with a sunrise, as it’s right on the boundaries of the daytime and nighttime. From there, the gibbous phase, the full Moon, and right onwards through to the next quarter (where the other half is lit), our central point of the Moon stays in sunlight. If we ever have a human outpost on the Moon, this two weeks of daylight followed by two weeks of night will be something to contend with - though I’m sure folks who have lived in the arctic or antarctic (where night can last several months in winter) can give our explorers some pointers.


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When we talk about the Universe's first second, what do we really mean?

In writings about the Big Bang, there are discussions of what happened in the first picosecond, billionth of a picosecond, etc., etc. My question is: what is the measure of time used by the writer? Our time as we experience here on Earth? The instantaneous time passage there, which would be influenced by the infinite concentration of mass and energy (a singularity?)? What is the time scale?
This illustration summarises the almost 14-billion-year long history of our Universe. Credit:  ESA – C. Carreau  

This illustration summarises the almost 14-billion-year long history of our Universe. Credit: ESA – C. Carreau 

This is a really fun question, because the answer is that these time points you’re seeing are for time as we experience it here on Earth, where we’re trying to use an objective ruler of time to describe how rapidly things were changing during those early moments of our Universe. All measurements of time are based on what we use here on Earth, where we humans first developed our timekeeping methods. The second is now a unit of measure used for all sorts of things, though pretty rarely in extragalactic astronomy (with a few exciting exceptions like events that trigger gravitational waves) because the distances involved often mean things happen on billion year timescales. 

But when we’re talking about the very beginning times our Universe went through, a lot of things did happen in the first second - the Universe underwent a lot of dramatic changes in that first second. It went from a soup of energy to filled with protons and neutrons in that time - a dramatic change! And when we say this, we really do mean the second that you could watch tick past on a watch. This second comes from taking the speed of our Earth’s rotation, and dividing it into twenty four hours, dividing each hour into sixty minutes, and each minute into sixty seconds. It’s that second, 1/86,400th of an Earth-spin, that we use to describe the initial changes of our Universe.

It’s fun to think that a fluke of angular momentum that gave us (approximately) a 24 hour day also gave us a useful metric for describing the early state of the Universe in precisely the units that we do. 

As time has wound on, we humans have sought to make our units of measure ever more precise. To do this, we often wind up redefining our units in terms of something more fundamental than where we had begun. The meter was redefined to be the distance that light travels in 1/299,792,458th of a second instead of “one ten-millionth of the distance from the equator to the North Pole”, and the kilogram was recently redefined to be a function of Planck’s constant, instead of a very specific, carefully guarded, lump of metal in a vault in Paris. The second has also undergone this transformation. 

Bell jar display of prototype kilogram replica,  public domain via National Institute of Standards and Technology  

Bell jar display of prototype kilogram replica, public domain via National Institute of Standards and Technology 

As we measured the Earth’s rotation to higher and higher precision, we encountered the need for leap seconds to account for the fact that our Earth’s rotation is intrinsically slowing by a tiny, but measurable amount.  Instead of using the Earth’s rotation speed, then, a more fundamental, reliably measurable feature of our Universe was adopted as the official definition of a second - the length of time it takes a cesium atom to vibrate between two hyperfine states 9,192,631,770 times. While this may seem like a much more complex unit of time, it’s actually a better definition in that anyone, anywhere in the universe, should be able to measure this unit of time consistently. 

During this redefinition of the second, the length of a second wasn’t changed, but now we have a more persistent method of measuring it. So that first nanosecond (10^-9) of the Universe is the same length of time it takes a cesium atom – in a vacuum, at absolute zero – to vibrate 9 times.


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Is there lightning on Mars?

Is there lightning on Mars? Would lightning strikes endanger astronauts on Mars? Would static electricity be a factor to consider on Mars?
An astronaut orbiting over Bolivia captured a close-up of a lightning flash beneath a thunderhead on January 9, 2011. Image credit:  NASA

An astronaut orbiting over Bolivia captured a close-up of a lightning flash beneath a thunderhead on January 9, 2011. Image credit: NASA

There is lightning on Mars! Or at least, something like lightning occurs on Mars. In 2009, the first detections of lightning strikes on Mars were recorded, confirming something that planetary scientists had suspected already - electricity should arc through the Martian skies.

We knew a fair amount about Mars’ weather patterns even before detecting lightning, from a combination of orbiting spacecraft and our landers on the surface. These outposts have painted a picture of a thin atmosphere frequently tumbled into large dust storms. Mars has huge annual storms which can envelop the entire planet, and other strong storms that pop up irregularly through the year. On top of that, the dust on Mars is extremely fine, so once you begin to swirl it around in a wind, it’s reasonable to guess that the dust particles will start to rub on each other, and as you do that, you’ll start to build up an electric charge.

This static charge does more than just gradually build towards lightning; it’s also part of why the Mars rovers get so dirty. The rovers are dealing with more than just a fine sifting of dust falling out of the atmosphere, which a light breeze might easily remove; that dust is stuck to them like packing peanuts stick to your hands. It takes a stronger breeze - a new storm, or a wandering dust devil - to remove some of that dust, and it’s something that the long-lived Spirit and Opportunity rovers were both able to make use of on a couple of occasions.

A self-portrait taken by NASA's Curiosity rover taken on Sol 2082 (June 15, 2018). A Martian dust storm has reduced sunlight and visibility at the rover's location in Gale Crater. Credit:  NASA/JPL-Caltech/MSSS

A self-portrait taken by NASA's Curiosity rover taken on Sol 2082 (June 15, 2018). A Martian dust storm has reduced sunlight and visibility at the rover's location in Gale Crater. Credit: NASA/JPL-Caltech/MSSS

However, as much as dust devils can help you out, they can also do the opposite, dumping more dust on top of your solar panels, which, for a solar powered craft, will limit the amount of energy you have available to do science with, and eventually drop the craft below the threshold of power it needs to operate. This is the current theory for what happened with both Spirit and Opportunity. The Curiosity rover is less affected by this particular issue since its power comes from radioactive decay, but Curiosity is still fully coated in the fine Martial soil. This dust is actually a concern for human exploration of Mars - it’s going to be hard to fully remove this dust from spacesuits, and breathing in a fine particulate is never good for your lungs.

The lightning itself is actually less likely to be a hazard to astronauts on the surface of Mars than the dust is; for one I would expect any humans on the surface of Mars to take shelter during these bigger storms. Unlike what was presented in The Martian, even the 60 mph winds that can occur during a dust storm wouldn’t feel as powerful as a similar wind on Earth, since the atmosphere is so much thinner. The air simply wouldn’t exert the same pressure against you in the same way. Even on Earth, the likelihood of being struck by lightning is very low, and on Mars the best guess is that the lightning would not really resemble the large bolts of lightning we see here on Earth.

More likely is that this lightning would resemble the arcing jolts of electricity you can create by shuffling along in socks on carpet and then touching a doorknob. In a dark room, you can see the filamentary discharge of electricity between your finger and the doorknob. On Mars, you might expect to see little flickers of electricity arcing between parts of the dust storm, faintly lighting up the night sky. To be a hazard to an astronaut or a rover, you’d have to be very, very unlucky.


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