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Saturday, June 19, 2010

Interstellar Tour


“Earth is mankind's cradle. But nobody stays in the cradle forever.”
Konstantin Tsiolkovsky (1857-1935)

“Reason not the need!”
King Lear

Project Icarus, proposed by the Tau Zero Foundation and the British Interplanetary Society, is a plan to send an unmanned space probe to a nearby star. It is a sequel to the 1978 Project Daedalus, also by the BIS. Although neither project has ever had a chance of being funded any time soon, because of the admittedly “astronomical” cost, it is still fun to speculate on the possibilities, and try to predict how long it will be before these things are feasible. See Ian Crawford’s article, making the case for an interstellar mission.

Any realistic mission to even the closest stars must involve attaining a speed that is a substantial fraction of the speed of light. We will want to get results back within the lifetimes of the people who will design and build and pay for the mission. Chemical propulsion systems, solar sails, ion drives, etc, will never do. So the first order of business is that we need a new propulsion system. But for now, I’m interested in the easier question of choosing a destination, so let’s assume that we have a ship that can attain, let’s say, 10% of the speed of light. We still have to imagine whether our vehicle can accelerate indefinitely at some constant rate, or whether it can thrust for a few hours or days, get up to relativistic speed, and then coast until the engines are needed again. I’m putting that on the back burner, for now. Just imagine that this “minor engineering problem” has somehow been overcome!

The obvious first choice for a destination would be the Centauri System. At 4.37 light years, it is the closest star system. One star, Alpha Centauri, is just a bit bigger and brighter than Sol, our Sun. The second, Beta Centauri, is somewhat smaller and dimmer, and somewhat orange. Alpha and Beta orbit their common center of mass, with a distance (between them) that varies from 11.2 AU to 35.6 AU. In other words, the orbits of both stars fit easily into a space the size of our Solar System. Besides Alpha and Beta, there is also a red dwarf star, Proxima Centauri, so called because it is currently the closest to us, at 4.22 light years. It is not known for sure whether Proxima is gravitationally bound to Alpha and Beta, or whether it is destined to continue on its own trajectory through the galaxy. At any rate, Proxima is so small and distant that it won’t affect the orbits of Alpha and Beta. However, it may be less likely to find stable orbits for planets in an essentially binary system like Centauri than in a single star system. (It used to be thought almost impossible for a planet to have a stable orbit in a binary system. Now that we understand more about resonant orbits, it seems more possible.)

Another popular candidate is Epsilon Eridani, at 10.5 light years. Read Winchell Chung’s blog about it. This is a single star, not too different from Sol, and it is the closest star known to have a planet. Although much younger and more active than Sol, Epsilon Eridani is a little smaller, dimmer and less massive.

About 80% of the nearby stars are red dwarfs. There may even be more red and brown dwarfs near us, that we have not even discovered yet, because they are so hard to detect. (See my previous blog about these small, dim stars.) There is much controversy as to whether life is more likely or less likely to be found on planets orbiting red dwarfs than on planets orbiting other stars. Be that as it may, it is becoming clear that most red dwarf stars - even the smaller, cooler, quieter ones - are capable of very large and unpredictable flares. This would seem to render the vicinity of a red dwarf star hostile to human colonies or passing spaceships. If we’re looking for a good spot for a permanent colony, we should probably concentrate on sun-like stars.

The purpose of a mission like Icarus would be to investigate nearby interstellar space, including one or more nearby stars, and possible planets. We might search for signs of life, or scout possible locations for future colonization. The probe would send pictures and scientific data back to Earth, by radio.

Given a target star or star system, we can either rendezvous or flyby. With a flyby mission, we can basically keep accelerating for the entire journey. This gives us maximum speed when we get there, and also gets us there as quickly as possible. The drawback is that we will go past the target so fast that we won’t be able to observe much.

With a rendezvous mission, the idea is that, when the vehicle gets to the halfway point, it turns around, with thrusters pointed toward the destination, and reverses all the velocity it picked up in the first half of the trip. Then it gets to the destination with low enough speed that it can go into orbit around the target star, and take measurements for years instead of a few minutes. A compromise might be made between rendezvous and flyby, where the vehicle slows down enough to get some good measurements, but not so slow as to prolong the mission unacceptably.

For example, the Pioneer and Voyager missions were flybys. They flew by several planets, taking pictures and measurements, and each eventually flew on their way out of the Solar System. They each made a kind of tour of the Solar System, using gravity assists to climb around from planet to planet. In contrast, the Galileo mission to Jupiter, and the Cassini mission to Saturn, went into orbit around their targets, and were able to send back a large amount of very detailed data.

What I would like to suggest is a kind of tour of nearby interstellar space. Given a sequence of target stars, the vehicle would slow down enough to take some good pictures, but also use the gravity of the star to deflect it toward the next target in the list.

Unfortunately, the stars near us are moving very slowly compared with the substantial fraction of the speed of light that our mission will require. So we won’t get much of a “gravity assist” in the sense of an increase in speed. The propulsion system will have to provide any increase or decrease in speed. However, we can get a change in direction from passing close to a massive object like a star. How much deflection depends on the vehicle’s speed, the mass of the star, and on how close we get. Of course the radius of the star puts a hard lower limit on how close we can get. But since the vehicle is unmanned, we might be able to shield it well enough so that it can pass within maybe 2 or 3 times the star’s radius.

I’m planning to work out the geometry of these interstellar tours. I’ll blog about it, soon. Before that I probably need to write up a blog explain the special relativistic aspects of interstellar missions. I’ve got one half-written, around here somewhere. Stay tuned! And please comment.

Sunday, June 6, 2010

Stealth in Space

“Fixed fortifications are monuments to the stupidity of man.”

General George S. Patton

Stealth has been an important aspect of military campaigns since prehistoric times. Two trends have continued since then. First, military assets have become easier to hide. Second, targets with known position have become easier to destroy.

Weapons have become incredibly accurate and reliable. If your enemy knows where you are, you’re dead.

Populations are especially vulnerable to modern weapons, because they are hard to hide. Hence the era of strategic nuclear warfare. Generally, the term “tactical warfare” refers to the battlefield, or limited theater of war, in which military units try to destroy each other, and “strategic warfare” involves each side using its military to destroy the population and civilian assets of the other. If you think the Cold War was MAD, just wait until you see it in space!

As we have seen with various missile defense programs, defending a fixed position is much more difficult than offense. You have to be able to outspend your enemy at least 100 to 1, to have any chance of defending a population. In space, that factor of 100 may increase to 1000 or more.

Future populations will have to become stealthy, in order to survive. That means no colonies on planets or moons, or anything too massive to be moved out of a predictable orbit. It means living in hollowed-out asteroids, or ships painted black, or ships disguised to look like natural objects. Above all, it means radio silence.

Detecting a threat at a distance of several millions of kilometers would be virtually impossible. To put this in perspective, consider our efforts at detecting near-Earth asteroids. A similar object large enough to carry thousands of H-bombs would go undetected until it entered our atmosphere. As another example, consider Voyager 1. It’s not even trying to be stealthy – in fact, it periodically sends out radio signals to Earth. But trying to find it, if you didn’t know where to look, would be very difficult with a radio telescope, and impossible with visual or infrared. Now imagine it is coming toward us at 170 km/sec, instead of away from us at 17 km/sec, and imagine that instead of 722 kg of scientific instruments, it carries 7000 kg of H-bombs. And it’s radio silent. We would never know what hit us!

A military ship, or any spaceship, would be more visible in the optical and infrared, when thrusting. More visible from the stern (more precisely, the direction of thrust) than the bow. The visibility depends on the type of engine used, but as long as it isn’t emitting a lot of radio energy, it won’t be detectable at great distance. As an example to illustrate this, recall that the volcanic activity on Io, one of Jupiter’s moons, was not discovered until Voyager 1 flew by it in March, 1979. I don’t know if they have been detected since then by any Earth-based or LEO-based optical or infrared telescopes, but the point is that they are very difficult to detect from the typical Earth-Jupiter distance. And they are very hot, and much bigger than any rocket engine yet proposed.

Radar may not play as important a role in space warfare as it has in Earth warfare. Radar returns are attenuated by a factor of 1/r^4. In other words, it takes 16 times as much power to detect something twice as far away. So you quickly reach a distance beyond which you can’t detect something as large as a ship. For modern military radars, that maximum range is classified, but a ballpark figure might be a few hundred, or maybe a thousand, kilometers. You might imagine a much more powerful radar, with 16 times the power, able to reach out to 2000 km, or with 256 times the power, at 4000 km. You can see that you are going to need an “astronomical” amout of power to get out to a few million km. That’s why radar is used in astronomy only for near Earth objects, or by sensors that get close to their targets.

If warfare becomes large-scale enough that light delay becomes a factor, then radar pays another penalty, for relying on a there-and-back light time.

From the stealth point of view, the bad thing about radio waves is that they travel great distances, through atmospheres and interplanetary dust, needing very little power. But on the positive side, they are hard to pin down, in terms of direction. It's difficult to tell exactly where a radio source is located. There are many ways around this, involving advanced antenna design, multiple sensors, etc, but the fundamental difficulty remains. The offense will probably have to send a missile in the general direction of a radio source, and then use radar or optical/infrared sensors mounted on the missile, when it gets close.

A population center might also deploy decoys (imagine a decoy city in space!) or other countermeasures. But the best policy is to turn off any source of radio. And hide under a very dark or camoflaged covering.

Even though radar won’t be as important in space warfare (at least at long range), the passive detection of radio signals will be crucial. The military will use radio telescopes to identify targets, and populations must avoid any radio emissions. Developing a civilization without radio emissions will be difficult, but the alternative is extinction.

Wednesday, May 19, 2010

Planets and Things

I’m a guy who likes to make lists and put things into categories. Give me a bucket of wheat cents and I’ll be occupied for hours. Give me a solar system with millions of objects, in a wide variety of shapes and sizes, and I’m ready to get to work. Give me a universe with strange and unexpected things being discovered or theorized every day, and I almost don’t know where to begin!

Classification is important because we need a common language. How can we have a meaningful conversation about planets if your definition of a planet is different from mine? The same goes for stars, dwarf planets, brown dwarfs, black holes, and so on.

The IAU has made attempts recently to clarify this situation. The most newsworthy outcome has been the reclassification of Pluto from planet to dwarf planet. Ceres has also been promoted from largest asteroid to dwarf planet. A few of the larger Kuiper Belt objects have been designated as dwarf planets as well. However, this classification only applies to our solar system. With 453 extrasolar planets discovered, some of them not much bigger than Earth, we are very soon going to need a classification system that applies to any solar system, or more generally, to any objects in the universe.

Many astronomers want to classify things according to the way they formed. An object that forms by accretion of a dust cloud would be different than one formed by collision of two large objects. A stellar remnant (what’s left of a star after its thermonuclear reactions have stopped) would be different from a brown dwarf of the same mass. The trouble with this is that it may be difficult to determine how an object formed. Our classification system should make clear distinctions based on observable properties.

Others would like to classify things in terms of their orbits. A planet, for example, must be orbiting a star. Under this definition, a planet that is gravitationally ejected from a solar system is not a planet any more. But it’s still the same object!

There is even a requirement that a planet must have cleared the neighborhood of its orbit of any debris. This would be really hard to verify without a very thorough survey.

Some rely on the shape of an object to determine its classification. Anything bigger than about 400 km in diameter gets pulled into a roughly spherical shape by its own gravity. These are sometimes called worlds. Objects less than 200 km tend to be much more irregular. Between 200 and 400 km we find a wide variety; some very spherical, some very irregular. The shape is generally hard to determine, until you get close.

What observable properties are easiest to detect? First would be thermonuclear reactions. That’s one point most astronomers agree on. A star is an object that is emitting radiation due to thermonuclear reactions. It’s thought that an object with more than about 13 times Jupiter’s mass will have enough pressure at its core to sustain the reaction that fuses hydrogen into deuterium. That factor of 13 depends on a lot of things, like chemical composition. In practice, it’s usually pretty easy to tell a star from a non-star. Although there are borderline cases!

Another property that is usually one of the first to be observed is mass. We can determine the mass of an object by the orbital characteristics of anything near it. Properties like size, shape, chemical composition and solidity of surface are harder to determine. You have to get close.

Also, the word dwarf is overused. A dwarf planet is smaller than a planet, but a brown dwarf is a big planet. Red dwarfs and white dwarfs are small stars. There are even dwarf galaxies!

Here’s what I humbly suggest. We classify objects and orbits separately. Any object can be in any orbit. Never mind how it got that way. Objects should be classified by thermonuclear reaction, then mass. A planet is just a non-thermonuclear object with mass greater than, let’s say, one-half Mercury. Wouldn’t that clarify the discussion?
This doesn’t apply to exotic objects like black holes. We can cross that wormhole when we come to it. And we will probably need something besides mass when we want to look at interplanetary or interstellar dust particles of various sizes. We can expect to find all imaginable shapes and sizes of things out there, and even some unimaginable!

Sunday, May 9, 2010

Name Change

I changed the name from Near Space to Nearby Space, because the former has come to mean Earth's upper atmosphere and stratosphere, the realm of ballonists and amateur rocket enthusiasts. The url is the same, though.

Tuesday, May 4, 2010

Interplanetary Golf?

Try this some weekend. Go to the highest peak on a nonrotating, nearly spherical moon or small body. Hit a golf ball and watch it fly. If you don’t hit it very hard, it will follow a nearly parabolic path, until it hits the surface.

The path isn’t really parabolic; it’s actually part of an ellipse, which intersects the surface at two points: let’s call them launch and impact. A parabola is what you would get if the gravitational field of the moon was the same strength and in the same direction everywhere. That’s approximately true in the small scale, but on a larger scale, the strength of gravity decreases with increasing altitude, and the direction changes because it always points toward the center.

The trajectory that the golf ball will follow depends on the speed and direction it has when it leaves the launch point. On Earth, the world record fastest golf ball, hit by Jason Zuback, had a launch speed of 91.2 m/sec. If you’re not a pro golfer, or if you’re wearing a cumbersome space suit, you might be lucky to manage 50 m/sec.

During the Apollo 14 mission, astronaut Alan Shepard actually hit a couple of golf balls, on the Moon. He used a six-iron, and had to swing with one hand because of the space suit. It’s not known how far the golf balls traveled, but Shepard said the second one went “mile and miles and miles.” That’s an exaggeration; encumbered as he was, Shepard probably had a shot that would have gone no more than 200 m on Earth, so 1200 m on the Moon. Still, it must qualify as the longest golf shot in history, on level ground.

If you hit your golf ball horizontally, at just the right speed, it will go into a circular orbit, just above the surface of the moon. This circular orbit is just a special case of an elliptical orbit. The speed required for this is called the circular orbit speed, or v_circ. It depends on the mass of the moon, and the distance from the center. Since we are launching from the highest point on an almost spherical body, the distance from the center is just slightly more than the radius.

Phoebe, one of Saturn’s moons, has dimensions 230 x 220 x 210 km, and it is one of the smaller nearly spherical objects in the Solar System. Maybe it formed out of molten rock from some catastrophic event, and has escaped being smashed up too badly since then. The circular orbit speed at the surface of Phoebe is about 70 m/sec. Standing on a mountain top on Phoebe, a very strong golfer could put a golf ball into orbit.

Mimas, another of Saturn’s moons, has dimensions 414.8 x 394.4 x 381.4 km, so it qualifies as nearly spherical. The circular orbit speed at the surface of Mimas is 112 m/sec. A golf ball would not have enough speed to go into a circular orbit, but it could easily travel 100 km or more. An 18-hole golf course on Mimas would have to cover pretty much the entire surface: about half a million square kilometers. That’s a big golf course!

If you hit your golf ball horizontally, with a little more than circular orbit speed, it will go into an elliptical orbit, which has the launch point as its perigee, or point with lowest altitude. So its launch and impact point are the same.

Now, if you hit it with a lot more than circular orbit speed, the ball will follow a hyperbolic trajectory, and eventually escape from the moon altogether. Specifically, the launch speed must be greater than the escape speed, v_esc, which is equal to v_circ, multiplied by the square root of 2. So it’s about 1.4 times as fast as v_circ.

If the launch speed is v_launch, then after a long time, the golf ball will be moving in essentially a straight line, with speed v_launch – v_esc leftover, and essentially free of the moon’s gravitational influence. It has given up v_esc of its speed to get away from the moon.

The borderline case between elliptical orbits, with v_launch < v_esc, and hyperbolic orbits, with v_launch > v_esc, is the parabolic case, with v_launch = v_esc. The speed has to be just right. So there are parabolic orbits around spherical bodies, just as there are in uniform gravitational fields. However, in this case, as the golf ball gets farther away, it slows down instead of speeding up, as it gives up all its speed to get away.

Of course, no body in our solar system is perfectly spherical, and the oblateness and lumpiness of bodies make orbits around them more complicated than simple ellipses and hyperbolas. Still, the above description is a useful approximation, sufficiently far above a sufficiently spherical body.

Also, none of the bodies in our solar system are perfectly nonrotating. A golfer has to take the Coriolis Effect into account. An easier way is to compute the velocity of the launch point relative to a nonrotating coordinate system, and use vector addition to add this to the launch velocity, relative to the ground. This becomes very complicated, if the body is highly irregular, because it may not simply spin on an axis. It may have a more complex spin state, like a precessing football, or worse!

The asteroid Eros, visited by the NEAR mission in 2000, is shaped like a bent potato. Mission planners had to continually revise the orbit around Eros, especially when the spacecraft got close.

Eros is only 34 x 11 x 11 km in size, with escape speed at the surface of about 10 m/sec. This could be expected to vary considerably over the surface, but it is safe to say that any golfer could hit or throw a ball fast enough to escape Eros. It might not be the best place for a golf course – you would lose a lot of golf balls! Besides, most of the surface is covered with a fine powder, pulverized by millions of years of bombardment by particles large and small. Your ball may be embedded in a powder sand trap. That could be a problem if you have to play it where it lies! In fact, in very low gravity, this powder may actually behave somewhat like a fluid. So the sand traps are like water hazards! Here is a very interesting article on this and related topics.

Hyperion, another moon of Saturn, is one of the largest highly irregular bodies in the Solar System, at 360 x 280 x 225 km. Generally speaking, objects with diameter larger than 400 km tend to be pulled into a roughly spherical shape by their own gravity, while objects less than 200 km tend to be very irregular.

The escape speed on the surface of Hyperion varies from 45 to 100 m/sec. A golfer, standing on one of the high points (far away from the center of mass), could hit a ball into orbit around Hyperion, and it just might escape Hyperion and go into Saturn orbit. At one of the low points, where the escape speed is 100 m/sec, even the best golfer would have trouble sending a tee shot into Saturn orbit.

Even though Hyperion is larger than Phoebe, its irregularity and lower density causes lower escape speeds at some points on the surface. This makes sporting events more complicated.

Playing golf from moon to moon would be very challenging. If you tee off from Atlas, one of the inner moons of Saturn, with a pretty impressive 60 m/sec tee shot, then since Atlas has an escape speed of about 6 m/sec, you end up in Saturn orbit, with a speed of 54 m/sec relative to Atlas, having spent only 6 m/sec getting away from Atlas. However, Atlas is moving around Saturn at 16.6 km/sec, over 300 times your speed relative to Atlas. So you have escaped Atlas, but you are travelling in almost exactly the same orbit. Your puny 54 m/sec may not be enough to get you to another moon. Luckily, there are a few other moons pretty close by. But getting out as far as Phoebe doesn’t seem feasible.

If that doesn’t seem cool enough, you might want to venture into Saturn’s rings. Some of the ring “particles” are as big as buildings. You could jump from rock to rock. Or, more precisely, ice chunk to ice chunk. This would be a very dangerous sport! Better stick to a nice game of catch, with your feet anchored so you don’t accidentally step out into space.

If we venture out to 23 million km, near the outer edge of Saturn’s system of moons, we find 3 or 4 small moons. They don’t get close together very often, because their orbits have different inclinations. For example, Ymir is only about 18 km in diameter, with an escape speed of 8.7 m/sec. A strong golfer could hit a ball off Ymir and into Saturn orbit, with 50 m/sec or more to spare. However, even though Ymir is very far from Saturn, it is still moving at over 1 km/sec relative to Saturn (the speed varies because the orbit is not circular), and that is 20 times the golf ball’s speed. So a golfer might be able to reach one of the other outer moons, if the timing is just right, but targets that never get close to Ymir’s orbit would be out of range. It would be a very tricky shot!

A high power rifle bullet, at around 1 km/sec, would be able to hit pretty much anything in the Saturn system, if fired from one of the outermost moons. Anyone in the inner Saturn system would need a lot more than a 1 km/sec gun if they want to shoot back. If you’re a military planner, you want to occupy the high ground.

A few of the outer moons of Uranus and Neptune slow down to 400 m/sec or less. So escaping from Uranus or Neptune, even from the orbit of an outer moon, would require around 600 m/sec. That’s well beyond the capability of any golfer. So I’m afraid interplanetary golf is not happening. But there is always the Kuiper Belt.


Oil on Earth

If only I were King of the US, and I had all these offshore oil deposits, I might consider just leaving them where they are, for future generations. Oil will be more valuable, and drilling technology will be better, and safer. Just wait until the Arab World has sold off all of its oil. Our grandchildren might have something to thank us for. We ruined the atmosphere and the oceans, but at least we didn't use up all the oil (and coal) as fast as we could dig it up.

Saturday, May 1, 2010

Red Dwarf Stars

“It may be that the old astrologers had the truth exactly reversed, when they believed that the stars controlled the destinies of men. The time may come when men control the destinies of stars.”

Arthur C. Clarke (First on the Moon, 1970)

As you get to know your stellar neighborhood, you will find that more than two-thirds of the nearby stars are red dwarfs. These stars are much smaller, cooler and dimmer than Sol (our Sun). Because they are so dim, even those nearest to us cannot be seen without a telescope. We might have a slightly better chance of seeing them if we could see in the infrared part of the spectrum, where they emit most of their energy.

Since they are so plentiful, red dwarfs (not dwarves!) and their planetary systems might seem to be good places to look for extraterrestrial life. They might also be promising for colonization. These are the subjects of a lot of debate recently, and there are good arguments to be made on both sides.

Red dwarfs may be small and dim, but they are hardly boring. For one thing, most of them are prone to violent convulsions. These are usually called flares, but they are much bigger, compared to the size of the star, than solar flares. A red dwarf flare can increase its power output fivefold or more, for a period of a few seconds or minutes. This would make life very exciting and dangerous for space travelers who venture too close.

Cool stars, like red dwarfs, burn their nuclear fuel so slowly that they last a very long time – the smaller, the longer. The smaller ones have lifetimes measured in trillions of years. Provided the Universe last that long! They cool gradually as they age, the flare activity settles down, and when they finally run out of fuel, they will turn into black dwarfs. (Sol will go through a red giant stage, then a white dwarf stage, and after many billions of years, it will also end its life as a black dwarf.) There are no black dwarfs yet, though. According to theory, at least. The Universe is not old enough yet to have produced any. Just wait.

Red dwarfs are so common in our immediate vicinity that, assuming our stellar neighborhood is not abnormal, it seems reasonable to extrapolate to the galaxy as a whole. Astronomers think that at least 80% of the stars in our Milky Way galaxy are red dwarfs. Even with powerful telescopes, we can usually only detect red dwarfs within a few hundred light years. Some of the nearest ones were only discovered in the mid 20th century, and there are undoubtedly many more, very near, but very dim, lurking in our stellar neighborhood. The number of star systems known to be within 33 light years has increased by 18% since 2000. That’s not because of newly discovered stars. Most of these stars were known before, but we didn’t know how close they were.

Whether there may also be an abundance of brown dwarfs – smaller bodies that have less than the 0.08 solar mass needed for sustained nuclear reaction – is more uncertain. They are not actually stars, but they do emit a small amount of infrared radiation. If they exist, that is. But it wouldn’t surprise anybody if it turned out that there were a few dozen (or more!) brown dwarfs closer to Sol than any of the stars. They would be practically invisible, and we would only know about them by their gravitational effects.

It’s pretty safe to say that the closest star to Sol, at a distance of 4.2 light years, is Proxima Centauri, a red dwarf. It is small and dim, even by red dwarf standards! With diameter approximately 200,000 km, it is somewhat bigger than Jupiter (diameter 143,000 km); it is 110 times as massive, and 36 times as dense. At 51 grams per cubic centimeter, it is 4.5 times as dense as lead. Its temperature is around 2,800°C, which is pretty cool for a star.

Like all red dwarfs, Proxima is composed almost entirely of hydrogen. In fact, since many red dwarfs are thought to have been born in the early Universe, when elements heavier than hydrogen were rare, it is somewhat of a mystery why there aren’t more red dwarfs with even lower amounts of heavier elements.

Red dwarfs convey heat from the core, where hydrogen is being converted to helium in a fusion reaction, to the surface by convection, rather than radiation. They are fully convective, like a pot of boiling liquid. They are not massive enough to generate the pressure at the core required to fuse helium into heavier elements, as the larger stars do.

When you start making a small planet, as you put in more mass, the diameter gets larger, and the pressure in the interior increases. When the pressure becomes high enough, the chemical bonds are overcome, and the material compresses. Adding more mass after this actually makes the planet smaller. So there is a maximum diameter, which is about 180,000 km, for a pure hydrogen planet. That’s about 0.13 times the diameter of Sol, or 1.3 times the diameter of Jupiter. So if you keep adding mass, the planet shrinks and heats up, until finally it ignites in a thermonuclear reaction, and starts converting hydrogen into helium. Now it is a star, and its size can increase, because it gets hotter, and because it keeps collecting matter that falls into it.

The next closest stars are Alpha and Beta Centauri, which, along with Proxima, form the Centauri system. Alpha is a Sol-like star, just a little bigger and brighter than Sol, and Beta is a reddish-orange dwarf, a little smaller and dimmer than Sol. They form a close binary pair, and Proxima orbits this pair at such a great distance that no one is really sure whether it is gravitationally bound to the system. In other words, Proxima may continue on a very large elliptical orbit around Alpha and Beta, with a period of roughly half a million years, or it may continue off on its own. At its current speed of 31 km/sec, it is just a bit faster than Earth, at 29.3 – 30.3 km/sec, relative to Sol.

Next in the list of nearest stars, at 6.0 light years, is Barnard’s Star, another red dwarf. It appears to be an old star, perhaps 11 – 12 billion years, more than twice the age of Sol. A little bigger and hotter than Proxima, it will probably only be another 40 billion years or so before its nuclear reaction stops, and it becomes a black dwarf. Although relatively old and quiet, it had a small flare event in 1998, so it has been designated as a flare, or variable star. With a surface temperature of about 3,100°C, it is an average red dwarf.

Barnard’s Star is moving at 142 km/sec, almost 5 times as fast as Proxima, and it will pass within 3.8 light years from Sol in about 10,000 years. Because of its high speed and nearness, Barnard’s Star has the largest proper motion of any star. In other words, its angular position, as seen from our solar system, is changing faster than any other star: 10.3 arcseconds, or 0.00286 degrees, per year. In 200 years, it will have crossed more than the width of the full moon, in angular position.

The next closest star, at 7.78 light years, is Wolf 359, another red dwarf. This one is probably about the same size as Proxima Centauri. It’s named after its discoverer, Max Wolf – not because of any reference to wolves! It is also known as CN Leonis. According to currently used models of stellar evolution, Wolf 359 appears to be a vey young star, somewhere between 100 and 350 million years. On the other hand, it has a slow rotation rate, which we can detect because rotation blurs the spectrum, through the Doppler Effect. This would seem to indicate an older star, since it takes a long time for magnetic effects to slow the rotation. Its radius is 1.6 times Jupiter’s radius, so its volume is about 4 times Jupiter’s volume. But its mass is 90 times Jupiter’s mass, making Wolf 359 about 22.5 times as dense as Jupiter, almost 30 times as dense as liquid water. Its rotation period is at least 67 hours, compared with 10 hours for Jupiter. Coincidentally, it is very close to the ecliptic, which is the plane containing the Earth’s orbit around Sol.

Next in the list, at 8.26 light years, is Lalande 21185. This is a larger red dwarf, with 0.46 times the mass of Sol, and also 0.46 times the radius of Sol. That makes it 10.3 times as dense. That’s much less dense than the smaller red dwarfs. The large size is supported by higher temperature, as indicated by the surface temperature of 3,400°C. Most of the other nearby stars are moving more or less with Sol, in their orbits around the galactic center. They were born in the “thin disk” of the galaxy, and will remain there, along with Sol, for billions of years. But Lalande 21185 is moving in a direction perpendicular to the disk, so it is just passing through our stellar neighborhood.

The brightest star in the sky is Sirius, only 8.6 light years distant. Sirius is actually two stars: Sirius A, which is about twice the mass of Sol, with 25 times the luminosity, and Sirius B, a small white dwarf companion. A whole book could be written on Sirius, but in this article, I want to talk about red dwarfs, so I just mention Sirius in passing.

Next, at 8.73 light years, is a binary system, Luyten 726-8. The two stars in the system are both red dwarfs, both about 0.1 times the mass of Sol, and both about 0.14 times the radius. Both have very low luminosity. They orbit their common center of mass in a highly eccentric orbit, coming as close as 2.1 AU and as far apart as 8.8 AU, with a period of 26.5 years. Luyten 726-8A is not much different than the other red dwarfs we have seen so far, besides being a bit smaller and dimmer. But its companion, Luyten 726-8B, also known as UV Ceti, is a remarkable flare star, exhibiting very violent outbursts of ultraviolet radiation. In 1952, within a period of 20 seconds, its luminosity increased by a factor of 75.

I’ve been talking about distances to stars, and their diameters, speeds, temperatures, etc; as if these are things we can measure. In practice, what we can actually measure very precisely is the angular position, as viewed from Earth. That takes 2 variables to describe – think of latitude and longitude. By making observations over a period of time, we can also determine the rate of change of a star’s angular position, or proper motion, as mentioned above. That’s 2 more variables. Now we have 4 variables that can be determined with very high precision. We can also measure the intensity of light reaching us from a star, in any band of wavelength. Putting this information together gives us the electromagnetic spectrum of all the light coming to us from the star. The spectrum can be determined very precisely, but it can change over time.

Astrometry, which involves determining the positions and motions of astronomical objects, is one of the most important parts of astronomy. As a general rule, distances are more difficult to determine than angles measured from Earth.

Using observations made from widely separated points in Earth’s orbit, the angular position of a star changes with the position of the observation. In other words, we can imagine a very acute triangle with the star at one vertex and the two observing points at the others. If we can work out the geometry of this triangle, then we know the distance to the star. It’s a pretty easy trigonometry problem. However, most stars are moving faster than the Earth moves, relative to Sol. Hence a star may move significantly between observations. The triangle gets a little bent out of shape, and you have to take this into account. This is called the method of parallax. It allows us to determine the distances to nearby stars to within a few percent, or better, for the nearest stars. It only works for objects within a few hundred light years, at most. We have Proxima Centauri pinned down to 4.243 ± 0.002 light years. For more distant objects, other methods must be used. In recent years, parallax measurements made by the satellite Hipparcos have greatly increased the accuracy of our stellar geography. Several ground-based and space-based efforts are under way or planned for the coming decade, which will greatly increase the accuracy of our stellar geography. Astronomers will go to great lengths to determine distances!

The surface temperature of a star can be determined pretty accurately (we think) by its spectrum. Hot stars, as hot as 10,000°C or more, radiate most of their energy at high frequencies, so they look blue. Yellow stars, like Sol, are medium on the temperature scale, around 5,500°C. Red dwarfs are on the cool side, at less than 3,500°C, which is why they appear red. Stars are usually much hotter in their interiors, due to nuclear reactions, but the surface, or photosphere, is where the light that reaches us comes from.

Given the distance and the intensity of all the light coming from a star, we can calculate how much total energy it is putting out in the form of light. That’s called the bolometric luminosity, L. We use a model (a mathematical equation) relating L with the surface temperature and radius. Basically, the model says that L is proportional to the square of the radius and the 4th power of the temperature. Of course, this is only a model, and it could be way off. We don’t have a really good way to test it. But it’s the best we have, so we use it to calculate the radius of a star, given its surface temperature and L. The results are good to within 10% at best.

We also have a model that says L is proportional to the 4th power (technically, it’s the 3.9th power) of its mass. So now we can compute the mass of the star. Again, the model could be way off. However, recent discoveries of planets orbiting red dwarfs give an independent way to measure the mass, using the radius and period of the orbit, so the model can be refined, if needed.

Several of the recently discovered exoplanets (planets orbiting stars other than Sol) are orbiting red dwarfs. That is partly because red dwarfs are so numerous, but also because their nearness to us and their low mass both cause the angular motion of the star, due to the planet’s orbit, as seen from Earth, to be detectable. The motion of the star due to its planet(s) provides the most common means of detecting exoplanets.

Imagine a red dwarf star in our Solar System, in place of Jupiter. It would have a dominating effect on the orbits of the other planets and asteroids, much more than Jupiter does now. Everything would either be ejected from the Solar System, or crash into something, or get captured by the Dwarf and become its moon, or else its orbit would evolve into a resonant one, in which the period is some low order rational multiple of the orbital period of the Dwarf. Because of its size, the Dwarf would be a little brighter than Jupiter, in terms of visible light. It would appear very red. Flare events would be very noticeable from Earth, but not dangerous, because of the distance. The solar wind from Sol would still dominate the electromagnetic environment in most of the Solar System, but the Dwarf would have its own domain, much larger than Jupiter’s. It would be interesting to have two solar winds, with different flavors.

Red dwarfs may not be the best candidates for colonization. They may not be the best places to look for life, for the same reasons. Since they put out so little energy for their mass, a spaceship, or planet, would have to get pretty close, in order to get enough heat. For a planet to have liquid water, it would have to orbit at 0.02 – 0.05 AU, or 1/50th to 1/20th of the average distance from Sol to the Earth. At this distance, the planet’s rotation would be tidally locked to its orbit, so that it would always keep one side facing its dwarf sun, just as the Moon keeps one side facing the Earth. One side would be a lot hotter than the other. There has been some argument lately as to whether this would make conditions unsuitable for life. Also, photosynthesis (as we know it) doesn’t work very well with red or infrared light. But there is a much bigger problem with orbiting so close to a red dwarf: the flares! Even red dwarfs that seem old and tired, like Barnard’s Star, can surprise you. A flare can appear in seconds, scorching any spaceship or colony that had been at a nice, comfortable distance before the flare.

On the other hand, many people are arguing that red dwarfs (actually, planets near red dwarfs) would be the most likely places to look for life. A planet with a strong magnetic field might have enough of a magnetosphere to protect its atmosphere from being blown away by flares. The atmosphere might just be able hold onto oxygen, making it possible for liquid water to exist on the surface.

Red dwarfs are like the glowing embers of the galaxy. They are invisible until you get close. Yet they comprise about 25% of the galactic mass. They might make nice places to visit.

Red dwarfs have made convenient venues for science fiction. The list is too long to include here, so I refer the reader to the Wikipedia article, Stars and Planetary Systems in Fiction.
A lot of good information about individual stars can be found at

Wikipedia has an excellent list of nearby stars. They also have an article on each individual star in the list, and they are pretty good about keeping up to date.

The RECONS (Research Consortium on Nearby Stars) website is also a great resource. They tend to focus on the kind of information scientists need, or can measure directly (angular position, proper motion, parallax, apparent magnitude) than on the kind of things an amateur would want to know (how big is it, how massive, how hot, how far away, what does it look like).
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