What Constitutes Space?

I’ve been writing about the assorted difficulties faced in astronautical engineering, but this presupposes a certain amount of background knowledge and was quickly getting out of hand. So let’s start with a simpler question: what is space, anyway?

Generally speaking, space is the zone beyond Earth’s atmosphere. This definition is problematic, however, because there’s no clean boundary between air and space. The US Standard Atmosphere goes up to 1000 km. The exosphere extends as high as 10,000 km. Yet many satellites (including the International Space Station) orbit much lower, and the conventional altitude considered to set the edge of space is only 100 km, or 62.1 miles.

This figure comes from the Hungarian engineer Theodore von Kármán. Among his considerable aerodynamic work, he performed a rough calculation of the altitude at which an airplane would need to travel orbital velocity to generate sufficient lift to counteract gravity, i.e. the transition from aeronautics to astronautics. It will vary moderately due to atmospheric conditions and usually lies slightly above 100 km, but that number has been widely accepted as a useful definition for the edge of space.

To better understand this value, we need to understand just what an orbit is.

Objects don’t stay in space because they’re high up. (It’s relatively easy to reach space, but considerably harder to stay there.) The gravity of any planet, Earth included, varies with an inverse square law, that is, the force which Earth exerts on an object is proportional to the reciprocal of the distance squared. This principle is known as Newton’s Law of Universal Gravitation. Its significance for the astronautical engineer is that moving a few hundred kilometers off the surface of Earth results in only a modest reduction of downward acceleration due to gravity.

To stay at altitude, a spacecraft does not counteract gravity, as an aircraft does. Instead, it travels laterally at sufficient speed that the arc of its curve is equal to the curvature of Earth itself. An orbit is a path to fall around an entire planet.

The classic example to illustrate this concept, which also comes from Newton, is a tremendous cannon placed atop a tall mountain (Everest’s height was not computed until the 1850s). As you can verify at home, an object thrown faster will land further away from the launch point, despite the downward acceleration being identical. In the case of our cannon, a projectile shot faster will land further from the foot of the mountain. Fire the projectile faster enough, and it will travel around a significant fraction of the Earth’s curvature. Firing it fast enough1 and after awhile it will swing back around to shatter the cannon from behind.

Newton_s_cannon_large.gif (313×242)

Source: European Space Agency

In this light, von Kármán’s definition is genius. While there is no theoretical lower bound on orbital altitude2, below about 100 km travelling at orbital velocity will result in a net upwards acceleration due to aerodynamic lift. Vehicles travelling below this altitude will essentially behave as airplanes, balancing the forces of thrust, lift, weight and drag—whereas vehicles above it will travel like satellites, relying entirely on their momentum to stay aloft indefinitely.

But we should really give consideration to aerodynamic drag in our analysis, because it poses a more practical limit on the altitude at which spacecraft can operate. Drag is the reason you won’t find airplanes flying at orbital speeds in the mesosphere, and the reason satellites don’t orbit just above the Kármán line. Even in the upper atmosphere, drag reduce a spacecraft’s forward velocity and therefore its kinetic energy, forcing it to orbit at a lower altitude.

This applies to all satellites, but above a few hundred kilometers is largely negligible. Spacecraft in low Earth orbit will generally decay after a number of years without repositioning; the International Space Station requires regular burns to maintain altitude. At a certain point, this drag will deorbit a satellite within a matter of days or even hours.

The precise altitude will depend on atmospheric conditions, orbital eccentricity, and the size, shape, and orientation of the satellite, but generally we state that stable orbits are not possible below 130 kilometers. This assumes a much higher apoapsis: a circular orbit below 150 km will decay just as quick. To stay aloft indefinitely, either frequent propulsion or a much higher orbit will be necessary3.

On the other hand, it is exceedingly difficult to fly a conventional airplane above the stratosphere, and even the rocket-powered X-15 had trouble breaking 50 miles, which is the US Air Force’s chosen definition. Only two X-15 flights crossed the Kármán line.

Ultimately, then, what constitutes the edge of space? From a strict scientific standpoint, there is no explicit boundary, but there are many practical ones. Which one to chose will depend on what purposes your definition needs to address. However, von Kármán’s suggestion of 100 km has been widely accepted by most major organizations, including the Fédération Aéronautique Internationale and NASA. Aircraft will rarely climb this high and spacecraft will rarely orbit so low, but perhaps having few flights through the ambiguous zone helps keep things less confusing.

1For most manned spaceflights, this works out to about 7,700 meters per second. The precise value will depend on altitude: higher spacecraft orbit slower, and lower spacecraft must orbit faster4. In our cannon example, it would be a fair bit higher, neglecting air resistance.

2The practical lower bound, of course, is the planet’s surface. The Newtonian view of orbits, however, works on the assumption that each planet can be approximated as a single point. This isn’t precisely true—a planet’s gravitation force will vary with the internal distribution of its mass, which astrodynamicists exploit to maintenance the orbits of satellites. That, however, goes beyond the scope of this introduction.

3The International Space Station orbits so low in part because most debris below 500 km reenters the atmosphere within a few years, reducing the risk of collision. This is no trivial concern—later shuttle missions to service the Hubble Space Telescope, which orbits at about 540 km, were orchestrated around the dangers posed by space junk.

4Paradoxically, we burn forward to raise an orbit, speeding up to eventually slow down. This makes perfect sense when we consider the reciprocal relationship between kinetic and potential energy, but that’s another post.

Book Review: Ignition!

Subtitled “An Informal History of Liquid Rocket Propellants”, Ignition! is John D. Clark’s personal account of working with rocket fuels from 1949 until his retirement in 1970.

Dr. Clark is introduced to us by Isaac Asimov. Clark was roommates with L. Sprague de Camp during his undergrad years at Caltech, and wrote a pair of science fiction stories before deciding the market wasn’t for him, though he remained active in the community. Dr. Asimov met him during the war, when he came to work with de Camp and Heinlein at the Philadelphia Naval Yard.

John Clark, like Asimov, was a chemist, working on the problem of chemical rockets for the majority of his career. He writes this book, he tells us, both “for the interested layman” and for:

[T]he professional engineer in the rocket business. For I have discovered that he is frequently abysmally ignorant of the history of his own profession, and, unless forcibly restrained, is almost certain to do something which, as we learned fifteen years ago, is not only stupid but is likely to result in catastrophe.

For the layman, he attempts (and, I think, succeeds) at writing in a manner which is nevertheless very accessible. The sections with heavy technical content can be skimmed over without losing too much of the overall picture, though a little background knowledge certainly helps. I’m not sure you could use this book as a reference without a basic understanding of engineering thermodynamics, but if you haven’t studied that what business do you have designing rocket engines?

Unfortunately, Dr. Clark gives relatively little in the way of citations or suggestions for further reading. This is both an artifact of the era—when technical reports and journal articles were essentially inaccessible to the general public if your local library didn’t have a copy—and a consequence of the fact that much of the source material was at the time still officially classified. At several points the discussion is cut short because he’s not at liberty to discuss the matter. He acknowledges these difficulties and makes not pretense of this being an authoritative textbook.

On a related note, the content is heavily focused on the research done in America and the United Kingdom, with a chapter devoted to what information came out of the Soviet Union in later years. Due to the date of publication, this book does not cover modern developments (though the final chapter makes a series of predictions I might come back and grade).

Nor does Clark address solid propellants or hybrid combinations in any significant detail, which is slightly disappointing given my current studies, but would have made for a much longer and more complicated read. Not that I would have particularly minded; Dr. Clark is an engaging storyteller, frequently giving us various background information on the scientists and organizations trying to develop early rockets, first for abstract research, later for the military, and finally for the National Aeronautics and Space Administration.

These anecdotes keep the reading fun even through the most tedious of minutiae on monoprops and halogen fuels. Clark frequently (if unpredictably) goes into detail on the chemistry of a particular propellant and how the molecules interact with one another. Such interludes eventually rekindled my interest in chemistry as a subject, which is fortunate since I need another credit hour of it to graduate. Hopefully some of the material I learn this summer will be relevant to aerospace propulsion work.

Overall, I found this to be a good introduction to rocket fuels and the history of that field. While useful for beginners such as myself and as a refresher, it probably shouldn’t be treated as any sort of reference guide or definitive citation.

ignition back cover

An engraving by Dr. Clark’s wife, Inga Pratt, presented to NARTS in 1959.

Hopefully one day Ignition! will be in print again, but for now most of us are stuck reading it from PDFs found online. Hard copies went for hundreds of dollars before the likes of Elon Musk and Scott Manley began publicly praising the book.

Bike-Shedding and Bottomless Pits

I see a pair of failure modes in social activism. One is bike-shedding. The other is trying to empty bottomless pits.

Bike-shedding refers to the tendency to focus on insignificant but comprehensible tasks, the nominal example being materials selection for the bike shed at a nuclear power plant. Everyone can understand bike sheds, only nuclear engineers are qualified to comment on the minutiae of reactor design. The latter is clearly more important than the former, but the former will likely get more discussion time in a layperson’s committee.

The same goes for social activism, where thousands of wannabe intellectuals fixate on relatively trivial issues because that’s what everyone can wrap their heads around.

If the true intellectuals spent their time on tractable problems, then this wouldn’t be a particularly troubling failure mode, because at least the wannabes aren’t getting in the way of serious work. Unfortunately, the leaders of any particular movement tend to be pursuing status within their community rather than the movement’s supposed goals.

The usual way the status competitions play out is through purity signalling. In this context, purity refers to loyalty towards the movement’s beliefs.  Whoever believes in the cause the most will garner more respect and acclamation. Intentionally or not, they begin to argue less and less actionable questions and make increasingly impractical demands upon the movement as a whole.

I’ve experienced this first-hand during my time in the libertarian movement. Many libertarians have such an affective death spiral around the non-aggression principle that they argue voting for third-party candidates is an act of violence. NAP uber alles was my reason for ultimately leaving the movement.

This phenomena is almost synonymous with the far-left. Constant in-fighting and purity debates hamstring many socialist, communist, and left-anarchist organizations, which I can’t say is necessarily a bad thing. But conservatives experience it, too; neoreaction was essentially the invention of right-wing impossibilism.

My speculation is that so many people tolerate impossibilism because it accelerates the transition from movement to community. As ideological questions detach from any sort of actionable agenda, there’s less urgency and more time for friendship and non-central discussion. Preference for a better world is a largely philosophical question (though social status makes it easier to accept an objectively unpleasant situation), while even self-described individualists recognize the joy from finding like minds. Even when the movement fails as such, it provided a significant benefit to its adherents.

The pattern repeats itself time and time again. I’ve seen it with the libertarian movement, with the rationalists, and with all sorts of less pleasant groups. I see no clear solution, beyond trying to decouple community from activism. Whether this will work remains to be seen.