# Asteroid Day 2018: Planetary Defense Progress Report

Earlier this month, the White House released a report detailing the current status of planetary defense efforts in the United States. The report discusses the ways that US government agencies would respond to an anticipated or unanticipated impact event, and outlines the steps that they should take to mitigate the danger. Unfortunately, this is just a report—any policy changes or future missions will require further action from the President and Congress.

This was a heartening but also concerning admission ahead of Asteroid Day. I’m encouraged that America is taking planetary defense seriously. Protecting against asteroid and comet impacts is arguably the single most important thing that we can be doing in space right now. However, it has not been the primary or even secondary focus of any major space agency. Much of the work has been limited to university researchers and private-sector organizations.

On this day, the 100th anniversary of the Tunguska Event, I would like to discuss our progress in planetary defense. While NASA and other organizations have done an excellent job tracking near-Earth asteroids and assessing their threat to humanity, we are not dramatically closer to impact prevention capabilities. Nevertheless, there is reason to be cautiously optimistic. Let’s discuss the major ongoing and future missions to explore and detect asteroids that could potentially threaten Earth.

To begin: just this week, the Japanese Hayabusa2 spacecraft arrived at the asteroid 162173 Ryugu. For the next eighteen months, Hayabusa2 will orbit the 900-meter-wide space rock. In addition to orbital observations, Hayabusa2 will release several surface probes and retrieve samples for return to Earth in late 2020. These samples will include material taken from the interior of the asteroid, extracted by detonating a small explosive device on the asteroid’s surface.

Hayabusa2 performs surface sample extraction at Ryugu.

Source: JAXA

Hayabusa2 is primarily focusing on planetary science, with consideration for eventual resource extraction. However, understanding the structure and dynamics of near-Earth asteroids is essential for predicting their impact odds and planning redirection maneuvers if need be.

Asteroid 162173 Ryugu as imaged on June 26.

Source: JAXA

Planetary defense is a major motivation of the OSIRIS-REx mission, which is continuing on its way towards asteroid 101955 Bennu. Astronomers estimate that there is a small chance that Bennu may impact Earth in about 200 years, so studying the asteroid up-close will considerably refine their calculations.

(Before someone asks: OSIRIS-REx Principal Investigator Dante Lauretta wrote a blog post specifically outlining the damage that Bennu would cause if it were to impact Earth. Note that all recent estimates place the impact odds far, far below one percent.)

OSIRIS-REx launched in 2016 and will arrive at Bennu in August of this year. The spacecraft performed a burn last January to put it on a trajectory for an Earth flyby, which occurred on September 22, 2017. This maneuver put the spacecraft on an appropriate orbit to rendezvous with the small asteroid.

Like Hayabusa2, OSIRIS-REx is also a sample return mission. Allowing scientists to study asteroidial material in laboratories on the ground massively increases the information we can glean from them, because many of the most interesting measurements and experiments are simply too heavy, bulky, or complex to cram within an interplanetary spacecraft.

OSIRIS-REx performs surface sample extraction at Bennu.

Source: NASA

Sample return is just one aspect of the OSIRIS-REx mission. In addition to the standard planetary science objectives, OSIRIS-REx will study the impact of non-gravitational forces on the orbit of a celestial body. Many of these forces are well-understood for conventional satellites, but the data for asteroids and comets is hazy when it exists. Characterizing these effects for objects like Bennu will go a long way towards predicting their orbits and thus the impact odds long-term.

Once we understand these risks, though, we need the capability to deflect any objects we find headed towards Earth. Here the progress has been less inspiring.

First, a mission is currently under development called the Double Asteroid Redirection Test, or DART. Planned to launch in December of 2020 or early 2021, DART will rendezvous with the asteroid 65803 Didymos in October of 2022. Didymos is actually a double asteroid, and DART with collide with the smaller moon when the asteroid is near its closest approach to Earth. Ground-based observers will measure the effect that the collision has on the moonlet, giving researchers some hard data on just how well the kinetic impact technique would work for asteroid deflection.

This is an interesting mission, both for its planetary defense implications and for its technology. DART is expected to be the first spacecraft to test the NASA Evolutionary Xenon Thruster (NEXT), and will sport the Roll-Out Solar Array (ROSA) design tested on the International Space Station in 2017. Unfortunately, there has been some uncertainty over whether this mission would actually fly. Though required by law, it was not included in the 2018 NASA Budget. The John Hopkins University Applied Physics Laboratory, however, has continued working on the project and as of April was discussing final design and fabrication later this year.

On a related note, the Asteroid Redirect Mission (ARM), which the mainstream science media so eloquently described as “giving the Moon a moon”, was recently cancelled in favor of pursuing manned Lunar missions. This is a questionable decision. ARM was a logical development conduit for key technologies in robotics, propulsion, and astrodynamics. All of these would have contributed greatly to manned exploration of the Solar System. Thankfully, much of this technological investment will be preserved, and may eventually pay dividends in planetary science and defense.

Source: NASA

Nevertheless, having a six-ton asteroid in Lunar orbit would have provided a compelling intermediate target for human spaceflight. (The Deep Space Gateway would naturally fill the role of an intermediate target, but I’ll save the discussion of its advantages and disadvantages for another day.) Landing is a much bigger challenge than just returning to cislunar space, and the scientific knowledge from returned samples would also have been tremendous.

Another important project has also faltered: the Sentinel Space Telescope. This mission was designed by the B612 Foundation to detect asteroids that Earth-based telescopes miss by putting a dedicated spacecraft in solar orbit near Venus. Sentinel would have launched on a Falcon 9 rocket in 2018 or 2019 and cost $450 million to develop. This proved way too expensive for a niche non-profit. NASA provided some funding, but this ended in late 2015, and B612 was unable to raise the remainder. Retired astronaut Ed Lu confirmed that the project was dead last year. Rendering of the Sentinel Space Telescope on-orbit. Source: B612 Foundation B612 is instead focusing on telescopes mounted to significantly smaller satellites. They will use a new technique called synthetic tracking to spot smaller asteroids than previously possible. Few and fewer potential “killer” asteroids remain to be discovered as better and better telescopes come online, so the overall emphasis is turning towards the smaller rocks. These can still be deadly: the Chelyabinsk meteor was only about 20 meters across but caused thousands of injuries and millions of dollars in damages. If mounting space telescopes on small satellites sounds ambitious, consider that the Canadian Space Agency launched a comparable spacecraft called NEOSSat with similar goals in 2013. Small satellites are much more affordable for non-governmental organizations, in part because launch vehicle cost can be distributed over multiple missions—NEOSSat rode to orbit with six other spacecraft. An audit in 2013 estimated the program was significantly over-budget. Total cost: CDN$25 million.

NASA and the Jet Propulsion Laboratory are also pursuing a Near Earth Object Camera, which would join the fleet at the Earth-Sun L1 point. NEOCam was passed over for the latest Discovery Mission opening, though was still under development as of April under the aegis of NASA’s Planetary Defense office. Without a clear funding commitment, though, mission planners are severely limited in developing the program.

This is a bit concerning, because NASA has a Congressional mandate to detect 90% of near-Earth objects 140-meters and larger by 2020. Much of this work was completed by the Wide-field Infrared Survey Explorer during its extended mission. WISE discovered over 3000 asteroids and comets, including 262 near-Earth asteroids. 47 of these are considered potentially hazardous. Detecting the remainder will probably require new hardware, so I’m doubtful that NASA will meet the Congressional mandate. If current legislators are serious abut this mission, they need to allocate funds—and quickly.

Artistic rendering of the WISE spacecraft.

Source: NASA

The probability that an undetected asteroid will hit Earth before that objective is met—on time or not—is low, but every day that passes risks another Chelyabinsk. Only once we know the threats can we take actions to mitigate them. Having the necessary technology ready-to-go would vastly improve our odds.

On the whole, I’m glad to see that the United States is taking planetary defense seriously, but there’s a lot of work left to do. Check back again next Asteroid Day to review the advances we make in the coming months.

# Book Review: Elements of Spacecraft Design

Most aerospace engineers are familiar with the AIAA Education book series, which provides instruction on topics ranging from structural design to hypersonic propulsion. Charles D. Brown was an aerospace engineer who worked at Lockheed Martin and taught at UC Boulder. Brown wrote several books for the AIAA Education Series in addition to his work on various space projects, most notably Magellan.1 Elements of Spacecraft Design is his attempt at a space vehicle design textbook.

Like most aerospace design books, it breaks out the final product into the various subsystems and discusses each of these in turn. There’s no universally agreed-upon list of aircraft or spacecraft systems, but Brown addresses most of the major ones. He begins with an introduction to spacecraft generally, a brief exploration of spacecraft systems engineering, and then proceeds into the elements of design.

These are not exclusively subsystems. Usually, aerospace design decisions are dominated by the intended flight profile. Aircraft designers estimate the requirements to complete the assorted mission phases. Spacecraft designers break things down using orbital mechanics. Only once the various maneuvers are established can we begin the process of selecting and sizing the propulsion system.

Of course, it may not be possible to complete a particular mission with the propulsion systems which are available (remember that pretty much anything short of an Apollo-level mad-dash will be budget-constrained). In that case, revise the trajectory. Design is an iterative process.

Note, too, that the propulsion systems on spacecraft frequently do double-duty as the attitude control system. These two chapters immediately follow orbital mechanics, and bring us about halfway through the book. It might feel like these are a mini-book of their own, and sort of are, since Brown also wrote a primer on spacecraft propulsion covering much of the same ground.

The non-spacecraft engineers in the audience may be wondering what else is left to discuss. Quite a lot, actually! Power systems lead us off, which for Brown’s purposes are almost exclusively solar panels and batteries. Radioisotope thermoelectric generators get one (1) page of attention, and nuclear reactors get none, which caused some consternation for my senior capstone class. It is an older book, granted, but the former warrants a few sizing equations at least.

Closely related to power (at least if we’re doing solar panels) is thermal control. Both are heavily affected by the orbital regime of the spacecraft and, potentially, the vehicle configuration. The chapter mostly focuses on preliminary spherical satellite analysis, though it also introduces the tools for more detailed studies. Properly modelling the heat flow through a spacecraft can be a pretty serious challenge, though, with entire books dedicated to the subject.

Finally, our attention turns towards the reason we launched the mission in the first place: obtaining or relaying important information. Remember, we’re not just doing this because it’s cool. There’s valuable scientific or commercial data which we want to process and return to Earth. Moreover, we have to maintain control of the spacecraft if we want to get it. Brown gives us a general introduction to the problems of command & data handling and telecommunications.

These chapters are somewhat weak. A good deal of the information is presented too briefly, and not always in the most logical order. It took the entire class several days to figure out that we needed a figure from the previous chapter to finish one of the telecommunication problems. It was hard to believe that we would be excited to start in on structures—but we were!

Of course, the structures chapter only briefly addresses sophomore-level material mechanics, and then segues into acoustics, which is a graduate class where I went to school (though the actual equations presented in the book seem inadequate for any serious analysis). For the most part, it addresses qualitatively the major factors which affect spacecraft configuration and material selection, with examples of the common solutions.

This is where the systems engineering aspect comes back in—quite often, different subsystems impose competing requirements on the spacecraft configuration. The designer has to figure out the optimal approach for the particular mission in question. Brown addresses this in a few exercises through the text, but there’s ultimately only so much a student can learn without feedback from an instructor (or with prototypes through trial-and-error).

Overall, I found Elements of Spacecraft Design to be an informative and pleasurable read. It’s a good book for learning about spacecraft hardware, but I would not recommend treating it as a full-fledged spacecraft design book. It includes many of the elements of spacecraft design, yes, but hardly constitutes a full periodic table.

Consider this exciting image, which some AIAA editor thought would make ideal cover art:

Wouldn’t a rendering of Magellan be more appropriate?

Ignoring the fact that block diagrams don’t need to be painfully asymmetric, the astute reader will note that Elements of Spacecraft Design only covers the areas under the “spacecraft” header. Each of the headers could have similar subheading trees, but those aren’t the focus of Brown’s text. He addresses the interface between the spacecraft and other project elements, but not in any great detail.

If you need that information, one could consult some of Brown’s references, or just pick up a more detailed textbook like SMAD. Brown entirely omits some important areas such as cost estimation and manufacturing considerations, so any serious designer will need to turn to other books regardless. For this reason, I have to recommend using SMAD or its sequel, Space Mission Engineering, as a primary design book. Space Vehicle Design by Michael D. Griffin2 and James R. French also addresses some aspects, such as atmospheric entry and reliability engineering, but still skips ground segment design.

Brown covers some things which these other books gloss over, however. Perhaps the most important is providing clearer algorithms for mass and power requirements of the spacecraft. These include equations to estimate the cabling and launch vehicle adaptor masses, which are easy to overlook and a frequent location of cost and weight overruns. The data and resultant equations are old, mind you, but most other books suffer from much the same problem.

Still, an updated edition is overdue. Brown and his coauthors made a lot of mistakes and unstated assumptions which the copy-editors didn’t catch, and cause all sorts of headaches when trying to solve the problems and follow the examples. Many of the equations also conflate weight and mass when switching between the customary and metric versions. The book should really pick one as the default and then use a common substitution algorithm to derive the other on-need. It wouldn’t be a hard problem to tackle, but it’s unlikely that anyone will until AIAA offers a paycheck for it.

As long as you’re mindful of these issues, however, Brown provides a solid introduction to the problem of spacecraft subsystem design. Elements of Spacecraft Design covers most of the major areas—and a number of the minor ones—in a generally accessible and clear manner. This is one of the few textbooks I found myself enjoying, as opposed to merely slogging through to extract the relevant information. Brown is an engaging writer (though note that some of the chapters written by other authors are considerably drier), and I’ll probably read some of his other books in the near future. I doubt that they will fully educate me on the subjects, but just like Elements of Spacecraft Design, should provide a valuable framework for absorbing later, more detailed texts.

1Most of the planetary examples in the book use either Venus generally or Magellan in particular. It became a bit of a running gag in the class.

2Space Vehicle Design is partially based on Griffin’s experience with the JHU Applied Physics Laboratory, which designed many famous spacecraft, including New Horizons, MESSENGER, and the Parker Solar Probe. Griffin later went on to be NASA Administrator from 2005 to 2009 and is currently Under Secretary of Defense for Research and Engineering.

# Book Review: To the End of the Solar System

James Dewar set out to the write the story of the nuclear rocket, and that’s exactly what he succeeded in doing. To the End of the Solar System is a nearly complete history of nuclear-thermal propulsion research from the discovery of radioactivity in the 1890s through the cancellation of the American research & development program in 1973. He discusses the work done in subsequent years, though through the book’s publication in 2004 that research was largely theoretical.1 Dewar consequently directs his attention to the period when nuclear propulsion was a near-term possibility.

It is not, primarily, a technical tale. The majority of the book focuses on the political, managerial, and bureaucratic aspects of the program. There is a good deal of technical detail, but ultimately the engineering challenges are not the biggest hurdle for those supporting nuclear propulsion. Securing long-term support and funding from industry and Congress will be much more difficult.

The book also necessarily focused on the American nuclear program, though addresses briefly Soviet work. Unfortunately, our knowledge of their program comes from only a handful of sources, sometimes contradicting one another. How much useful information we can glean from them is uncertain.

The Cold War played a major role in the development of the nuclear rocket, but the story begins well before the Russian Revolution. A number of early rocketry theorists, including Robert Goddard, Konstantin Tsiolkovsky, and Hermann Oberth speculated on using the energy released from radioactive decay to propel spacecraft, but both the quantity available and isotopic energy output was minute. Discussion remained entirely abstract and largely an aside in the development of rocket propulsion until after the Second World War.

The ultimate motivation was military. As atomic bombs grew larger and larger, existing aircraft and missile designs struggled to keep up. A handful of scientists floated nuclear options to deliver these weapons, either in aircraft, missile, or pulse-propulsion form. The Pentagon developed a nuclear airplane program as a joint venture between the Air Force and Atomic Energy Commission with the express goal of developing an aircraft capable of delivering a hydrogen bomb inside the Iron Curtain.

Oak Ridge National Laboratory hired a young physicist named Robert Bussard2 to work on the nuclear airplane project. Brussard did excellent work but insisted on studying nuclear rockets alongside his official duties. Through months of feverish lucubration, he developed some of the first viable nuclear rocket concepts. His classified publications attracted the interest of several prominent physicists. Teams formed at Los Alamos and Livermore National Laboratories to develop Bussard’s concepts. Los Alamos eventually came to favor nuclear turbojets, while Livermore concluded that nuclear rockets were more viable.

When Congress got involved a few years later, the need for nuclear aircraft or missiles was waning as bomb mass fell and chemical launcher capability grew. However, Washington was beginning to think about spaceflight, and decided to continue funding both programs. Ironically, the AEC assigned Los Alamos to study rockets and Livermore to study nuclear jet engines. These became Projects Rover and Pluto, respectively.

Los Alamos began constructing facilities at the Nevada Test Site to put their series of reactor designs through the paces. Each reactor was a hard-won concession from Congress, which was worried about just how many tests and iterations would be necessary to develop a viable system. Throughout the program, many in Washington opposed Project Rover or believed that it should be transferred to the civilian space program. NASA was very skeptical of the program, however, and so a small clique of Senators fought to keep it under AEC aegis. Ultimately NASA and the AEC found a reasonable compromise, forming a joint Space Nuclear Propulsion Office.

The early Space Race initially helped Rover’s prospects, as the Soviet Union sped ahead in missions and technological firsts. Nuclear propulsion would enable much more impressive projects, such as manned planetary landings, massive probes to the outer Solar System, space stations, and Lunar bases.

In Nevada, reactors were steadily improving. Their thrust and successful burn-time grew, though several failures occurred, including one which required an expensive clean-up effort. Through a series of redesigns, however, the test articles began to closely match the existing aerothermodynamic models. Better designs were coming, but a large question mark hovered over the program: when would Rover get a reactor in-flight test?

RIFT was well-named, as it became a political hot-button issue. Early concepts involved dumping the used reactor into the ocean or using it to perform orbital insertion as a Saturn upper stage. Both of these concepts were eventually abandoned on safety grounds, but did nothing to advance the issue in Congress.

Ultimately, nuclear rockets became a chicken-and-egg problem. Congress and NASA leadership did not want to approve a program that required nuclear propulsion until the technology was ready, but also hesitated to develop nuclear technology until a mission required it.

Much of the opposition stemmed from budgetary concerns. NASA was a rapidly-growing slice of the federal budget, competing with the Vietnam War and Great Society for a shrinking set of tax dollars. Recall that fiscal conservatism was once common in both political parties, rather than a fringe movement within one of them. Few wanted to commit to the large, expensive missions which nuclear propulsion would enable (such missions being prohibitively expensive—in the extreme—with chemical propulsion).

The concept of preeminence rapidly fell out of favor. Washington decided that Apollo would be the extent of trying to upshow the Soviet with big flashy projects. After Skylab, the Space Race would be abandoned in favor of developing the “economical” space transportation system. Los Alamos was still developing reactors, including the most powerful reactor ever run, but the tide was shifting towards smaller reactors to complete technology validation. Stacking small reactors, it was thought, would provide adequate thrust and cut down burn durations.

Even the space transportation system came under attack as tax revenue continued to shrink in the Nixon years. The original plan included nuclear orbital tugs, the chemical shuttle, and a space station. Ultimately, only the shuttle was funded, with the design of its cargo bay becoming a proxy battle over the future of nuclear propulsion. Small nuclear engines could be carried to orbit in the shuttle cargo bay, after which they would be attached to larger spacecraft and activated once astronauts had left the vicinity.

The Space Transportation System concept in 1970.

Source: Marshall Space Flight Center

Quite suddenly, though, all funding was terminated in 1973. Congressional funding was falling but still there, and researchers thought they were approaching flight test readiness. The change was ultimately a decision made by bureaucrats in the executive branch, which reprogrammed the funds without the consent of Congress or the President.

Believe it or not, this was technically a legal move. Several Senators were enraged by it, including Barry Goldwater—not exactly a friend of large, expensive federal programs. Within a few years, laws were introduced which required the Executive Branch to spend funds on the programs which Congress had allocated them for.

The defunding took the Soviets by surprise, to the point that they suspected it was a false-flag move to classify the work. Unfortunately, this does not appear to be the case. In fact, some of the officials involved in cancelling Rover were involved in the later Air Force Project Timberwind, which again attempted to develop nuclear propulsion. This too was cancelled after the end of the Cold War, without producing any real results.

All of this was really fascinating history, which I think should be discussed more widely in the spaceflight community. Nuclear propulsion, despite some extreme challenges, came very close to practicality. In the end, it was cancelled by politicians who failed to see the opportunities it provided rather than for the technological difficulties it faced.

It is quite arguable that Project Rover was well-worth the cost, and could have been justified on technology-development grounds alone. The program created entirely new industries, such as commercially-affordable cryogenics, and demonstrated all kinds of new material sciences. One would expect spaceflight advocates to mention this more often.

To the End of the Solar System does discuss the technical details, but is ultimately a political history. The style is somewhat confusing in this regard, routinely switching between Washington and Nevada—and not necessarily in chronological order. I would like to reread it to see if contextualization improves the narrative, but sadly it goes back to the school library tomorrow. Maybe one day I’ll buy a personal copy.

However, the appendices are worth reading. They provide a decent introduction to the major aspects of nuclear propulsion, without drowning the reader in technical minutiae. The discussion of radiation safety, for instance, was extremely informative and should allay many fears about the dangers of nuclear rocket testing. Dewar also dedicates a section to the Russian nuclear propulsion program. These are a good introduction to the subject, though hardly an expert make. I’ll be diving into dedicated nucleonics and advanced propulsion resources Soon™.

On the whole, To the End of the Solar System: The Story of the Nuclear Rocket is a rich resource for those studying the history of nuclear propulsion, whether for technical or non-technical reasons. Understanding the story of advanced propulsion is essential for those of us who wish to see humanity spread out into the Solar System, and James Dewar has written an excellent introduction. The book does not appear to be particularly common in print3, but if you get the chance to read it, you definitely should.

1Dewar mentions Project Prometheus to explain that it was too early in the program life-cycle to discuss. As it turns out, Project Prometheus went nowhere. In 2017, NASA issued new hardware contracts for exploring the manufacturing and testing requirements for making nuclear propulsion viable, but it is too early to say whether these will yield results, either.

2Bussard is better known for his later work on advanced propulsion, proposing a fusion ramjet fueled by the interstellar medium.

3I believe that it has had only two printings: initially from the University of Kentucky Press in 2004, and a second run from Apogee Books later in the decade. New hardbacks are hundreds of dollars on Amazon. There might be a PDF version floating around, but if there is, I haven’t come across it. Libraries are probably the best bet.

# Some Things That Affect Spacecraft Orbits

The derelict Chinese space station Tiangong-1 is expected to re-enter this weekend. The precise time and location aren’t easy to predict, and this has caused some concern among various members of the public. A space station is much bigger than a normal satellite, and it’s conceivable that larger pieces could cause major property damage or even injuries on impact. So why don’t we know where it will hit?

The answer is actually pretty complicated, because there many, many things which affect the paths of even simple, Earth-orbiting satellites. Some are immediately obvious, like drag from the upper atmosphere and Lunar perturbations. A lot are more subtle, like interference from Earth’s magnetic field. In this post I’d like to briefly explain all the significant factors, without going into too much math. Hopefully this will emphasize to specialists and laymen alike the value of responsible debris mitigation and the importance of safely disposing old spacecraft before ground controllers lose contact.

Atmospheric drag is, of course, the largest force affecting satellite orbits, and the reason Tiangong-1 is re-entering. As I explained in my last post about orbital mechanics, there is no clear upper edge to the atmosphere. Below about 500 kilometers, the atmosphere is still sufficiently thick to de-orbit most debris. Satellites above this altitude can remain in space for decades without any maintenance, and geosynchronous orbiters will last centuries or even millennia.

Low Earth Orbit is the natural regime to place crewed spacecraft, since the debris risk is dramatically lower. (The radiation hazards are also significantly higher in the medium orbits, and our current manned capsules can’t easily punch through the Van Allen belts.) This is fine as long as the spacecraft is operational and performing orbital maintenance maneuvers. The International Space Station has to perform these regularly.

ISS altitude over the last year. Discontinuities between decay regions represent maneuvers to raise the orbital height.

Source: heavens-above.com

Atmospheric drag on spacecraft is governed by a simple equation, which will be extremely familiar to even underclassmen aerospace engineers:

$F_D = \frac{1}{2} m C_D \rho A V^2$

In essence, this equation states that drag force $F_D$ on the spacecraft is equal to half the product of the spacecraft mass $m$, cross-sectional area $A$, atmospheric density $\rho$ and the square of the relative velocity $V^2$, all multiplied by a fudge factor $C_D$. We call the fudge factor the drag coefficient, and for satellites it tends to fall between 2.1 and 2.3, though higher values are common depending on the spacecraft configuration and materials used.

Density is the biggest unknown factor. It varies based on the altitude, time of day, time of the year, and how active the Sun has been lately. A number of these factors also affect relative velocity, because the atmosphere isn’t still. Upper atmospheric winds can be significant, often hundreds of meters per second.

Altitude plays a role, because different gases have different masses.  Mass is related to velocity via kinetic energy and the ideal gas law, which essentially states that the velocity of a particle, for a given internal energy, with be greater if the particle has a lower mass. Essentially, heavier gases like molecular oxygen and nitrogen will hug the planet, while lighter gases such as hydrogen and helium can easily climb into the thermosphere.

Additionally, the amount of solar and cosmic radiation is higher the further one rises. Collisions with energetic particles cause molecules to break into their components, so the frequency of atomic oxygen and nitrogen increases dramatically. This affects the effective density of the upper atmosphere and therefore the drag force. Since the amount of solar radiation is highly variable over the short term and changes with the eleven-year solar cycle, the numerical density of the upper atmosphere isn’t at all constant.

Solar radiation was ultimately responsible for the failure of a previous space station: Skylab. Initially NASA expected it to remain on-orbit till the early 1980s, when the space shuttle could have pushed it higher. The sun was particularly active during that era, however, and by the mid-1970s it was clear that the station would re-enter much earlier. A special mission would have saved it, but NASA never seriously planned one and Congress never allocated any funds. Skylab disintegrated over Australia on July 11, 1979. Despite widespread concerns, there was very little damage and no one was hurt, though one jurisdiction fined NASA \$400 for littering.

Skylab photographed by the last departing crew in February 1974.

Source: NASA

Temperature changes over the course of the day and year also affect the upper atmospheric density. Warm gases move faster and rise higher, and which can be seen in aggregate as an increase in pressure. Warm air near the surface displaces upwards, effectively increasing the size of the atmosphere. This can significantly increase the drag which a satellite experiences.

Generally speaking, day is warmer than night. Summer is warmer than winter, though of course that depends on which part of Earth you’re considering. (Remember that seasons are caused by axial tilt, not the eccentricity of our path around the Sun.) Advanced density models take all of these factors into consideration—date, time of day, latitude, longitude, altitude, and multiple indices of solar activity.

Atmospheric density is the biggest effect that astrodynamicists have to consider, especially for satellites in low orbits, but there are several other major forces which can cause significant accelerations, particularly upon smaller objects. From Newton’s Second Law, the acceleration a force has on an object is directly related to the mass of the object in question. Space stations have high masses, so only large forces can affect them. Cubesats have much lower masses, and can see large perturbations from forces that space station controllers happily ignore.

One of the larger effects we have to worry about is Earth oblateness, usually abbreviated as $J_2$. This is a low-order model of Earth’s shape, which is actually really complicated. High-fidelity models often reach high two-digit orders, though these are only needed for the most precise of missions.

The effect of $J_2$ is to reduce the inclination of an orbit, while also causing the orbit to change its orientation around Earth. The essential mechanism is that, because Earth is not exactly a sphere, when the spacecraft is north of the equator, it will be experienced an unbalanced force pulling it south, which the reverse occurs when it passes below the equator again. Over time, the satellite trajectory will approach an equatorial orbit, precessing around the pole.

We can define a $J_2$ value for every planet, because their non-sphericity is caused by rotation. Other gravitational effects may also be present, though these can usually be neglected. Luna is a notable exception. The internal mass distribution of our moon is so irregular than only a handful of orbital inclinations are stable. We learned this the hard way when Apollo astronauts left hand-launched microsatellites in orbit. One lasted for over a year, while other crashed within weeks.

This alludes to another important point: anything the size and density of a planet is not going to be perfectly rigid. In addition to ocean tides, gravitational effects from the Sun and Luna also cause internal tides, as the solid material within the planet bends slightly. These are called solid Earth tides, and affect satellite orbits about an order of magnitude more than the ocean tides. Usually these can be neglected, but precision gravity models need to taken them into account.

Accelerations of about the same order of magnitude ($\approx 10^{-12} \ \textrm{km}/\textrm{s}^2$) arise from general relativity. Because the spacecraft is travelling around a deep planetary gravity well, there will actually be a small but measurable change in velocity over time due to the spacecraft’s velocity through space. Mathematically, this is stated as:

$a_r = -3\frac{\mu}{r^2}\frac{v^2}{c^2}$

where $a_r$ is the relativistic acceleration, $\mu$ is the standard gravitational parameter for the body in question, $r$ is the distance of the spacecraft from the body, $v$ is the instantaneous velocity of the spacecraft, and $c$ is the speed of light. This acceleration will get smaller the further the spacecraft is from the primary body, and the slower it is moving (which, incidentally, spacecraft in higher orbits tend to do).

Generally, the position effects of relativity will be on the order of a centimeter, so orbit determination on larger scales can neglect that easily. Spacecraft in higher orbits probably won’t be affected, though spacecraft in very low orbits may see significant effects if they remain in space for a long time. The planet Mercury, orbiting so close to the massive Sun, experiences a dramatic relativistic acceleration. Astronomers once suspected that another planet lurked close to the Sun, perturbing Mercury’s orbit in a more typical way, until Einstein’s theory closely predicted the observed variations.

The Sun and Luna cause the greatest gravitational perturbations to Earth orbiting satellites, dragging the satellite slightly astray as it swings around our green planet. If we want to be really precise, though, we need to consider accelerations from other worlds, as well. Astrodynamicists rarely find a case where any besides Venus and Jupiter can be worth the trouble (and even those rarely). Venus is important because it is close to Earth, while faraway Jupiter is merely massive. Mars is nearly as close as Venus during much of its orbit, but is so much less massive that we neglect it entirely.

There’s one final type of force which affects orbits directly: radiation pressure. This can be somewhat counter-intuitive, because the majority of the radiation in question comes in the form of massless photons. $F = ma$ would seem to break down. Massless though they be, photons carry momentum. The rigorous definition of Newton’s Second Law of Motion is really that force is the change in momentum, which is the product of mass and velocity. We simply assume that mass remains constant in most applications.

Since photons carry momentum, however, they can produce a force directly. It’s not much, but when you consider how many photons are streaming through space each second, it turns out to be significant. The radiation flux from the Sun is usually around 1376 $\textrm{W}/\textrm{m}^2$, while the reflected radiation from Earth is around 459 $\textrm{W}/\textrm{m}^2$. Dividing by the speed of light, we find the two radiation pressures.

The force $F_s$ from this pressure $P_s$ is a function of the cross-sectional area of the spacecraft and the angle $\alpha$ between it and the incoming photons:

$F_s = P_s\cos\alpha$

The same equation can be used to calculate the effect of Earth radiation pressure, though the incidence angle will necessarily be different.

At this point, let’s return to the question of Tiangong-1. We’ve seen a great many reasons why it is challenging to make long-term predictions about its orbit. However, there is another problem which affects derelict spacecraft in particular: we don’t know its orientation in space. Now a large spacecraft can be imaged by radar, which gives us some idea about its orientation, but that will not work for smaller satellites. To make matters worse, it turns out Tiangong-1 is rotating, so its orientation will be different depending on when we look.

“What causes this rotation?” you might be wondering. I’m glad you asked. There are four major disturbance torques that attitude control engineers have to consider, though several of the above forces can also cause smaller torques.

At low altitudes, the largest torque by far is aerodynamic torque $T_a$. Recall the drag force equation I introduced above. Any offset between the center of the cross-sectional area and the center of mass will produce a moment arm $L$, over which the the force can act to induce rotation:

$T_a = F_D L$

We again find ourselves facing the fact that we may not know the cross-sectional area. If the precise forces and and orientation are well-known when ground controllers lose contact, we can model its rotation forward for a time, but not long enough to predict the re-entry of Tiangong-1.

But that’s not the end of it. There’s also force from Earth’s magnetic field, which will align any magnetized object with it, including spacecraft. The magnetic torque $T_m$ is a function of the residual magnetic dipole $M$ on the spacecraft, the Earth’s magnetic field strength $B$, and the misalignment $\theta$ between the two:

$T_m = MB\sin\theta$

The magnetic field strength is a function of altitude $r$ and latitude $l$, as follows:

$B = \frac{B_0 r_0^3}{r^3}\sqrt{3sin^2l + 1}$

where $B_0$ is the magnetic field strength at sea level ($3\times 10^{-5}\ \textrm{T}$) and $r_0$ is the average radius of Earth (about $6,370\ \textrm{km}$).

Finally, the spacecraft orientation leads to torques due to the small gravity gradient between its highest and lowest components. Measuring gravity gradient torque $T_g$ requires very accurate information about the moment of inertia distribution, which is often difficult to determine without detailed blueprints. It is also a function of altitude above the planet, because gravitation force (and therefore torque) drops off with increasing distance, and the angle $\theta$ off vertical”

$T_g = \frac{3\mu}{r^3}\lvert I_z - I_y\rvert\theta$

where $I_y$ and $I_z$ are the moments of inertia about the $y$– and $z$-axes, respectively.

As a general rule, the aerodynamic and magnetic torques dominate at lower altitudes, but may be significant for higher orbits or with special spacecraft configurations. These have to be determined on a case-by-case basis.

So that’s why we don’t know exactly when or where Tiangong-1 will re-enter. There’s a lot of variables involved, many of which are difficult to estimate, and often are strangely coupled at higher orders. There are many things which can be improved if we’re willing to spend enough money, such as building better atmospheric and gravitational models or tracking debris more regularly. Ultimately, though, there’s no substitute for responsible disposal at the end of a spacecraft’s mission, either into a stable graveyard orbit or by de-orbiting at a safe location.

…and all of this assumes that the spacecraft generates no thrust. Imagine how complex it gets when we consider outgassing!

### References

• Brown, C. D., Dukes, E. M., Elements of Spacecraft Design, edited by J. S. Przemieniecki, AIAA Education Series, AIAA, New York, 2003.
• Knipp, D. J., Understanding Space Weather and the Physics Behind It, 1st ed., McGraw Hill, New York, 2011.
• Moe, K., Moe, M. M., “Gas-surface interactions and satellite drag coefficients,” Planetary and Space Science, Vol. 53, No. 8, 2005, pp. 793–801
• Montenbruck, O., Gill, E., Satellite Orbits: Models, Methods, and Applications, 1st ed., Springer-Verlag, Berlin, 2000.
• Vallado, D. A., Fundamentals of Astrodynamics and Applications, 4th ed., Microcosm, Hawthorne CA, 2013.

# How To Make An Astronautical Engineer

Like quite a few aerospace engineering majors, I’m not really here for the aircraft material. Now, planes and helicopters are interesting in their own right, and the overlap between the two fields makes perfect sense historically. My disinclination to the aeronautical courses (which, at my school—and most others—represent the bulk of the curriculum) stems mainly from the fact that that’s not where I want to spend my working years, and college is too damn expensive to waste my time and my parents’ money on irrelevant material.

The major argument for the current arrangement is that space-focused students represent a minority of the department’s undergrads. While this is generally true, it is also misleading: the lack of astronautics classes deters many interested high-schoolers from applying. To magnify the distortion, a lot of the kids who do enroll jump ship for propulsion and fluid dynamics once they realize how few options are open to them.

In seeking a more balanced plan of study, let’s take things to extremes and consider what a dedicated astronautical engineering curriculum would look like. A few such departments do exist, sometimes even operating alongside aerospace engineering programs at the same institution. As the opportunities to work in strictly space-related roles expand in the coming decades, it may be worthwhile to rehabilitate aeronautical engineering as an independent major while astronautical engineering comes into its own.

Before we begin, I’d like to discuss a few issues with engineering curricula in general.

First, the approach to teaching math and science generally is deeply flawed. It makes absolutely no sense to teach so much algebra, trigonometry, vector geometry, and so on before so much as showing the poor kids a derivative. Supposedly our math curriculum was designed to churn out aerospace engineers after the Sputnik Crisis, but fear must have clouded their judgement, because hiding the beauty of mathematics behind semesters of drudgery seems to scare off more students than it’s worth. The fact is, it’s easier to buckle down and work on a problem when the kid appreciates its applications.

This is closely related to another criticism, which is that students get very little experience with the subject matter of their major until basic math and science requirements are complete. This is not only unpleasant for the student, but dangerous. It may be that the student will absolutely hate the field of engineering they’ve chosen to study, but won’t find out until two years of college tuition have already been sunk. By that point, it may be financially impossible to change majors.1

None of that would be a problem if public schools were capable of turning out educated adults, but it would seem that they aren’t, so it is. The same goes for reading, composition, and oral communication, to say nothing of economics, ethics, and epistemology.

But it’s not clear to me that you need multivariate calculus to learn the history of spaceflight. I would recommend integrating some sort of dedicated, big picture class into every semester of the underclassman curriculum.2 Considering how many of us arrived at our capstone class here without a coherent concept of airplane dynamics, this seems like a good addition to the baseline program. The vast majority of the curriculum I propose, though, would consist of substitutions. Only one or two classes would I remove outright.

Before we talk about that, though, let me zoom out for a moment and explain the major areas of aerospace engineering. (If you already know this, bear with me—I’m not writing solely for aerospace engineers, or even engineers generally.)

The five major areas of aerospace engineering are aerodynamics, controls, propulsion, structures, and design. (One could make the case for spinning out a separate focus on hardware from design and structures, but this is not generally recognized. A bit more on that later.) Design is somewhat distinct from the other areas as a synthesis that cannot stand alone. The degree to which this is true, of course, depends on just how abstract the dividing line between design and subsystem application is. In many cases, the entire question is quite fuzzy, which is fine. A lot of the best work happens in that region.

By number of workers, structures is the biggest area of aerospace engineering. On the order of 70% of aerospace engineers will work in structural analysis at some point in their careers. Oddly enough, this is one of the areas I have the most difficultly explaining to my non-engineer family members. Structures is….structures. It’s all the structure that holds an airplane together. It’s the frame of your house keeping the roof from caving it, it’s the frame of your chair keeping you off the ground. The aircraft structure holds the engines to the wing and the wing to the fuselage and the fuselage together.

Propulsion is easier to see: it’s the engines pushing the plane through the sky. These can be propeller or jets of various types, and less frequently, rocket engines. Spacecraft propulsion, of course, is almost entirely based on different forms of rocketry, though there are proposals to use jet engines to carry launch vehicles part of the way through the atmosphere.

Aerodynamics is the art of minimizing drag on the vehicle as it moves through the atmosphere, and—for aircraft—transforming a portion of the longitudinal force from the engine into lift. This is a bit more difficult to visualize,3 but relatively straightforward. It would have a much smaller role in an astronautical engineering curriculum, but a role nonetheless.

Controls is considerably more abstract. It combines aerodynamics, propulsion, and avionics to maintain static or dynamic stability for the vehicle, and make it do what the operator wants. Interestingly, this is both were hardware applications and systems engineering come in. It’s all about making the actuators, computers, and cabling play nicely together.

All of these fields would appear in an astronautical engineering curriculum, one way or another. With that out of the way, let me break down the approximate manner in which I would assemble it.

Firstly, I would substitute epistemology and economics for the worldly perspective requirements. Composition and oral communications would stay, though doing those in-house is obviously desirable.

Basic science and mathematics would necessarily stay, though I would personally prefer to see the course content described properly. For instance, instead of call it Physics I & Physics II, I would describe them as Mechanics and Electrophysics. The same goes for structural analysis—what we know here as Aerospace Structures I & II would be Determinate Structural Analysis and Indeterminate Structural Analysis, i.e. finite element analysis. That doesn’t necessarily communicate more information to freshmen, but it hardly communicates less. The rest of the structures curriculum is mostly fine—statics & dynamics, materials, and so on.

Propulsion would see significant changes away from air-breathing and towards vacuum-capable systems. Beginning with fluid mechanics and thermodynamics, we would explore spacecraft aerodynamics, rocket propulsion, and finally spacecraft propulsion. Aerodynamics is necessary for the controls curriculum, which would begin with basic orbital mechanics before moving on to spacecraft flight dynamics (including attitude control) and then move on to astrodynamics. A propulsion prerequisite might be useful, depending on the precise plan-of-study.

In the spacecraft systems focus area, we would begin with programming and electrophysics before moving on to circuits, spacecraft hardware, and instrumentation. These are some of the areas where I feel least confident in my engineering education thus far—despite spending a little time assembly a model airplane kit and the lab section of our electronics class, we didn’t really get much hands-on experience until the senior manufacturing project in Aerospace Materials & Processes. A dedicated hardware course might be worth the trouble.

Finally, the design courses. In most curricula, the various sequences culminate in a senior capstone. I question this approach. My current situation in airplane design is feeling dozens of disparate threads coming together immediately after the report block where I needed to understand them. I would vastly prefer to have this process happen earlier, so senior design could focus on skillful application.

My solution to this is to maintain some sort of integrating coursework throughout the undergraduate experience. My suggestion is to begin with an introduction to astronautics as a freshman seminar. This could progress to a history of spaceflight in the sophomore year. As a junior, I’d recommend an introduction to space system design and space mission architecture.

All told, my proposed curriculum looks something like this:

Note the suggested technical electives listed. Students could spend their senior year taking these alongside the spacecraft design capstone. The full list would be much more extensive; these are just a few obvious areas which might be interesting to focus in on. Advanced spacecraft propulsion, structures, or astrodynamics classes would also be offered.

I may enumerate a semester-by-semester plan of study after a bit more thought, but right now I’m not sufficiently certain which classes should go in which semester. Balancing the workload is important, in my experience, to avoid burnout in otherwise perfectly capable students. Just as the high school can’t be depended on to teach students mathematics, we can’t rely on them to teach coping and study skills. A carefully-curated ramp up will be necessary.4

Perhaps that will change by the time that such a curriculum is widely needed, though. In any case, dedicated astronautical engineering won’t be a common major for several decades, at least. I’m writing this mainly to satisfy my own curiosity, but also to discuss what the nascent programs should be doing in the meantime. As you may have noticed, I think developing practical, economic spaceflight is very important. We aren’t there yet, not by a long shot, but I’d like to hit the ground running when the powers that be get the message.

Till then, however, it’s all about squeezing what astronautics material I can from a pretty aeronautical-focused program. Speaking of which, I should probably go finish that spacecraft telecommunications homework.

1You will recall that I flunked out after two years of school. I returned at a different institution in the same major, and after another year found myself doubting the decision. If I could do it over, I would probably tell myself to study in engineering physics or mechanical engineering to pursue a more manageable and personally-relevant plan of study. By the time I’d realized this, however, I was absolutely not going to ask my parents to finance another two years of university just because I’d been ignorant going in. By now I’m entirely committed.

2Here at the University of Kansas, I would recommend dusting off that Global History of Aerospace Technology class, and getting it approved to fulfill the Cultural & Diversity Awareness goal. This would be such a logical and productive use of engineering credit hours that I cannot possibly expect it to be accepted by the Mickey Mouse departments.

3One of my structures professors once described aerodynamics as one of “the magic subjects” in comparison to his own field. I politely refrained to telling him that I found aerodynamics relatively transparent next to structures, which then even more than now felt like black magic. My suspicion is that this stems primarily from my extremely visual thinking style, which translates better to aerothermodynamics and orbital mechanics than to structural analysis.

4This is another point of criticism towards the program here: just when you think you’ve gotten the hang of things, the airplane of your academic performance slams into the concrete wall of junior year.

# Cassini and Me

Early this morning, while I lay sleeping, the Cassini spacecraft plunged into Saturn’s upper atmosphere. It had been in space over twenty years, and at Saturn for over thirteen.

The last image transmitted by Cassini, about 15 hours before impact.

Like the Galileo spacecraft before it, mission controllers intentionally configured Cassini to deorbit when it reached the end of operational life. Once the supply of maneuvering fuel is exhausted, there’s no way to control a spacecraft’s trajectory. Cassini would, eventually, crash into one of Saturn’s moons.

This isn’t a problem in-and-of itself—we don’t have much compunction about littering the Solar System with terrestrial debris. But we wouldn’t have any control over which moon, and that is a problem.

One of Cassini’s big discoveries was that Enceladus has liquid water plumes coming from its south pole. Both Enceladus and Titan (which is loaded with organic and pre-biotic molecules) could be potential abodes for life. Given that we can’t perfectly guarantee our spacecraft are sterilized of Terran microbes, disposing of Cassini in Saturn’s atmosphere is better than risking planetary contamination. The final, ring-grazing orbits concluded with a fly-by of Titan, a distant interaction robbing Cassini of just enough mechanical energy to send it into clouds below.

I agree with that logic, but the decision is bittersweet. In many ways, Cassini was the first probe that I followed through its entire science mission. I was paying attention when Cassini arrived, when the Huygens lander touched down on Titan, when the plumes were found on Enceladus, when the hexagonal storm was spotted at Saturn’s north pole. The other real contender for that title would be the Mars Exploration Rovers, Spirit and Opportunity, but the latter is still operating. Cassini, as of this morning, is over.

This famous Chesley Bonestell painting of Saturn from the surface of Titan greatly anchored my expectations for the Huygens probe.

The joy of discovery, however, is far from finished. Unless NASA finally comes around to nuclear propulsion or outer-planet aerocapture there won’t be many more Saturn probes in my lifetime, but most of Cassini’s results still haven’t reached my eyes. Even the Huygens probe, which only operated for a few hours during descent and landing, probably has some pictures I haven’t yet laid my hands on. And that’s before we consider the data from other instruments.

Space science, you see, isn’t just about snapping the prettiest photographs—though that’s certainly a part of it. We’re gathering information to test existing models of reality, and to begin the process of building new ones. Some will be refinements to our existing ideas, and some will be new notions entirely. When a scientist in twenty years has an idea about the way gas planets or their moons behave, they’ll have a wealth of information waiting to validate it with.

Artist’s rending of Cassini at Saturn. Note the high orbital inclination.

But there’s a lot of scientific value in those beautiful images Cassini sent back to us, too. Every kilo counts, and we didn’t cart those cameras to Saturn for the hell of it. We sent them to understand the planet’s atmosphere, its rings, its moons. We’ve learned so much we didn’t even know to ask about in 1997. Those pictures give us a better perspective on the science, and on our place in the universe.

Even the picture I’ve been using a personal motif the last couple years, of Earth seen from under the rings, is a Cassini image. Space exploration lets us see the view from a height, of our planet, of ourselves, and of our universe. This mission had to end, but it didn’t have to happen in the first place. We didn’t have to expand our knowledge and perception, because there’s no cosmic law dictating humanity choose wisdom over ignorance. We chose to send Cassini-Huygens to Saturn, and I’m very glad that we did.

## Wrong, Wrong, Wrong

### Aside

[You’ll have to take my word that this post was planned before Megan left a comment to much the same effect on Facebook. I still wrote it, because I love sharing space trivia, but because it took several more days to finish, my summer schlamperei cannot be questioned.]

Last week I discussed a mistaken explanation in one of my engineering textbooks. The specific explanation was wrong, but there’s two other issues with that innocuous caption in chapter one.

Hibbeler attributes a NASA image to a PhotoShop artist on Shutterstock. Now there’s nothing wrong with getting images from there. I find them a bit overthetop personally, but when has that ever been an impediment to the authors of textbooks on serious topics? Never, that’s when.

But why would you go through a stock image company when NASA images are public domain? It seems unnecessary, strongly suggests that author or graphic artist did a quick Google search, rather than having a clear image in mind. That brings us to the other problem.

This is a very specific, very recognizable image of Bruce McCandless operating the Manned Maneuvering Unit during STS-41B. You even see the same cloud patterns on the NASA website. And the last I heard, Bruce McCandless is a man.

Misgendering McCandless was obviously done for inclusion, but would it have been so hard to get a picture of a woman astronaut? It certainly would go further toward fixing the image of female spacetravelers in the reader’s mind.

Unfortunately for Hibbeler, there aren’t any pictures of women EVAing without a tether because no woman has ever operated the MMU. If that seems problematic, consider that the MMU was an experimental piece of technology that was really too dangerous to use regularly. Only six astronauts ever wore them, the last in November of 19841. After the Challenger disaster, NASA cancelled all the potential flights which might use the MMU and unofficially retired them from use.

But, we don’t really need a picture of a female astronaut operating untethered, because Hibbeler got it wrong. Astronauts aren’t weightless in orbit because they’re far removed from Earth’s gravity; they’re weightless because they’re falling around Earth at the same rate as their spacecraft and everything in it2. We can use an interior photo, this classic picture of Mae Jemison aboard Endeavour being a logical choice:

Now was that really so hard?

1To be explicit about it: including that final mission, only four American women had reached orbit, and only one had performed an EVA. The Soviet Union, meanwhile, only ever sent up two female cosmonauts. Tereshkova, in 1963, was basically a publicity stunt: she never returned to space and the Soviets resumed all-male crews until Svetlana Savitskaya launched in 1982, by which point it was clear that American women were going to space to stay. Nevertheless, Savitskaya beat Kathryn Sullivan to the first female spacewalk by 78 days.

2If we wanted pictures where the inverse squared law has kicked in, our selection is limited to the deep space EVAs during Apollo 15, 16, and 17. Performed during the coast back to Earth, terrestrial gravity had lessened, though their weightlessness was still attributable to free fall. However, our selection is all-male: Al Worden, Ken Mattingly, and Ron Evans.

# 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.

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.

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.

# Book Review: How to Live on Mars

I first read this book in high school, flushed on newly-found philosophy and bristling with plans for life as a commercial astronaut. SpaceX was just ramping up their ISS resupply program; Bigelow Aerospace was planning to launch another module before 2014. The possibilities seemed limitless.

That’s not the world we ended up living in. Astronauts haven’t launched from the United States in over five years. Virgin Galactic experienced LCOV during a 2014 test flight and put space tourism plans on hold while fixing the spacecraft’s control system. The biggest leaps forward has been landing Falcon 9 first stages, but it’s only in the last week that a used stage flew again. Falcon Heavy  still hasn’t been tested flown.

As such, the overall mood of Zubrin’s book feels….overconfident. Misplaced. Premature.

Our narrator is a congenial Martian colonist, giving us the down-low on what it takes to survive on Mars. It’s quite easy, he informs us, provided your follow his advice.

From choosing the correct transfer method to how to start a family, Zubrin (the Martian, not the 20th century astronautical engineer) walks us through the steps of becoming an economic and social success on the red planet. While many of the specifics are tailored to a fictional future history, the basic science is strictly factual.

It ranges from the mundane to the transcendental. At the more everyday end of things, we learn how to make plastics and almost every other raw material from the Martian soil and atmosphere. Through this avatar, Dr. Zubrin is making the case that living on Mars is entirely feasible. Steel and cement for construction, oxygen for breathing, nitrates for food—it’s all there. A few things would be a challenge (fictional Zubrin recommends stealing rocket parts as the best way to obtain aluminum), but the low-gravity environment greatly reduces the difficulty imposed by all sorts of engineering projects.

On the other end of the scale, we’re explained the general process of terraforming Mars into a habitable planet (and how to profit off it in the meantime). Now quite a few of these suggestions rely on a fairly specific potential architecture for the project, but the technical information holds.

This future history is amusing, though evokes a more cynical reaction from me after the last few years. I’m less optimistic about the odds of us reaching Mars before 2040, and less skeptical of NASA’s ability to get things done. To me, the issue seems to be less one of organizational competence and more of insufficient dedication at the highest levels (mostly Congress). While I’d like to believe that the private sector can fill that gap, it seems increasingly unlikely that they can achieve those ends at a plausible cost as the march of 21st century politics continues.

One thing he’ll probably have gotten right: the decay of terrestrial society into atomized, post-modern nihilism. I hope he’ll be proven wrong but there’s no strong signals to suggest that that trend is slowing.

On the whole, though, an optimistic book about the capacity for human ingenuity to conquer new frontiers and expand our understanding of the universe. Those interested in the project of space colonization, but unsure where to begin learning about, would be well advised to start with How to Live on Mars.