Category Archives: Science

Apollo and Dionysus

Neil Armstrong, in the LM after his historic lunar EVA with Buzz Aldrin

As I write this, it is 50 years to the moment after the Lunar Module Eagle ascended from the surface of the Moon, carrying a victorious Neil Armstrong and Buzz Aldrin up to their rendezvous with crewmate Mike Collins in the Command Module Columbia. Although I am too young to have personal memories of this event, I’ve been following the mission on its 50th anniversary through the web site Apollo in Real Time. It’s been exciting, and I, like many others involved in the space industry, have been driven introspective.

Why did we send Apollo 11 to the Moon, and why should we keep sending people to explore space?

The first question is all about geopolitics. The United States sent Apollo 11 to land on the Moon because the country wanted a very public way to demonstrate the superiority of its technical capabilities over the Soviet Union. The deep political worry at the time was that the USSR would not only beat the US to the Moon, but that they would emplace weapons there that the US could not counter-target — messing up the strike and counter-strike strategies underlying the insanity of mutually assured destruction. So, the US also decided to conduct its lunar landing in a way that would establish a specific set of norms for space exploration activities: We do this on behalf of all the people of Earth. We are here for science and knowledge. We show the world everything we do, as we do it. We come in peace, for all mankind. Apollo 11 literally left a model of an olive branch on the Moon.

But now the race is long over, and the norms established are taken for granted (if we remember them). Why continue? I find this a difficult question for me to answer — partly because I don’t believe several of the common arguments to be very compelling. Those arguments are science, spinoff technology, and inspiration.

Science is the easiest to dispense: our robotic probes reach across the Solar System, relaying extensive data back to scientists on Earth. The time, effort, and expense of sending a human mission to, say, Mars, absolutely dwarfs the cost of a robotic science mission. As an example, a recent report estimated the cost of a 2037 Mars mission as $120 billion (not including some other significant developments like a precursor lunar landing); the NASA Science Mission Directorate puts a cost cap of about $600 million on Discovery-class missions like the InSight lander, meaning we could send 200 robotic missions for the cost of one human mission. We would have to make sure that the science output of a human mission is at least 200 times better than the science of a robotic mission, and I’m not sure that’s a case one can make. Likewise, while space exploration, and human spaceflight in particular, has produced a great deal of technology that we now use on Earth in engineering, science, medicine, and daily life — those “spin-off technologies” are, almost by definition, ancillary benefits of a development program that had a different objective. This isn’t a bad thing (and NASA investment is far better at spinning off technology than, say, military investment)…but if we as a society have the goal of getting those technologies, we would just fund their development in the first place, rather than hoping that useful spin-offs come out of another program.

It seems to me like inspirational power is the most common reason cited to continue human spaceflight activities. Here, for example, is the current NASA administrator on Twitter:

Whenever someone tells me that the United States needs to inspire more students to study scientific and engineering fields, I want to ask them: What comes after this great inspiration? When a student says that NASA activities make them want to study math and science — are we, as a nation, going to invest in a technical education system to support their ambitions? Because, right now, we do not; those students are left hanging with the means already at their family’s disposal. And then suppose that these inspired students do get a degree in science or engineering: what do they do with it? Supposedly there has been a “STEM shortage” for years, but I do not see it materializing in a shower of job offers for recent graduates. Where are the university science departments desperate to fill vacant professorships? Where is the bipartisan call to expand the civil services of NASA, NOAA, NSF, CDC, and other national scientific agencies? Where are the private research and development organizations with a backlog of open lab positions to fill? Where are the engineering firm recruiters waiting eagerly outside the doors of college engineering buildings? Our lack of national investment in technology, research, and development belies our stated goals. And, in the vacuum, our previously inspired students are off to Google and Facebook to tweak the algorithms for selling users’ private data to advertisers.

My engineer’s brain struggles with the fact that I can come up with other rationales for human spaceflight, but they seem somehow squishier than the arguments above — the ones I don’t find very resonant after a little thought. After all, the arguments I described so far seem quantifiable: number of undergraduate degrees awarded in STEM fields. Number of scientific papers written by human spaceflight researchers. Number of commercialized technologies. Maybe the solution is to look at the problem with something other than an engineer’s brain.

I think the purpose of human spaceflight should be to expand human life out into the Solar System.

I also think that the reason we don’t often hear this statement articulated is that spaceflight proponents (especially NASA staff) don’t believe this argument will resonate with the public, but I believe they are wrong about that.

People get invested with spaceflight when the engineers, scientists, and astronauts involved connect spaceflight with human experience. Look at Neil Armstrong’s contemplative words as he took his first steps on the Moon. Look at Chris Hadfield singing “Space Oddity” aboard his own tin can. Look at the engineers at JPL whooping as a robot touches down on Mars. And look at the way these things catch the public eye, in a way that a purely technical accomplishment does not. Human experience has a value all its own — despite seeing the pictures and reading about the scientific results, I still want to ask the surviving Apollo astronauts, what was it like?! No, really, what was it like, on the Moon? I think it is worth having people living and working in space, for the sake of connecting the awesome experience of our cosmos to our humanity, and for creating an enduring example of what humans can achieve when we pull together and decide to build something.

Ultimately, I want to see permanent human habitation in space and on other planets. Beyond the romantic notions, there are some simple economic drivers that ought to push us in that direction. Any economic model that assumes growth, on a finite planet, is going to run into trouble eventually — and considering some of the anticipated resource shortages connected to the climate crisis, that point may come sooner than we think. (For another thing, with the world’s most powerful militaries blindly chasing “capabilities” in a way that brings us ever closer to nuclear war, I’d feel a lot more comfortable for the future of humanity if some of us were outside their reach.) No place that we’ve yet discovered will be as amenable to human life as the Earth, even in the face of climate crisis or asteroid impact, but that fact does not mean that we won’t eventually need to have humans off the Earth’s surface.

Now, if that’s really the winning justification for human spaceflight — having humans living in space and developing a culture that connects back to people on Earth — then that implies some changes to NASA’s objectives. Instead of having astronauts “learn to live and work in space,” NASA ought to get people actually living and working in space. This brings to light another reason why we may not see human habitation put forward as the reason for human spaceflight: I am asking for a major, concerted effort on NASA’s part; one that emphasizes long-term approaches to human spaceflight and spacecraft at the expense of the Apollo short-term race approach. We should be looking at regular launches to low Earth orbit, major development effort on in-situ resource utilization, designing and building large habitats that are amenable to long-term human life and work, and allowing a great deal of autonomy to the people in space. But, just as it’s nearly impossible for the US government to close unneeded military bases, it’s proven impossible to reorient NASA from the same kinds of work that has been done at each NASA field center for decades, going all the way back to the 1960s.

Which brings us, of course, to the reason why no humans have set foot on the Moon since the Apollo program: politicians like to have NASA, but they don’t like the implications of having NASA do things. Having NASA do things requires allocation (and re-allocation) of resources. They’ve tried to have it both ways, for decades, by splitting the difference. And we’re left trying to justify the space program as it is, with unconvincing arguments, instead of having a rationale behind the total human spaceflight endeavor and building a space program to satisfy that rationale.

Having a resonant driving force behind human spaceflight could help NASA maintain consistent direction in the decades to come. Do I have the winning argument? I really don’t know. But one thing’s for sure: the arguments we’ve been using so far aren’t working very well, if holding human spaceflight to steady progress is the goal.

Scientists Should March

Scientists are planning a “March for Science” in Washington, DC and many other cities on 22 April 2017. Some commentators seem to think this is a bad idea, because it would politicize science.

Before I continue, let me suggest the form an intellectually honest debate about global warming would take:


Global warming is happening.

It will cost $X to stop and/or mitigate global warming. If we do not stop and/or mitigate it, it will cost $Y to deal with the resulting property damage, logistical problems, loss of standard of living, food supply shortages, disease outbreaks, and security threats. $Y is much bigger than $X.


Okay. We think that from an economic, social, and security standpoint, we would be better off paying the smaller amount up front, $X, than having to deal with all those problems individually later on.


Okay. We think that the impact to certain market sectors would be too great to pay the $X up front. We think we are better able to pay installments of the larger cost $Y later on, as those various problems crop up.

Now, allow me to summarize the form the actual debate about global warming seems to be taking in the United States:


Global warming is happening.

It will cost $X to stop and/or mitigate global warming. If we do not stop and/or mitigate it, it will cost $Y to deal with the resulting property damage, logistical problems, loss of standard of living, food supply shortages, disease outbreaks, and security threats. $Y is much bigger than $X.


Okay. We think that from an economic, social, and security standpoint, we would be better off paying the smaller amount up front, $X, than having to deal with all those problems individually later on.


Global warming is not happening.


But we just told you that it is, and presented our evidence, and told you the cost of ignoring–


Stop doing science.

It’s easy to say that scientists should keep themselves in the business of producing scientific evidence and scientific conclusions, and stay out of the business of figuring out how to act on those conclusions. Science, after all, doesn’t tell us anything about morality or ideals, it just describes what happens in the world.

What does someone do, though, if they hold a particular position, and science produces definitive evidence suggesting that their position does not give them the result they want? In my field of engineering, the correct response to this scenario is to redesign my system so that I do get the result I want. I have to trust that the most up-to-date scientific theory is the most accurate description available of how my design will actually work, regardless of what I want my design to do. However, more and more, we are seeing a different strategy emerge in the field of politics: attack the science itself. Cast aspersions on the scientists. Talk about presenting “alternative facts,” as though physics behaves differently depending on one’s ideals. Cut off the ability of scientists to conduct their work, if one thinks that they will uncover evidence disfavoring one’s suggested course of action.

This is not a good way to solve problems.

What I believe scientists are standing up for in their march is simply the idea that decisions should be based on evidence. Conclusions should be based on a strong argument. Engineers know this. Businesspeople know this. Doctors know this. Scientists know this. Politicians should, too.

Scientists may not be perfect people, and an individual scientist’s conclusions may not be completely correct. Lots of factors feed into this: the tenure process, aggressive university publishing policies, limited funding, and severe competition leading to hype. But that is why we conduct science as a community, and as part of a larger iterative process. Scientists as a whole are always improving the state of knowledge. Others follow to correct and refine previous knowledge. As such, the current state of the art does represent the best available scientific description of the world. And, in many cases, that description has been converging. So, I can say with confidence: Global warming is happening, and human-caused, and has real economic costs. Vaccines don’t cause autism. GMOs are fine to grow and eat. The collapse of the bee population is going to cause big problems for agriculture. Coal power is just more expensive than natural gas (and, soon, wind and solar). Tax cuts for the wealthy are not as effective at stimulating the economy as government investment. No refugee from the Middle East has committed a terrorist attack in the United States. American police shoot black people at a disproportionately high rate. These are all things we can measure, facts based on evidence. There are no alternatives.

What do we do about these things? Do we do anything about them? Yes, those are questions for politicians to debate. But I can tell you this definitively: cutting off support for the science that produced evidence of a problem does not make things better. Politicians who advocate doing so are not going to help solve those problems, and we all need to remember who they are and how they are exacerbating our problems.

That is why scientists should call attention to their work and to their efforts. They need to remind everyone that evidence matters and decisions based on evidence matter. They need to remind people that experts have expertise. This march is not just about science, it is about the very idea that we can observe the world and use our observations to inform our expectations about the future. It’s about stating the reality of reality as opposed to “alternative facts.”

The idea that scientific evidence is a description of reality is not a political statement. I can understand how that might be hard to grasp, though, for a party whose paragon once took an incorrect position and said, “my heart and my best intentions still tell me that’s true, but the facts and the evidence tell me it is not.”

Guess what? The facts and evidence were right.

Space programs are not ambitious enough

This week, NASA announced the selection of nine instruments for a proposed mission to Europa. Europa is probably the best place we know about to find alien life, and the discovery of alien life would surely be an achievement rivaling the moon landing in NASA – and human – history. I have an issue with the thinking presented by NASA in its press releases, though. Agency spokespeople say things indicating that the purpose of the Europa mission is to determine whether or not Europa “could be habitable.” The exact phrase on the web site linked to above is that this mission is part of “our search for oases that could support life” (emphasis mine). That’s not what I want from a mission to Europa. Probes to outer planets come decades apart, so I want to get as much done in a single shot as possible. What I want is to determine whether or not there is life on Europa.

The important difference between those two statements – determine whether Europa could support life and determine whether Europa has life – betrays a slight difference in ambition. I want the big-risk, big-reward activities and objectives of a true moonshot. NASA is hedging its statements, and lowering the bar of its mission goals.

I’m coming to believe that the statement about Europa Clipper’s objectives is symptomatic of a general lack of ambition in NASA’s modern thinking. You can see it in other statements the agency makes: Mars Science Lab Curiosity‘s mission was to determine whether Mars, at some point in its past, could once have been an environment that supported life. The oft-repeated purpose of the “proving ground” activities in the human spaceflight program’s “Journey to Mars” campaign is to “learn how to live and work in space.”

I don’t want to do those things. I want to find out if there is life on Europa; similarly I want to find out if there is (or was) life on Mars, and I want people to live and work in space.

Ironic that a space program – of all things – would lack ambition, isn’t it?

You might think that this is just the public relations spin. NASA is trying to manage expectations, so that they know they can achieve the first objectives of any mission and claim success immediately. Then they can parade that success in front of Congress, while the scientists go after their real scientific objectives in the “extended mission.” But I think the underlying philosophy here is penetrating beyond the publicity level into the actual mission design. It’s easy to find statements from scientists, engineers, and NASA spokespeople that Curiosity couldn’t actually find life on Mars unless that life walked in front of its camera and waved hello. To me, those statements beg the question: why not? We sent a nuclear-powered jetpack-landed laser-toting robot all the way to Mars, why wouldn’t we put some instruments on it that can identify basic things like amino acids? Similarly: NASA sends a probe to Jupiter approximately once per decade (and slowing). Since that rate keeps dropping as time passes, why wouldn’t we try to answer the big questions as soon as we can?

The way NASA now formulates its missions, I can just imagine a variation of Kennedy’s famous moon landing speech: “Our nation should dedicate itself to the goal, before this decade is out, of lifting a man five inches above the surface of the Earth. If that is achieved, this mission is a complete success. As a stretch goal, we might have that flight go to the Moon.”

The great thing about opening up the ambitions of our space program is that it would enable engineers to implement known solutions to the problems we face in space. For example: we know that humans have health problems after spending long periods of time in microgravity. Do we need to keep answering the question of whether or not humans have health problems after spending long periods of time in microgravity? Or can we instead think about the details of building spacecraft that spin to provide artificial gravity? Similarly, we know that there are extreme logistical challenges in sending people to Mars. Do we think about long a mission we could run given the amount of food we can send up with our astronauts, or can we think about the details of having them grow food on Mars?

The difference between those questions is the difference between “learning to live and work in space” and “living and working in space.”

It’s also the difference between the space program we have, and the space program we imagine.

What is the nature of the STEM crisis?

There is a recent National Science Foundation report out that says, over the decade from 1993 to 2013, the number of college graduates in science and engineering fields grew faster than the number of graduates in any other fields. By 2013, we got up to 27% of college graduates getting their degrees in science or engineering. Hooray! STEM crisis solved, right?

I actually see something in this report that I find quite worrying, and a sad commentary on the state of science and engineering in the United States.

The report says that only 10% of all college graduates got jobs in science or engineering fields. That statistic means that, although 27% of our graduates are in STEM fields, at least 17% of graduates got their degree in science or engineering but couldn’t find a job in any scientific or engineering field. Put another way, at least 63% of STEM graduates couldn’t get a job in STEM fields!

The STEM crisis, in my opinion, isn’t about the number of graduates. It’s about the support our country and society gives to science and engineering. Our government has forsaken basic research in favor of maintenance-level defense tasks and austerity. Our companies have forsaken applied research in favor of “killer apps” and next-quarter profits. In light of those actions, it’s no wonder that we’re now worried that other nations might leapfrog us technologically.

If we want to get out of this hole we dug, we need to dramatically increase our support for science, engineering, and innovation.

Threat assessment

Sometimes, I wish I had more Republican Congressmen to write to.

Human-caused climate change is a national security issue. It threatens our lives, our property, and our way of life. And it is the only thing that we know, for a scientific fact, will threaten the American people in the future. We ought to start treating it as such, and start investing, on a national scale, in stopping it.

Ignoring the problem is, in my mind, tantamount to embracing Chamberlain’s security strategy in the late 1930s: a course for further destruction and calamity.

Despite tactical errors, Bill Nye is right

Tuesday night, Bill Nye (the Science Guy) had a webcast debate with Ken Ham, founder of the Creation Museum. In many respects, this was a silly idea. Nye wasn’t going to change any minds, and I think he fell into the traps creationists try to set: distracting him into side issues, for example, or redefining the terms of the debate. Moreover, the Creation Museum benefited monetarily from the event.

I admire Nye for being willing to make the attempt, but in the end, I think the event was a wasted opportunity. The whole reason for the debate was not to contest the relative merits of creationism versus science. Rather, the spark for the event was Nye’s contention that teaching creationism in schools is dangerous. And I agree with him – for two fundamental reasons that Ham illustrated beautifully throughout the debate, but I don’t think Nye ever articulated. Continue reading Despite tactical errors, Bill Nye is right

Let’s go to Europa already!

I’ve been thinking I should write something about the recent discovery of geysers from Europa’s subsurface ocean, but Casey Dreier at the Planetary Society blog basically said everything I want to already.

Europa appears to have all the ingredients for life as we know it: liquid water, energy sources, organic molecules. Scientists have known these things since the Galileo mission to Jupiter. But we haven’t gone back to look for life under the ice – because designing and mounting a mission to do so would be a multi-year, expensive effort. It’s much simpler, and less expensive, to think about smaller missions to Mars, which could launch at a cadence of once every couple years. However, the scientific, societal, psychological, educational, inspirational, and public reward of discovering extraterrestrial life certainly would make a multibilliondollar Europa mission worthwhile.

What the new discovery gives us is easy access to Europa’s subsurface material. Perhaps we can sail a probe through these geyser plumes, testing for biological components. Perhaps we can trawl a few space squid while we’re at it. The easy access, while not up to the same level as Mars, certainly makes a Europa mission easier to think about than one that has to drill through a hundred kilometers of ice!



So, the Mars Science Laboratory “Curiosity” has discovered evidence that, about three billion years ago, the environment on the planet Mars could have supported Earth-like microbial life. Some news outlets (including the MSL Twitter feed) are billing this discovery as the accomplishment of Curiosity’s mission.

I have a confession to make.

I don’t really find this discovery all that exciting.

The MSL team’s discovery is a confirmation of a long-expected hypothesis. (Indeed, with the number of planetary environments out there, it would be statistically silly to think that Earth is the only life-supporting place!) It’s valuable to know, and it’s important to the scientific method to rack up such confirmations even when we’re as sure as we can be, but it doesn’t exactly have the same allure as striking out into the unknown. I think the spirit of exploration is important to maintain in our space programs, because brand-new missions and discoveries are what keeps space exploration in the public eye. After all, a recent study shows that not only do most Americans want to see exploring Mars as a national priority, but most Americans want to see a human mission to Mars and three-quarters of Americans want to see the NASA budget doubled. I am confident that the dramatic landing of the Curiosity rover, with its brand-new mission architecture, has something to do with that enthusiasm.

There’s also something I find slightly foreboding about Curiosity’s confirmation. In 2011, the National Research Council’s Planetary Sciences Decal Survey of Solar System exploration listed and prioritized the objectives of our planetary science program for 2013 through 2022. This is a study done every ten years to identify which of the flagship-sized missions NASA should fund, design, and launch in the coming decade. First on the list for 2013-2022: a mission to return samples of Martian rock and soil to Earth. The announced “Mars 2020” rover is in line with that objective.

I’m going to go out on a limb and predict the conclusion sentence of scientific findings from a Mars sample return mission:

Chemicals and minerals present on the surface of Mars indicate that ancient Mars may have included wet environments able to support Earth-like microbial life.

In other words, I don’t think a Mars sample return mission will give us any dramatically new information that we didn’t already have from MSL, MER, MRO, or any of the Martian samples we already have. See what’s got me worried? I don’t think we’re going to actually discover life – in fact, I would be very surprised if the 2020 rover included any instruments actually capable of recognizing a Martian if it walked right up, poked the rover with a Martian stick, and walked away. (Curiosity doesn’t!) I am afraid that we will put this rover on the Red Planet in 2020, cache a sample, retrieve the sample in 2030, and the public response will be, “wait a minute, we spent two decades confirming what we already knew in 2013? Come on, space program…where’s my jetpack?”

A Mars sample return mission would be a triumph…for the niche sub-field of Martian geochemistry. I don’t think it would have the sort of broad scientific and public impact that we should expect from a flagship-scale mission. Basic research science plods along, making incremental improvements in understanding and slow-but-steady progress. NASA should be sticking its neck out, thinking big, and going for the most challenging – and rewarding – missions. Instead of looking for environments that might have been habitable three billion years ago, we should be looking for actual life.

You see, even before MSL’s discovery, we already knew of the existence of a watery, potentially life-supporting environment. Jupiter’s moon Europa has an icy crust with a subsurface water ocean beneath. The ocean is warm enough to be liquid, because of the energy input from Jupiter’s tides. And scientists have found that that ocean contains lots of salts and minerals – and even organic (carbon-containing) compounds. Liquid water, energy sources, and chemical building blocks: everything an Earth-like life form needs! The main difference between Europa and Mars is that, while we’ve been able to observe the desolation of the Martian surface for decades and know that we could only expect to find evidence of ancient microbes, we have no idea what’s under the Europan ice sheet. It could be nothing…but it could also be life as rich and complex as what we find, on Earth, under Antarctic ice, in sealed cave systems, or around hydrothermal vents. Unlike Mars, where we have been forming preliminary conclusions for years, we won’t know until we get something under that ice layer. That’s the kind of exciting exploration work that I want to see from my NASA flagship missions.

The Decadal Survey did recognize the potential for alien life on Europa. Its executive summary says that “the second highest priority Flagship mission for the decade 2013-2022 is the Jupiter Europa Orbiter” but notes that “that both a decrease in mission scope and an increase in NASA’s planetary budget are necessary” to fly a mission to Europa. Personally, I’d prefer to discover alien creatures within my lifetime…but I don’t make policy or control the purse-strings. So, instead, off to Mars we’ll go again.

Original Fiction: “Conference” (final draft)

I had been trying to sell this story for a while now, but was not successful. There’s a bit of a catch-22 to selling a short story for the first time: without any feedback from editors and readers, there is no way for me to tell whether a rejection was because the story didn’t align with a publication’s interest at the time, or whether they didn’t think the story was very good. (And if it wasn’t very good…what it did wrong.)

This makes me sad, because I got lots of positive feedback from people who went to graduate school in a technical field. I think that maybe that’s the problem: the story appeals to too much of a niche crowd.

Anyway, here it is, the version of the story I most recently tried to sell. It’s about a young scientist presenting her findings at a research conference, and the unexpected reception she encounters there. It was inspired by some of my own experiences in grad school.


The numbers didn’t match up. Ceren Aydomi tapped her desk, frowning at the resonance spectra before her. The projections cast pale purple and green light over Ceren’s face, spilling down the front of her body and glinting from the polished glass surface of her desk. The peaks of each spectrum marched onward, rapidly deviating from her calculations. And the Three Hundred Seventy-Eighth Channel Interstice Studies Meeting was only two days away. Continue reading Original Fiction: “Conference” (final draft)

What’s the deal with Lagrange Points?

You may have read about rumors that NASA is considering building a space station at a place called the “Earth-Moon L2 Point.” The “L” is short for “Lagrange,” and this is one of the places in space known as a “Lagrange Point.” Unless you’re familiar with the basics of orbit mechanics, you may be wondering – who the heck is Lagrange, and why does he have points in space? More to the point (ha!), why is NASA interested in building a space station there?

To explain what a Lagrange Point is, I’m going to take you through a couple analogies.

Imagine you are standing on the top of a perfectly rounded, symmetric hill.

Right where you are, the ground is flat and level. You don’t feel any forces moving you one way or the other: you are in equilibrium. But if you take a step in any direction, the ground begins to slope and a force pulls you out further away from the top of the hill. The magnitude of this force is your weight, times a factor that accounts for the angle of slope:

The force always pulls you out from the center of the hill. Let’s call this direction r, for “radial.” There’s another direction on the hill, the “circumferential” direction c – this is a direction that always takes you walking around the hill in a circle. There is no component of force pulling you in this direction.

From physics classes, you are probably familiar with the idea of potential energy. Potential energy is a quality associated with points in space, and we express that quality with a single number measured in joules. Where I am sitting, space might have a potential energy of six joules, and where you are standing space might have a potential energy of ten joules. This energy comes from sources like gravity or magnetism. The difference in potential energy between two points tells us how much work it takes to move something from one point to the other: if I want to visit you, I need to spend four joules of energy. If you visit me, you actually get four joules out of the deal, which you can spend on something else (such as moving faster).

Potential energy has a direct connection to force. If you are in a place which has a high potential energy, and nearby is a place with low potential energy, you will feel a force pushing you towards the lower-energy spot. Mathematically, we say that the force is equal to the gradient of the potential energy. So, on this hill, the top of the hill has the most potential energy (we’ll call it zero, though) and there is less and less energy as we move off in the +r direction. In the c direction, the potential energy is always the same, depending on your current position in the r direction. If you go up the hill, in the direction –r, you will go towards higher potential energy and the force of your weight will work against you. You could imagine making a topographic map of the hill, only instead of the contour representing different heights, they represent different potential energy levels.

If you were to let yourself go and slide down the hill, your total energy would be about constant. You may recall the definition of kinetic energy: mv2/2, where m is your mass and v is your speed. The sum of potential and kinetic energy must stay the same, so as you roll and your potential energy drops, your kinetic energy (therefore, your speed) will rise. The equation for your total energy will have the pieces from both, though: E = U + K = –mgrsin(theta) + mv2/2. Notice that in this equation we have one term that depends on our position in space and on term that depends on our speed.

Got the hill down? Great. Now I’m going to stick you someplace else!

Suppose we go and find a merry-go-round, and we convince the operator to clear out all the horses and chariots and stuff so that it’s just a big, flat, rotating disk. Let’s also put a curtain around the outer edge, so that we can’t see outside from within. Then, you go and stand in the very center and we slowly start rotating the disk until it reaches a constant, slow angular velocity.

In the exact middle of the disk, you will notice very little. However, take one step away – in the +r direction – and you will begin to feel a centrifugal force: a force that you perceive as pulling you outwards. But thinking about forces in rotating reference frames is hard, and we’ll immediately get into pedantic debates about which forces exist and which don’t. So let’s think about energy again!

The disk is flat, so every point on it will have the same gravitational potential energy – it doesn’t really matter what that energy value actually is, since it’s differences in potential energy that are valuable, so let’s call it all zero. As you walk in the +r direction, you will have kinetic energy from two sources. First, there is your own motion, which contributes energy mv2/2. Second, there is the energy you have from spinning in a circle, because your feet are on the disk. If the spin rate w of the disk is slow enough, you might not notice it, but it’s there – and the energy is mr2w2.

Your total energy, therefore, is U + Kmr2w2mv2/2. Now–

Huh. Wait a second. That equation has a term that depends on your position in space and a term that depends on your speed. The piece that depends on speed is exactly what we had on the hill, too!

The piece that depends on position doesn’t quite look the same as it did on the hill. However, it has one very similar property: when you move out in +r, the value of that term changes. And, therefore, the magnitude of your speed v must change to keep the total energy constant! We can debate about whether centrifugal or centripetal forces are real, but effectively, the equation for your total energy behaves in the same kind of way on the spinning disk as it does on a hill. Effectively, your entire kinetic energy trades back and forth between the “translational” mv2/2 part and the “rotational” mr2w2 part, just as on the hill it traded between K and U.

So let’s call mr2w2 your “effective potential energy” on the disk! It behaves just like any other kind of potential energy – gravitational, magnetic, chemical, whatever – would, because it is energy that depends only on your position in space, even though it’s actually kinetic energy. We could even make a contour map of the effective potential energy.

Okay, then. Lagrange points, right?

Imagine the Earth and the Moon, sitting in space near each other. Don’t worry about orbital motions yet – just pretend that the two are fixed. Each body has a gravitational field, which we can visualize by a contour map of potential energy levels: far away from both the Earth and Moon, an object would fall generally inwards toward them, with potential energy decreasing as it goes in. The closer an object gets to either body, the stronger the gravitational pull, so the contour lines must be spaced closer together. And somewhere in the middle, the gravitational force of the Earth and Moon will balance each other exactly, so there is a level spot in the potential energy map.

This isn’t the whole story about bodies in space, though, because the Earth and the Moon aren’t fixed. They orbit around each other. An object we place near the Earth and Moon will also orbit around them. And because of that orbital motion, the energy of the object must include a component from rotation – which we can incorporate into the effective potential energy map around the Earth and Moon. Picture sitting in a spaceship somewhere “above” the Earth-Moon system that rotates at the same rate as the Moon orbits the Earth, such that from your perspective the Earth and Moon appear fixed in space. Then the effective potential energy map must have a component accounting for that rotation, just like on the merry-go-round. The map will look something like this:

Notice that there are five places on the map where the “topography” is locally flat – meaning that there is no net force acting on an object there. Between the Moon’s gravity, the Earth’s gravity, and the objects’ own orbital rotation, objects in those locations are at equilibrium!

These are the Lagrange points, and this is what makes them special: place a satellite at a Lagrange point, and it will stay there.

The reason why these points are attractive places to put a space station is because it’s easier to get to Lagrange points from the Earth’s surface than it is to go all the way to the Moon – and vice-versa.  In terms of our effective potential energy map, we have to cross fewer contour lines to get from the Earth to, say, L2 than we do to get to the Lunar surface. Every time we want to cross a contour line, we gave to make our spaceship gain or lose kinetic energy, and that means firing the engine – so crossing fewer contour lines directly corresponds to using less propellant or power.

If NASA located a space station at L2, then it could launch crews to the station with a smaller rocket than it would need to put the same crew on the Moon. NASA could also launch exploration vehicles and extra fuel to the station, so that the crew could eventually shuttle from the Earth to the station, and then take the station-to-Moon express from that point, at their leisure.

So: The reason why a station at L2 is exciting is not that L2 is an especially exciting place, but that the station would be part of a larger space exploration architecture. Not just flags and footprints, but more stations and vehicles and astronauts!