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.

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 + K = mr²w² + mv²/2. 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!