In the critically acclaimed video game Outer Wilds, you play as an astronaut from a newly space-faring species in a little solar system. With your wooden spacecraft, you can explore your solar system and unravel the archeological mysteries left behind by another space-faring race. I’ve been playing through it with a group of friends, and one thing that struck me is how self-consistent the game’s physics engine is. For example, momentum is conserved, each planet has a gravity well, and gravitational slingshots seem to be possible. So I decided to see how far I could take this idea.

For those of you who don’t know me, I’m a card-carrying professional astrophysicist. In this article, I do my best to leverage this expertise to reverse-engineer some of the physics in the game.

The constants of Nature

As a first pass, I am going to assume that the fundamental laws of physics in the game are the same as our universe. In other words, I’m going to assume that the equations that govern Outer Wilds are the same as our universe. But I am going to allow the physical constants that go into these equations to change. In other words, the numbers in those equations are allowed to vary. This is things like Newton’s constant of universal gravitation, which controls the force of gravity, and the speed of light.

This is obviously not entirely satisfied; many parts of the game are not physically accurate. The game is under no obligation to obey the laws of our universe. It’s a work of fiction, after all. It has an obligation to take liberties when those liberties serve the narrative and the player experience. Indeed, we’ll find we run into issues pretty quickly. However, let’s see how far we can take it.

In the process, I hope to show you a little bit about how an astrophysicist thinks about measurement, and how astrophysical knowledge is built up piece by piece by a sequence of measurements. All of the calculations we’re going to do are something a first year physics student could perform. There will be some basic math and equations in this article, but I will try to explain what they mean in words so you don’t actually have to read the math if you don’t want to.

On spoilers

Outer Wilds is a game with some pretty big twists and I’m going to do my best not to spoil you, at least in this article. I am going to say place names and name some tools in the game. I am also going to slightly spoil one location. However, none of the puzzles, central conceits, or central mystery will be spoiled. If you want to play the game completely blind, stop reading here. If you’re okay with minor spoilers, read on.

Strategy

So how in the world (or off of it) are we going to measure physical constants? We can’t exactly set up an experimental apparatus. The game gives us a few tools to help us make measurements. When we travel between locations, the game gives us a current speed in meters per second (I assume). Additionally, we get coarse distances to locations we travel to. We also have a key tool: the scout launcher. The scout launcher lets us launch a little probe. We can take pictures with the probe, but we can also drop it in a location and the game will tell us how far away we are from our probe no matter where we are. This means the player character and the scout form two ends of a measuring tape. We can place the scout at one end of a distance we want to measure, then travel to the other end. Over the course of playing with some friends, I made many of these measurements and recorded them in my laboratory notebook for you, dear reader.

As I go through the analysis, I will be showing you pages from my notebook. This is partly because I think it’s fun, partly because I think the diagrams are useful, and partly because I want to give you receipts. Note that these notes are pretty sloppy by scientist standards. I’m a sloppy guy, but also this is for fun, so I’m not being as careful about measurement errors, significant figures, etc.

We are also going to need to measure times. This is more challenging, as the game gives us no tools to measure duration. The best we can do is measure things during gameplay with a stopwatch.

A time unit

The first thing to confirm, then, is that time passes in the game world at the same rate as in our world. The game reports velocities in meters per second: is that a reported game meter per a second as measured by my stopwatch? Or not? To confirm this, I and my esteemed colleagues (friends playing with me) performed the following experiment: Measure the distance between a planet and the surface of the sun, and then fly into the sun at a velocity as close as possible to a fixed number, as reported by the game. If the seconds reported by the game are really the same seconds as experienced by the player, the amount of time it takes for us to fall into the sun and die should be given by:

time = distance / speed

We chose to launch ourselves into the sun from Timber Hearth, which is the home planet of the player character. To measure the distance to the sun, we dropped a probe on “Sun Station,” a little space station orbiting just above the surface of the sun. We performed the experiment with a velocity of 200 m/s and a velocity of 100 m/s, the best we could. Since the gravity of the sun pulled us towards the planet, this required a steady hand on the retro-rockets. Here’s the page from my lab notebook:

Fortunately, it does appear that a second as measured on my stopwatch corresponds to a second as described by the game. This will come up again later, as the times in the game are, obviously, quite short to support player interaction and the small, self-contained game world. (The game world has no, ZERO, loading screens by the way.)

Newton’s constant

Armed with the knowledge we can trust our stopwatch, let’s now compute Newton’s constant. This is the constant in Newton’s law of universal gravitation:

where here is the force of gravity experienced by two masses and , is how far apart the two masses are, and is Newton’s constant, the thing we want to measure. To measure Newton’s constant, we’re going to borrow a bit from modern astrophysics and a bit from the fascinating history of measuring this constant in our own universe.

A common measurement in modern astrophysics is to use orbital periods to measure masses of distant planets. This is because Keppler’s famous laws of planetary motion tell us that the time it takes for a planet to orbit a star is determined only by the distance it is from the star and the masses of the planet and of the star. Intuitively, this is because the force of gravity is required to hold the planet in a circular orbit, otherwise it would fly off in a straight line and the acceleration due to gravity must resist the inertia the planet has, which is proportional to how fast it’s going.

Indeed, tight binary star systems such as pulsar binaries are excellent targets for measurements of this kind, because they have very short orbital periods. Many precision tests of nuclear physics and general relativity have been made this way, including a Nobel Prize-winning measurement.

Fortunately for us, there is a binary planet system in the solar system of Outer Wilds: the Hourglass Twins. The Hourglass Twins are the planets closest to this system’s sun. They’re approximately the same size and they orbit each other with a very short orbital period. We can make use of the orbital period of the twins and Keppler’s laws to compute that the product of the mass of one of the twins and Newton’s constant is given by

where is the math constant, is the orbital separation, and is the orbital period. To go further, though, we need the mass of one of the twins. (We’ll assume they’re equal mass.)

In my article The Men Who Weighed Mountains, I described an early attempt to measure Newton’s constant where scientists measured the force experienced by a test mass from the gravitational pull of mountains. To do this, they had to estimate the mass of the mountains in question. They did so by estimating the volume of the mountain, measuring composition the best they could, and assuming uniform density (density being mass per unit volume). We will do something similar.

Rocky planets like our planet Earth are mostly made up of a mix of iron and nickel. Metals of this kind are fairly incompressible; it takes enormous force to make them denser than they want to be. So to good approximation, rocky planets are of roughly constant density. Somewhat arbitrarily, I’m going to assume the Hourglass Twins are roughly the same average density as Mars, which is roughly 4 gcm, or four grams per cubic centimeter. That’s roughly four times the density of water. Now if we know the volume of one of the Twins, we compute the mass as simply

mass = density volume

We can get the volume by computing the radius and using the formula

So to summarize, we need to use our scout to measure:

• The orbital separation of the Twins
• The radius or diameter (equivalent) of one of the Twins
• The orbital period of the Twins as they orbit each other

Here’s my lab notebook page with the measurements:

If we work out the numbers, we find that:

• The volume of an individual Twin is about cm
• The mass of an individual Twin is roughly g
• Our estimate for Newton’s constant is dyn cmg

To give you a sense of scale, the volume of Lake Erie (which is essentially a freshwater inland sea) is cubic centimeters, so 100,000 times larger than the volume of one of the Twins. Each Twin would roughly fit into a medium-sized pond. Newton’s constant in our universe is about dyn cmg. So the force of gravity in the universe of Outer Wilds is roughly 100,000 times stronger than in our universe.

You’ll note that I’ve moved to using centimeters, grams, and seconds as units, rather than meters, kilograms, and seconds. This is just habit from astrophysics, where the former unit system is much more common. The scientifically savvy among you might also notice I’m being very sloppy with my significant figures. Assume we’re good to about two no matter how many I report.

On the simplicity of assumptions

The scientifically savvy among you may also notice a lot of typical physicist “assume spherical cow” in my calculations so far. This will continue. The reasons for this are a few-fold. First, I am a physicist so it’s in my nature to assume spherical cow. Second, we are limited to what we can actually measure in the game, which is not a lot. Finally, the numbers we’re computing have big exponents in them: Newton’s constant in this universe is 100,000 times larger than in ours. If I mess up a measurement by even a factor of two, I might change that 100,000 to a 200,000 or a 50,000, but I’m not going to change it to a 10.

The calculations I’m performing here are what physicists and astrophysicists call a “back-of-the-envelope” calculation. It’s a rough, quick-and-dirty, calculation to get an answer that is qualitatively right, but may not be quantitatively 100% right. It’s an essential skill in the field. In astrophysics, the numbers are often huge, so back-of-the-envelope frequently plays a bigger role.

The speed of light

This is a fun one, but it does involve spoiling you a little bit. One of the planets in Outer Wilds is Brittle Hollow. Brittle Hollow is a rocky planet, but as you explore it, you quickly discover that the interior has mostly been consumed by a black hole at the center of the planet. I love this for a lot of reasons. For one thing, the gravity on the planet’s surface is normal, as it would be if the mass in the planet’s interior had been completely transformed into a black hole; after all, it’s the same amount of mass, just in a smaller space. For another thing, the game has gravitational lensing effects showing light bending around the black hole near the event horizon. It’s just… fantastic.

One surprising thing about the black hole, though, is that it’s so big! In our universe, a black hole the mass of the Earth would have a radius of about one centimeter! So what’s up with the event horizon of Brittle Hollow’s black hole? Well, to understand that, let’s first very briefly discuss what an event horizon is. A black hole’s event horizon isn’t really the black hole’s surface; rather, it’s the distance away from a black hole where the gravity is so strong that even light can’t escape.

But let’s think of it a different way. You may have heard the term “escape velocity.” The escape velocity is the speed you need to be going to get away from the gravitational pull of a planet. (Formally it’s the speed where your kinetic energy is equal to the gravitational potential energy of the planet’s potential well.) The escape velocity for planets is typically defined in a way that assumes the escaping object is starting from the planet’s surface. But there’s an escape velocity for every distance from a planet. Infinitely far away from Earth, Earth’s escape velocity approaches zero. You can think of an event horizon as the distance from the black hole where the escape velocity is the speed of light. Since the speed of light is the speed limit of the universe, that’s it. You can’t escape.

This fact explains Schwarzschild’s famous formula for the radius of the event horizon of a non-spinning black hole:

where here is Newton’s constant, is the mass of the black hole, and is the speed of light. (Fun fact: this exact escape velocity argument was made long before general relativity was discovered, although you need GR to make accurate quantitative predictions.) So if we can somehow estimate the mass of the black hole and the radius of the event horizon, we can compute the speed of light!

We’ll compute the mass of the black hole by computing the mass of Brittle Hollow the same we computed the mass of the Hourglass Twins, and then we’ll assume the black hole has eaten up most of the planet, say 75% (arbitrarily). The diameter of Brittle Hollow can be computed easily by placing the scout on the north pole and walking to the south pole. To compute the radius of the event horizon, we fall through a hole in the crust of the planet near our scout and measure the maximum distance before we fall into the black hole. That gives us the following measurements as shown in my lab notebook:

From there, we can calculate the radius of the event horizon by taking the radius of Brittle Hollow (which is half the diameter) and subtracting the distance we fell. The long and short of it is that:

• Brittle Hollow has a radius of 308 meters or cm.
• The event horizon of the black hole has a radius of 53 meters, or 5300 cm.
• This gives Brittle Hollow a volume cubic centimeters.
• And this means the black hole has a mass of grams.

If we invert all that, we get a speed of light of centimeters per second. This is about 3 million times slower than the speed of light in our universe. In fact, it’s about the same as the speed of sound in water! The implications of such a slow speed of light are too broad for me to examine here, but they’d be fun to think about!

Measuring the mass of the sun: It all breaks down

As scientists, it’s important that we cross-check our conclusions. Do all the assumptions we’ve used make sense? If we try to make another measurement in a different way, does it agree with what we’ve computed here? If not, something is wrong. I wanted to live by this wisdom, so to that end, let’s check ourselves. We can compute the mass of the sun in much the same way that we computed Newton’s constant with the Hourglass Twins.

We can take a planet and measure how long it takes to orbit the sun. Because we already computed Newton’s constant, we can then use Keppler’s formula again to compute the mass of the central body about which the planet orbits: the sun. I chose Timber Hearth, since I’d already measured it carefully for the timing measurements above. (Note that Keppler’s formula for the Twins and for the Timber Hearth orbit differ by a factor of 2, because I assumed the twins have the same mass. Here, on the other hand, I assume the sun’s mass dominates over Timber Hearth’s.) Here’s the notebook page:

I was only able to get measurements of the distances from the planet to the far and near sides of the sun, which are pretty different from each other, because the sun is huge (by the game’s standards). However, we need the distance to the sun’s center for Keppler’s formula to work, so I average the distances to find that the distance from the center of Timber Hearth to the center of the sun is 8.6 kilometers, or centimeters. The orbital period of Timber Hearth is 250 seconds.

When we plug these numbers into Keppler’s formula, though, we hit a snag. We get a mass for the sun that’s about grams. That’s smaller than Brittle Hollow! This is a huge consistency issue, because I’ve been assuming that the sun is much more massive than the planets, by many orders of magnitude. It needs to be for the planets to orbit it properly. The sun is certainly visibly much bigger than the planets by eye.

This suggests we’ve done something wrong. A few possibilities:

• Perhaps it was not safe to assume constant density to compute the masses of planets. Or perhaps the densities we chose were off. The mass of Brittle Hollow is so much larger than the sun that we’d have to be way off, though. If the rocky planets are in fact made up of compressible material, that might have implications.
• Perhaps, due to Brittle Hollow’s unique structure, the mass it should have is very different from what one gets by simply measuring the volume enclosed by the surface.
• Perhaps Newton’s constant in this game is not a constant at all and varies by distance. This would be akin to saying we got the laws of physics wrong. An analogous issue in the real world would be our lack of understanding of, say, dark matter.
• Perhaps the black hole is less massive than we thought due to its special properties. There’s something here I don’t want to spoil, but suffice to say, perhaps that black hole has some special properties.
• Similarly, perhaps my assumption that the sun obeys the laws of physics as I understand them is not correct. Again, I don’t want to spoil, but the plot of the game may indicate something like that is the case.

Or perhaps we’ve simply reached as far as we can go, given that this is a video game and not necessarily a physically self-consistent universe. I think that’s probably where I land. In any case, I’m not sure where to go from here. We could attempt to compute the mass of the sun another way, for example by using the physics of stellar structure. But unfortunately there’s another physical constant required for that modelling, Planck’s constant, which we never nailed down.

If we had measured Planck’s constant, we would have in some sense gotten everything. All physical constants can be derived from three starting constants, and Newton’s constant, the speed of light, and Planck’s constant are the canonical three that are usually chosen. I had hoped to use the sun’s mass from the above calculation to help me compute Planck’s constant by measuring properties of the sun and solar fusion. But it’s not to be this time.

Summary and outlook

An astrophysicist in our universe has very few tools. One can’t set up an experiment and see what happens. One can only measure whatever events and objects Nature deigns to share. As one learns, one can bootstrap off previous knowledge to learn more and more. I wanted to replicate that experience in Outer Wilds, which is a captivating game.

In Outer Wilds, we had limited measuring tools. We could measure distances if we were clever, speeds if we moved, and times with a real-world stopwatch next to our computer. I started with a classic trick in the astronomer’s toolbox: timing orbits. With that we were able to measure Newton’s constant. With Newton’s constant in hand, we used the physics of event horizons and black holes to measure the speed of light. Unfortunately, our sanity checks failed and that’s as far as we got. But it was a good run.

But what do you think? Do you see some strategy to measure that I missed? Some way to climb higher on the ladder of knowledge? Were my assumptions reasonable? And did you enjoy this kind of article? I’m starting to get back into blogging, so if this was something you enjoyed, I might go this direction again. Or if more opportunities to dig into the physics of Outer Wilds emerge, I might try to do so more deeply. One thing I considered doing was talking about what things in Outer Wilds didn’t match my physical intuition and explain why. That would very likely involve spoilers, though. Let me know if you’re interested.

Acknowledgements

A big thanks to my friends who inspired me to write this post, helped me take measurements in-game, and put up with the tedium of making said measurements in game. Thanks y’all.